![1
1 Introduction
1.1 Demands on future mobile radio systems
The target of a mobile radio system is the provision of communication services to multiple
mobile terminals (MTs). Due to the demand for mobility of the MTs, each MT in a mobile
radio system communicates with at least one fixed access point (AP) by means of transmission
of electromagnetic waves with frequencies in the radio frequency band [Gib99, Ste92, DB96,
Wes02]. Each AP communicates either directly or indirectly with other fixed entities of the
mobile radio system such as mobile switching centers [GSM98], which perform tasks related to
the proper forwarding of information to and from the APs. Such fixed entities are collectively
described by the term core network of the mobile radio system. The wireless interface between
the MTs and the fixed APs is called the air interface of the mobile radio system. Concerning
the air interface one can discern between uplink (UL) and downlink (DL) transmission [Gib99,
Ste92, DB96], depending on whether information is sent from the MTs to the APs or vice
versa. Performance measures of high importance to mobile radio system operators such as the
quality of service [Ste92, HT02] or the number of MTs which can be simultaneously supported
in a given bandwidth B and area A [Lee89, Vit91, Ste92] are essentially determined by the air
interface. Hence, the design of the air interface of future mobile radio systems is of paramount
importance and forms the main focus of the present thesis.
As the following considerations of this Section are valid for the UL as well as for the DL, the
more general terms transmitters and receivers will be used in this Section instead of the terms
MTs and APs in order to describe the air interface independently of the direction of information
flow in the air interface, i.e., independently of whether the UL or the DL is considered. Setting
out from a group of antennas which are jointly available, a transmitter in a mobile radio system
is an entity generating transmit signals for a group of antennas and a receiver corresponds to an
entity obtaining the signals received by a group of antennas. Hence, the MTs are the transmitters
in the UL and the receivers in the DL. On the other hand, in the general case no direct relation
between APs and receivers in the UL and between APs and transmitters in the DL can be
postulated. However, in the special case that only the antennas of each AP are jointly available
the APs correspond to the receivers in the UL and to the transmitters in the DL.
If a linear transmission scheme is employed at each transmitter in the mobile radio system, then
the signal at the location of each receiver consists of a superposition of a number of information
bearing partial signals, each corresponding to a different MT, along with signals stemming from
sources other than the transmitters of the considered mobile radio system, such as other mobile
radio systems, or thermal and cosmic noise sources. Considering the detection of the infor-
mation of a particular MT, the corresponding partial received signal is termed useful received](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-11-320.jpg)
![2 Chapter 1: Introduction
signal. The remaining partial received signals corresponding to other MTs disturb the useful
received signal, and therefore act as multiple access interference [Gib99, Ste92, DB96, Wes02].
However, if nonlinear transmission schemes are employed, the signal at a specific receiver in
general cannot be viewed as a superposition of partial received signals, each corresponding to
an MT. For this reason, the definition of multiple access interference in the case of nonlinear
transmission schemes is an open problem. Moreover, although the term interference is often
used in a more general context to collectively describe all received signals not related to the
detection of a particular data symbol, it is used in the following to denote only multiple access
interference, which forms the main focus of the present thesis.
In state-of-the-art mobile radio systems, which are characterized by a high density of transmit-
ters and receivers and high transmit powers, interference dominates the nonuseful part of the
received signal in such a way that the effect of other noise signal sources, such as thermal or
cosmic noise, can be safely neglected in the design of a mobile radio system. Therefore, mobile
radio systems are interference limited [Cal88, Lee82]. The number K of MTs which can be
supported with a given quality of service [Ste92, HT02], normalized to the system bandwidth
B and the area A which is covered by the mobile radio system, is the spectrum capacity
ηc =
K
B A
(1.1)
of the mobile radio system [Lee89, Vit91, Ste92]. The spectrum capacity ηc of (1.1) is a measure
for the efficiency of the use of the available frequency bandwidth B of a mobile radio system.
An efficient use of the available frequency bandwidth B is of great importance to mobile radio
system operators as it has been demonstrated above all by the outcome of auctions for the 3G
mobile radio system spectrum, e.g., in Germany, where nearly 50 billion Euros were spent
for the corresponding licenses by the mobile radio system operators [ntz00a, ntz00b]. In an
interference limited system, the interference present at the antennas of the receivers limits the
achievable spectrum capacity ηc of (1.1) [Sha48, CT91, Roh95]. Therefore, considering future
mobile radio systems, an air interface should be developed, in which the adverse effects of the
interfering signals are kept at a low level.
In what follows the radio channel of the air interface of mobile radio systems is dealt with.
Mobile radio system operators use multiple APs to support a large number of MTs. However,
for the purpose of modelling the air interface of a mobile radio system, instead of the total air
interface with the usually very large number of transmitters and receivers, an excerpt of the mo-
bile radio system is considered containing transmitters and receivers of a cohesive geographical
area. Moreover, the said excerpt is chosen to be self-contained, i.e., no wireless communication
takes place across its borders. Therefore, all signals stemming from transmitters outside the
considered excerpt act as interference and are modelled as additive noise to the received signals
in the considered excerpt. Hence, due to the fact that the modelling of the interference, e.g., as](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-12-320.jpg)
![1.1 Demands on future mobile radio systems 3
Gaussian noise, is merely an approximation, the larger the excerpt of the mobile radio system
is chosen, the more precise the resulting air interface model is.
In the considered excerpt of the mobile radio system, if special cases of obstructed radio chan-
nels, e.g., due to physical obstacles are not considered, signals radiated from each of the transmit
antennas impinge at all the receive antennas. Hence, the radio channel of the considered excerpt
of a mobile radio system in the UL as well in the DL is modelled as a multiple-input-multiple-
output (MIMO) channel [Fos96, FG98, Tel99], in which the inputs are the multiple transmit
antennas in which the transmit signals are fed and the outputs are the multiple receive antennas
from which the received signals are obtained. Moreover, systems in which the channel is mod-
elled as a MIMO channel, such as the chosen excerpt of a mobile radio system, are known
as MIMO systems [Ala98, DCGV02, CS00, Ahl73, CT91, FCG+
03, GFVW98, GFVW99,
Hug00, JVG01, JVG02, TSC98, VJG02, YC01, YRBC01]. If neighboring MIMO systems use
the same frequency bands, then signals corresponding to MTs of neighboring MIMO systems
are received by the receivers of a certain MIMO system and such signals act as interference to
the useful received signals of the considered MIMO system. To mitigate the aforementioned
performance degrading interference, the bandwidth B available to the mobile radio system op-
erator is partitioned into disjoint frequency subbands and different subbands are allocated to
neighboring MIMO systems. This way, transmissions in a MIMO system do not interfere with
transmissions in directly neighboring MIMO systems. However, if the concept of bandwidth
partitioning would be strictly applied as described, given the large number of MIMO systems
in a mobile radio system, a very large system bandwidth B would be required to totally avoid
interferences in a mobile radio system. Therefore, the subband allocated to a reference MIMO
system is reused after a certain distance large enough so that the attenuation of the electromag-
netic waves received in the reference MIMO system stemming from MIMO systems using the
same frequency subband is sufficiently large and the induced interference by the reuse of the
same frequency subband is acceptable [McD79]. The number of disjoint subbands in which the
system bandwidth B is partitioned is called reuse factor of the mobile radio system [McD79].
In terms of achievable channel capacity [Sha48], the best case for a MIMO system is that all
inputs and outputs of the MIMO channel are jointly available for joint processing and that
perfect knowledge of the MIMO channel is present at both transmit and receive side [Tel99].
But in the case of the MIMO channel of the considered excerpt of a mobile radio system in
general not all the inputs and outputs of the MIMO channel are jointly available, due to the
spatial separation of the transmitters and receivers. For example, it is not possible to perform
signal processing tasks jointly for different MTs, at least with a reasonable overhead, due to the
fact that different MTs are spatially separated. Fig. 1.1 depicts the MIMO channel of a mobile
radio system with N transmit and M receive antennas in total. Transmit and receive antennas
of the MIMO channel in Fig. 1.1 form NB and MB groups corresponding to the NB and MB](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-13-320.jpg)
![4 Chapter 1: Introduction
transmitters and receivers, respectively, to indicate that only the antennas of each of the groups,
i.e., of each of the transmitters or receivers, are jointly available.
Transmitter 1
channel
MIMO
1
Receiver 1
MN
1
Receiver MBTransmitter NB
Figure 1.1. MIMO channel of an excerpt of a mobile radio system with NB transmitters and
MB receivers
Depending on the value of NB and MB, different special cases of MIMO channel structures can
be distinguished, as Table 1.1 shows.
Table 1.1. Classification of MIMO channel structures depending on the number NB of transmit
antennas and the number MB of receive antennas
case number NB MB MIMO structure
1 1 1 point-to-point channel
2 1 > 1 broadcast channel
3 > 1 1 multiple access channel
4 > 1 > 1 multipoint-to-multipoint channel
The first case corresponds to a point-to-point MIMO channel which means that all N inputs
and M outputs of the MIMO channel are jointly available. Pioneering work on the point-to-
point MIMO channel in [Tel99, Fos96, FG98] shows that in the presence of rich scattering and
if perfect channel knowledge is available at least at the receiver, impressive gains in terms of
channel capacity [Sha48] and spectrum efficiency [BBS97, Bla98] are achievable as compared
to single antenna systems using signals of the same transmit energy. These high gains, almost
for free, only at the cost of some increased hardware complexity, initiated a worldwide research
on MIMO systems [Ala98, DCGV02, CS00, Ahl73, CT91, FCG+
03, GFVW98, GFVW99,
Hug00, JVG01, JVG02, TSC98, VJG02, YC01, YRBC01]. The point-to-point MIMO channel
corresponds to the case where the considered excerpt of the mobile radio system consists of a
single transmitter communicating with a single receiver.
In the MIMO channel structure of the second case of Table 1.1 all inputs of the MIMO chan-](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-14-320.jpg)
![1.2 Service area based architectures versus cellular architectures 5
nel are jointly available whereas not all outputs are jointly available. This second case corre-
sponds to the case where in the considered excerpt of the mobile radio system a single trans-
mitter communicates with multiple receivers. In literature, such MIMO channels are known as
broadcast channels [CS00, CT91]. Assuming that the transmitter disposes of channel knowl-
edge a joint transmit signal processing could aim at reducing interference at the receivers
[MBW+
00, WMS+
02].
The third case of Table 1.1 represents a MIMO channel structure, dual to the second case, where
all outputs are jointly available whereas not all inputs of the MIMO channel are jointly avail-
able. Such MIMO channels are known as multiple access channels. Multiple access channels
correspond to the case where multiple transmitters communicate with a single receiver in the
considered excerpt of the mobile radio system. A joint signal processing at the receiver could
aim at reducing interferences among the multiple transmitters [Kle96, WMS+
02].
In the most general last case of Table 1.1 of multipoint-to-multipoint MIMO channels, neither
all the inputs nor all the outputs of the MIMO channel are jointly available. This corresponds
to the case where multiple transmitters and multiple receivers exist in the considered excerpt
of the mobile radio system. Due to the said dislocation between the transmitters and between
the receivers interference suppression in multipoint-to-multipoint MIMO channels is a difficult
task.
According to the author, the research towards future mobile radio systems should aim at an
efficient utilization of the available frequency bandwidth B, i.e., high spectrum capacities ηc
should be strived for. As high system capacities can be achieved by mitigating the adverse
effects of interference, the demand for the development of air interface architectures targeted at
the suppression of the interference between the useful signals of the active MTs follows. Given
the MIMO nature of the radio channel of an excerpt of a mobile radio system, shown in Fig.
1.1, it is shown that such a goal can be approached by employing an air interface in which all
inputs to the MIMO channel in the DL and all outputs of the MIMO channel in the UL are
jointly available. Hence, the cases of multiple access channels and broadcast channels shown
in Table 1.1 are of special interest as far as the design of the air interface of future mobile radio
systems is concerned. The present thesis deals with such an air interface proposal for future
mobile radio systems.
1.2 Service area based architectures versus cellular architec-
tures
As demonstrated in the previous Section, there exists the demand for future mobile radio system
air interfaces to yield high spectrum capacities ηc. The objective of this Section is to introduce a](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-15-320.jpg)
![6 Chapter 1: Introduction
novel air interface architecture by the employment of which the adverse effects of interference
between the useful signals of the simultaneously active MTs in a MIMO system can be mitigated
and therefore high spectral capacities ηc can be achieved. In order to better illuminate the basic
characteristics of the novel air interface architecture, a brief overview of the characteristics of
the cellular architecture, employed in state-of-the-art mobile radio systems, is performed.
The cellular architecture [McD79] is employed in mobile radio systems of the first-, second-
and third generation. The fundamental concept of cellular systems is the cell, which is the
geographical area of responsibility of an AP, i.e., the area in which the MTs associated with
the particular AP reside [McD79, Gib99, DB96, Wes02]. In a cellular mobile radio system,
the association of MTs to APs is performed according to criteria such as the quality of the
propagation conditions, and is based on the premise that from the viewpoint of a certain MT
there exists typically one AP to which the propagation conditions are most favorable. Due to
this association of MTs to APs a partitioning of the whole geographical area of the mobile radio
system into cells follows naturally.
In cellular mobile radio systems it can be discerned between two basic types of interference,
depending on whether the signals of MTs of the same cell or of MTs of different cells interfere.
In the case of interference between the signals of MTs of the same cell, the interference is
called intracell interference. Intracell interference can be combated by techniques such as joint
detection [Kle96, KB92] or joint transmission [MBW+
00, TWMB01]. On the other hand,
if the useful signals of MTs of neighboring cells interfere, the interference is called intercell
interference. The effects of intercell interference are mitigated in 2G mobile radio systems by
means of partitioning of the bandwidth B, as explained in Section 1.1. However, due to the said
partitioning of the bandwidth B an inefficient use of the system bandwidth B results.
Fig. 1.2 shows an excerpt of a mobile radio system based on the cellular concept consisting of
twelve cells grouped in three clusters of four cells. As can be seen from Fig. 1.2, each cell has an
AP. The APs in turn are connected to the core network of the mobile radio system which is the
data source and data sink for the information sent to and received from the MTs, respectively.
Following the argumentation of Section 1.1, higher spectral capacities ηc of (1.1) can be achieved
if a larger number of inputs of the MIMO channel in the DL or of outputs of the MIMO channel
at the UL at the fixed side of the wireless communication channel are jointly available than
in cellular mobile radio systems. The transition from the cellular architecture to the novel air
interface architecture can be visualized as the result of merging of a group of neighboring cells.
The merging of the neighboring cells consists in establishing a communication link between
each of the APs and a central unit (CU), which is in turn connected to the core network of the
mobile radio system. Each such group of APs defines a service area (SA) and the resulting](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-16-320.jpg)
![8 Chapter 1: Introduction
mobile radio system air interface architecture is called service area based (SA-based) architec-
ture [WMS+
02, SWC+
02, SWBC02, MWS+
02]. The crux of the novel SA-based air interface
architecture consists in the fact that as a result of the merge of a number of cells in a single
SA, the intercell interference between the useful signals corresponding to the MTs active in
the said cells becomes intra-SA interference in the case of SA-based systems and can be easily
combated by interference suppression techniques [Kle96, MBW+
00, WMS+
02]. Fig. 1.3 illus-
trates an excerpt from a mobile radio system employing the SA-based air interface architecture
with three SAs, each consisting of four APs. Comparing Fig. 1.2 to Fig. 1.3, in the exemplary
excerpt of the considered mobile radio system, each SA can be thought of as a union of four
cells in terms of cellular architectures.
In the UL transmission in a SA, the signals transmitted from each MT are received by all
APs of the SA and fed to the CU, which performs the signal processing tasks. If the SA is
chosen to be the MIMO system of Fig. 1.1, all the outputs of the SA MIMO wireless channel
are jointly available to the CU and therefore the MIMO channel in the UL of a SA-based air
interface architecture is modelled as a multiple access channel [Ahl73], in which the MTs are
the multiple transmitters and the CU is the receiver. If not all the outputs of the MIMO channel
were jointly available, i.e., if the signals received by each of the APs were considered separately,
as it is the case in the APs in cellular architectures, the mitigation of the interference from the
partial received signals stemming from the other MTs of the SA caused to the useful received
signal of a specific MT would be possible only in a limited extent at a certain AP [Ost01].
However, as in the UL of SA-based architectures all outputs of the MIMO channel are jointly
available and given that the CU disposes of knowledge concerning the transmission properties
of the MIMO channel of the SA, which is the result of a channel estimation procedure in the UL
[SMW+
01, MWS+
02], the structure of each of the partial received signals at the APs is known
at the CU. In the exemplary case of linear JD, the CU has knowledge of the vector subspace to
which each of the partial received signals belongs and can therefore minimize the interference
caused to the partial received signal of a desired MT by the partial received signals correspond-
ing to the other MTs of the SA. This means that the CU can combine the received signals from
the APs in an optimum way in terms of suppression of interference between the various simul-
taneously active MTs, i.e., the CU in the UL transmission in a SA-based architecture performs
joint detection (JD) [WMS+
02, Kle96, KB92, SWC+
02, SWBC02].
In the DL transmission, information is sent from the core network to the MTs. For this purpose
the CU generates AP-specific signals and each MT in the DL transmission receives the signals
from all APs. Therefore, the channel valid for the DL in SA-based air interface architectures is
modelled as a MIMO broadcast channel [CS00], in which the CU is the transmitter and the MTs
are the multiple receivers. As it is the case with the UL transmission, if the transmit signals were](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-18-320.jpg)
![1.2 Service area based architectures versus cellular architectures 9
generated independently for each of the MTs, as is the case in cellular mobile radio systems,
then each MT would also receive signals intended for the other MTs of the SA, i.e., signals
which cannot be constructively utilized and act as interference to each of the MTs.
In SA-based architectures, the CU has knowledge concerning the MIMO broadcast channel
valid for the DL transmission in the SA. Such a fact can hold, for example, if time division
duplexing (TDD) [Pro95] is used and the time elapsing between UL and DL transmission is
sufficiently smaller than the coherence time of the channel. In this case, channel knowledge re-
sulting from a channel estimation process in the UL can be assumed to be valid also for the DL
transmission. This reciprocity between UL and DL channels is known as channel reciprocity
and given the parametrization of state-of-the-art mobile radio systems [ENS97, MBW+
00], the
said channel reciprocity is a major advantage of TDD systems as compared to frequency divi-
sion duplexing (FDD) systems in which the coherence bandwidth of the mobile radio channel
[Par92] is typically smaller than the bandwidth of the frequency bands of UL and DL transmis-
sion.
Additionally to the channel knowledge, the receiver algorithms employed in the MTs active in
a SA are known to the CU and this knowledge is exploited for the generation of the AP-specific
transmit signals in the DL transmission. Transmission schemes which utilize knowledge con-
cerning the structure of the receiver and of the mobile radio channel in order to generate the
transmit signals are known as receiver oriented schemes, in contrast to transmitter oriented
schemes, which adjust the receiver according to the structure of the transmitter. The advantage
of receiver oriented schemes if applied on the DL is that no resources have to be spent for chan-
nel estimation in the DL and that a variety of MT structures, even very simple MTs, can be
supported [MBW+
00, TWMB01, WMS+
02].
As all inputs to the MIMO broadcast channel are jointly available and the characteristics of the
mobile radio channel valid for the DL transmission are known, the CU has a priori knowledge
of the structure of the received signal at each MT for given transmit signals. Moreover, by
exploiting the knowledge concerning the structure of the MTs, the CU can design transmit
signals for the APs in such a way that the estimates of the sent data symbols at each of the MTs
satisfy given criteria, e.g., are free from intra-SA interference. In a SA-based architecture the
CU can design transmit signals jointly for all MTs of the SA in order to mitigate the effects of
intra-SA interference, i.e., the CU in the DL transmission in a SA performs joint transmission
(JT) [WMS+
02, MBW+
00, TWMB01, TWMB01].
It follows that the crux of the SA-based architectures consists in the availability of all the an-
tennas of the APs to the CU, i.e., in the availability of all outputs to the multiple access channel
in the UL and of all inputs of the broadcast channel in the DL. The CU can then employ JD and](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-19-320.jpg)
![10 Chapter 1: Introduction
JT in the UL and DL transmission, respectively, to minimize the interference between the MTs.
Hence, in SA-based systems by means of JD and JT a significant portion of the intercell inter-
ference, which would be present in a cellular system, is combated. In the present thesis a variety
of algorithms for JD and JT is investigated, such as linear, nonlinear and iterative algorithms.
1.3 OFDM transmission technique
At the transmitter side in a mobile radio system multiple data carrying signals are merged into a
single transmit signal which is fed into one of the inputs of the time-continuous MIMO mobile
radio channel. At the receiver side the multiple data carrying received signals are extracted
from the received signal. The techniques of transmission of multiple data carrying signals us-
ing a single signal for each input and output of the MIMO mobile radio channel are called
multiplexing techniques, the choice of which is an important aspect in the design of a mobile
radio system. Orthogonal frequency division multiplexing (OFDM) is a multiplexing technique
gaining considerable interest the last years. Moreover, OFDM is applied in numerous com-
munications systems over the world [ETS97a, ETS97b, RCLF89, RS95, TL97, Cim85, Bin91,
CTC91, Jon95, IEE99, CWKS97, vNAM+
99, ETS96, ETS99], is contained in a proposal for
3G systems in Europe [ETS98] and is considered to be the leading candidate multiplexing tech-
nique for beyond 3G mobile radio systems [RGG01b, Roh00, RGG01a]. In what follows, after
describing the principles of some basic multiplexing techniques, an outline of the characteristics
of an OFDM system is performed. Blockwise transmission is assumed and each block is called
symbol slot.
A first choice regarding multiplexing is time division multiplexing where each symbol slot con-
tains a serial concatenation in time of the data carrying signals. However, due to the multipath
propagation in the wireless channel [Par92], in a mobile radio system employing time division
multiplexing the part of the received signal corresponding to a particular data carrying signal
contains apart from the desired data carrying signal signal portions caused by time delayed
echoes of previously sent data carrying signals, an effect known as intersymbol interference.
Future mobile radio systems are characterized by a demand for higher data rates, which trans-
lates in the case of time division multiplexing systems into shorter time durations of the data
carrying signals and therefore a larger impact of intersymbol interference. In time division mul-
tiplexing systems a guard interval can be employed to combat intersymbol interference the use
of which however introduces an overhead in the data transmission especially undesired in the
case of high data rates.
In a system in which frequency division multiplexing is employed, the data carrying signals
are sent in parallel, i.e., each of the data carrying signals modulates a sinusoidal signal of a](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-20-320.jpg)
![1.3 OFDM transmission technique 11
specific subcarrier frequency, called a subcarrier. Multiplexing techniques characterized by the
modulation of multiple subcarriers with the data carrying signals are also known as multicarrier
modulation techniques [GW00]. A decisive advantage offered by the frequency division mul-
tiplexing techniques and by multicarrier modulation techniques in general is the possibility to
accommodate high data rates, as higher data rates require solely a larger number of subcarriers
[vNP00] and are not limited by the amount of time dispersiveness of the mobile radio channel.
If subcarrier spacings are chosen to be large enough so that spectra of different subcarriers do
not overlap significantly, the available frequency bandwidth B is inefficiently used in frequency
division multiplexing systems. Hence, as far as multicarrier modulation techniques are con-
cerned, it is imperative to realize a tight subcarrier spacing and at the same time mitigate the
effects of the undesired crosstalk between different subcarriers.
Much research has been conducted in the development of a multicarrier modulation system with
a tight subcarrier spacing [FL61, Sal67]. OFDM [WE71, KZ89] is a multicarrier modulation
technique in which the spectra of different subcarriers overlap without causing intercarrier in-
terference. The interference free overlap of different subcarriers in OFDM systems is achieved
by choosing subcarrier frequencies which satisfy an orthogonality relationship, thanks to which
the signals corresponding to different subcarriers in an OFDM system are orthogonal to each
other. The receiver in an OFDM system considers only a part of the total received signal, during
which the aforementioned orthogonality of the signals is preserved. Hence, an OFDM system
achieves an efficient use of the available bandwidth B, as a tight spacing of the subcarriers be-
comes possible. The physical transmission model of OFDM-based MIMO systems is treated in
detail in Chapter 3.
The fundamentals of the OFDM technique are first presented in the paper of Weinstein and Er-
bert in 1971 [WE71], where a DFT structure is presented to realize the OFDM technique. But
it was not until the realization of an OFDM system by highly efficient FFT structures in combi-
nation with its appealing simplicity when intensive research in OFDM was sparkled regarding,
e.g., the application of different multiple access algorithms in OFDM systems [GRC+
01, RG97,
RGG01b, GRC+
02], or the employment of adaptive modulation at each of the OFDM subcar-
riers [HH, CCB95, FH96, GR00].
OFDM is part of the digital video broadcasting (DVB) and digital audio broadcasting (DAB)
systems in Europe [ETS97a, ETS97b, RCLF89, RS95, TL97, Cim85] and is applied in the
digital subscriber line (DSL) standards in the USA [Bin91, CTC91, Jon95]. Moreover, many
wireless local area network (WLAN) systems are based on OFDM, such as the IEEE 802.11a
[IEE99, CWKS97, vNAM+
99], the IEEE 802.11g [IEE03] and the HIPERLAN and HIPER-
LAN/2 systems [ETS96, ETS99].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-21-320.jpg)
![12 Chapter 1: Introduction
1.4 State of the art and open questions
Two dominating characteristics of the SA-based air interface architecture are the MIMO nature
of the wireless channel of the SA and the employment of the multiuser algorithms of JD and JT
in order to mitigate the interference between MTs in the SA. Literature on mobile radio systems
abides in investigations concerning MIMO channels and in multiuser algorithms. In particular,
since the initial ground breaking discovery of the potential of MIMO systems, an explosion
of the number of investigations on MIMO systems is observed. On the other hand, multiuser
algorithms are continuously a topic of investigation since the early 80s and therefore a variety of
relevant publications is available. In this Section, the most important, according to the author,
literature citations on MIMO systems and on multiuser algorithms are listed and the citations
relevant to the considerations in the present thesis are highlighted. At the end of this Section,
open questions regarding the air interface of future mobile radio systems are pointed out.
Table 1.2 lists the most important contributions in the field of MIMO systems, dealing with the
achievable capacity of MIMO channels and with specific algorithms targeted at the achievement
of significant portions of the available MIMO capacity. In order to provide a more comprehen-
sive overview, the publications in Table 1.2 are grouped in the two categories:
I:
II:
theoretical investigations on the capacity of MIMO systems, and
near capacity-achieving MIMO algorithms for point-to-point MIMO channels.
Category I contains publications regarding the derivation of the capacity formulas for the MIMO
point-to-point wireless link, and for the MIMO multiple access channel and the MIMO broad-
cast channel for various cases regarding, e.g., whether channel state information is available
at the transmitter or at the receiver or neither at the receiver and the transmitter. Complemen-
tary to the theoretical considerations concerning the capacity of MIMO channels of Category
I, investigations of two practical algorithms for MIMO systems targeted at achieving at least
a significant portion of the theoretically available capacity of the MIMO channel, space time
coding and Bell Labs layered space time (BLAST), are listed in Category II.
[Tel99] and [Fos96] are two seminal works on the capacity of point-to-point MIMO channels
which unveil the large capacity potential of MIMO systems and sparkled a worldwide research
activity. In [Tel99] and [Fos96] a N × M point-to-point MIMO channel is investigated. If
a rich scattering environment provides independent channels between each pair of transmit
and receive antennas and the channel can be accurately tracked at the receiver, it is shown in
[Tel99] and [Fos96] that the use of a fraction of the total available transmit energy in each of
the equivalent min{N, M} independent single-input-single-output channels is counterbalanced
by the exploitation of the cross-couplings of the MIMO channel, resulting in a MIMO channel](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-22-320.jpg)
![1.4 State of the art and open questions 13
Table 1.2. Contributions on MIMO systems
category reference remarks
I [Tel99],[Fos96],[FG98],[VM01], capacity of point-to-point
[JVG01],[JG04],[MH99] MIMO channels
[YRBC01],[Ahl73],[CT91], capacity of multiple access channels
[VTA01],[JVG02]
[CT91],[CS00],[YC01], capacity of broadcast channels
[VT03],[VJG02],[JVG02]
II [Wit93],[SW94],[TSC98], space time coding
[Ala98],[TJC99]
[Fos96],[FG98], D-BLAST, V-BLAST
[GFVW98],[GFVW99]
capacity which scales linearly with min{N, M}. However, it is not always possible to track the
channel accurately, e.g., in the case that rapid motion of the receiver or the transmitter results
in a fast variation of the channel. The case of partial channel state information is treated in
[VM01, JVG01, JG04, MH99].
MIMO multiple access channels were first dealt with in [Ahl73] and in [CT91]. Considering the
distributions of the input signals to the MIMO multiple access channel achieving the capacity
regions, in [YRBC01] a modified iterative version of the waterfilling technique [CT91] is intro-
duced and a numerical technique is employed to find the capacity region achieving covariance
matrices of the input signals to the MIMO multiple access channel.
Concerning the capacity regions of the MIMO broadcast channel, the work of Costa [Cos83]
attracted a lot of attention. Given that the transmitter for a single-input-single-output channel
has knowledge of the interference at the receiver, Costa in [Cos83] shows that the capacity of
the point-to-point single-input-single-output channel with additive Gaussian interference is the
same as if interference was not present. In [CT91] an initial work on the capacity regions of
the broadcast channel for the case that the transmitter has a single antenna is carried out and
in [CS00] some first results on the broadcast channel with multiple antennas at the transmitter
are presented. Yu and Cioffi in [YC01] introduce the Trellis precoding scheme and extend the
considerations on the broadcast channel to the multi-antenna receiver case. Despite of serious
efforts, the derivation of a closed capacity formula directly for the generalized broadcast channel
remained a complex problem, until Jafar and Goldsmith in [JG04] revealed a duality in the rate
regions between the broadcast channel and the multiple access channel, by the use of which the
optimum covariance matrices can be found for the multiple access channel case using standard
optimization techniques and then can be transformed to obtain the optimum covariance matrices
for the dual broadcast channel, according to [JG04].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-23-320.jpg)
![14 Chapter 1: Introduction
The quality of the estimation of a particular data symbol in terms of signal to noise ratio (SNR),
after transmission through a distorting wireless channel can be greatly improved by providing
an additional replica of the transmitted signal to the receiver via another channel. A system
providing more than one independent channel from the transmitter to the receiver is said to
provide diversity. For instance, in a SA-based system spatial diversity is provided by the em-
ployment of multiple APs in the SA. The transmit diversity scheme dominating in the literature
is space time coding [Wit93, SW94, TSC98, Ala98], according to which each data symbol to
be transmitted is encoded in time and in space, i.e., in time and along the various transmit an-
tennas jointly available to the transmitter. Space time coding algorithms primarily focus on
point-to-point MIMO channels as all inputs and outputs of the MIMO channel must be jointly
available to implement joint space-time coding and decoding, respectively. The first space time
coding proposal is considered to be from Winters [SW94], who was inspired by the multipath
diversity scheme introduced by Wittneben in [Wit93]. The first decisive contribution however
in the field of space time coding is considered to be the introduction of the space time trellis
coding scheme by Tarokh et. al [TSC98], in which convolutional codes are employed for the
temporal and spatial coding. Considering the application of block codes instead of convolu-
tional codes, an important representative of the block space time coding approaches is the space
time block coding algorithm by Alamouti [Ala98], which offers the same diversity benefit as
space time trellis coding while having a decisively smaller decoding complexity. The space
time block coding scheme by Alamouti has gained worldwide attention and is also adopted in
the wideband CDMA and cdma2000 standards [w3G99, TIA00].
Instead of introducing redundancy, as it is the case in space time coding, in the case of the
BLAST architecture [Fos96, FG98, GFVW98, GFVW99] independent data streams are trans-
mitted from each transmit antenna. In this way, spatial diversity is sacrificed for an increased
spectrum efficiency of the MIMO system. BLAST as well as space time coding, is an architec-
ture for point-to-point MIMO channels as it requires joint availability of the inputs and outputs
of the MIMO channel.
The support of multiple MTs in a SA-based system is achieved by the application of JD [Kle96]
in the UL and JT [MBW+
00] in the DL, as described in Section 1.2. JD and JT are algorithms
belonging to the category of multiuser algorithms, the most important literature for which is
contained in Table 1.3. As can be seen from Table 1.3, literature on multiuser algorithms can
be classified into two main Categories:
I:
II:
transmitter oriented multiuser algorithms and
receiver oriented multiuser algorithms.
In wireless channels where transmitter oriented multiuser algorithms are applied, the receiver is
designed according to the structure of the transmitter. Because literature on transmitter oriented](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-24-320.jpg)
![1.4 State of the art and open questions 15
multiuser algorithms, which are also known as multiuser detection or multiuser estimation al-
gorithms, is quite extensive, Category I contains only the most representative, according to the
author, publications on transmitter oriented multiuser algorithms. Dual to transmitter oriented
multiuser algorithms, in receiver oriented multiuser algorithms the transmitter adapts itself to
the receiver, as for example in JT. In Category II the most important publications related to
receiver oriented multiuser algorithms are listed.
Table 1.3. Contributions on multiuser systems
category reference remarks
Ia [Ver98],[Ver86a],[Ver86b] optimum multiuser detection
Ib [LV89],[XSR90],[LV90], linear multiuser estimation
[KB92],[KB93],[Kle96], - RxZF JD
[Mil88],[BFKM93],[FKB94],[KKKB94], - MMSE
[KKKB96],[MH94],[Gra81]
[VA90],[PH94],[VA91], iterative multiuser detection
[Var95],[Lam00b],[Lam00a], - multistage detection
[YKI93],[KIHP90],[HL98], - parallel interference cancellation
[DSR98]
[Hag97],[BG96],[BM96], turbo multiuser detection
[HOP96],[BDMP98],[BGT93],
[ARAS99],[Moh98],[RSAA98],
[Hag96],[AGR98],[VW98]
II [Fis02],[WR01],[Bar02], receiver oriented algorithms
[VJ98],[MBW+
00],[KM00], - Joint precoding/Joint Predistortion
[BOS98],[JKG+
02] - TxZF JT
- transmit Wiener Filter
Concerning transmitter oriented multiuser algorithms, it can be discerned among two main
groups of algorithms:
• multiuser detection algorithms, producing discrete output values belonging to a prede-
fined alphabet, and
• multiuser estimation algorithms, producing continuous output values, which are quan-
tized with respect to the predefined alphabet in a separate step.
It follows that the concatenation of a multiuser estimator with the quantizer can be also seen as
a multiuser detector.
The optimum multiuser detector in terms of the probability of erroneous detection is described
in [Ver86a, Ver86b, Ver98]. Such an optimum detector yields estimates of the transmitted data](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-25-320.jpg)
![16 Chapter 1: Introduction
symbols in a nonlinear fashion, according to the maximum a posteriori (MAP) or maximum
likelihood (ML) criterion using a priori knowledge concerning the transmitted data symbols.
However, given the parametrization of state-of-the-art multiuser mobile radio systems, the op-
timum multiuser detector is highly complex and hence not realizable. Suboptimum multiuser
detectors present a tradeoff between performance in terms of erroneous decision and implemen-
tation complexity and yield the estimates of the transmitted data symbols either linearly or in
an iterative fashion.
Linear multiuser estimators yield continuous valued estimates of the transmitted data symbols
by performing a linear operation on the received signal. Various linear multiuser estimators
exist, which differ in the performance criterion which the estimates of the data symbols satisfy.
In [KB92, KB93, Kle96, BFKM93, FKB94, LV90] receive zero-forcing JD (RxZF JD) is in-
vestigated, which delivers interference free estimates of the sent data symbols. The estimator
applying the minimum mean square error (MMSE) principle investigated in [MH94, Gra81,
LV89, XSR90, LV90, BFKM93, KKKB94, KKKB96] trades off interference suppression for
an improved SNR of the estimated data symbols as compared to RxZF JD.
Alternatively to linear estimation, detection of the multiple transmitted data symbols can be
performed in an iterative fashion. If convergent, iterative multiuser algorithms yield estimates
of the transmitted data symbols in multiple iterations or stages, being at the same time less
complex than linear multiuser algorithms. To the category of iterative multiuser detection al-
gorithms belong multistage detection [VA90, VA91, YKI93, HL98] and parallel interference
cancellation [Lam00b, Lam00a, DSR98, PH94, Var95, KIHP90], which are governed by the
same general principles. An iterative data detection algorithm gaining considerable attention is
turbo multiuser detection [DJB+
95, Moh98, RSAA98, WP99], which is based on the turbo prin-
ciple [Hag96, Hag97, BG96, BGT93] originally designed for decoding concatenated forward
error correcting (FEC) codes.
In receiver oriented multiuser algorithms, the transmitter generates transmit signals based on
the knowledge of the structure of the receiver and of the wireless MIMO channel. The pro-
cess of generation of transmit signals in receiver oriented algorithms is known as precoding or
predistortion [Fis02, Bar02, YC01, Tom71, HM72]. A special case of predcoding algorithms
are algorithms in which the transmit signals are generated by performing a linear operation
on the data symbols [MBW+
00, TWMB01, KM00, JUN01, JKG+
02, VJ98]. Common to all
precoding and predistortion algorithms is that the wireless channel is pre-equalized at the trans-
mitter side. As in receiver oriented multiuser algorithms the signal processing tasks related to
channel equalization are performed by the transmitter, multiuser precoding and predistortion
algorithms are especially attractive for the application in the broadcast channel where multiple
low complexity MTs are served.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-26-320.jpg)
![1.4 State of the art and open questions 17
The first precoding algorithm is considered to be the Tomlinson-Harashima precoding algorithm
[Tom71, HM72]. According to the Tomlinson-Harashima precoding algorithm, the channel is
pre-equalized at the transmitter by means of an inversion of the channel matrix and in order
to avoid the peaks in the transmit power which would result at frequencies coinciding with
channel fades, the amplitude of the transmit signal is restricted to a specific interval by means
of a modulo-2 addition of the data symbols with a precoding sequence, which depends on
the modulation used. Though the Tomlinson-Harashima precoding algorithm as described in
[Tom71, HM72] is not a multiuser algorithm in its nature, Yu and Cioffi in [YC01] extend the
Tomlinson-Harashima algorithm to the broadcast channel.
Linear predistortion and precoding algorithms differ in the way the linear transformation ma-
trix is applied to the data symbols to be transmitted. In the predistortion method proposed
for CDMA systems by Vojˇci´c and Jang [VJ98], the linearly transformed data symbols are
spread and then fed into the channel, whereas in the Joint Predistortion algorithm proposed by
Kowalewski and Mangold [KM00, BOS98], the linear transformation is applied on the spread
signals. On the other hand, in the case of JT [MBW+
00], the spreading process in the trans-
mitter is not performed separately from the linear transformation. Given the structure of the
receiver and of the wireless MIMO channel, the linear transformation matrix in JT is chosen
in such a way that interference free estimates of the data symbols are obtained at the receivers
and that the transmit signals are of minimum energy. Due to the interference free transmission,
linear JT is also known as transmit ZF JT (TxZF JT) demonstrating the duality to RxZF JD in
transmitter oriented multiuser algorithms. The search for the analogon of MMSE for the case
of receiver oriented multiuser algorithms led to the derivation of the transmit Wiener filter by
Joham et al. in [JKG+
02], which represents a trade-off between receive energy exploitation and
interference suppression achieved by the transmit matched filtering (TxMF) and the TxZF JT
algorithms, respectively, just as MMSE JD represents a trade-off between matched filter (MF)
and RxZF JD in transmitter oriented multiuser algorithms.
As stated in Section 1.1, high spectrum capacities ηc should characterize future mobile radio
systems. Due to the fact that mobile radio systems are interference limited, the high spectrum
capacities can be achieved mainly by combatting interference. However, in cellular architec-
tures intercell interference limits the achievable spectrum capacity ηc. According to the knowl-
edge of the author, proposals regarding future mobile radio systems [AMAS02, WWR], as well
as the contributions in Tables 1.2 and 1.3, refer to cell-based architectures. As such, they fail
to address the issue of the suppression of interference, as shown in Section 1.2, and are thus
inherently suboptimum with respect to the provision of high spectrum capacities ηc.
Hence, the need for the development of an alternative air interface architecture for future mobile
radio systems is evident. The design of such an air interface architecture should be aimed at the](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-27-320.jpg)
![20 Chapter 2: Channel modelling
2 Channel modelling
2.1 Introduction
The design of a SA-based air interface architecture, as of any air interface architecture, is con-
siderably aided by computer simulations. Profound knowledge concerning the characteristics
of the mobile radio channel of the SA is essential in order to be able to model the wireless chan-
nel of the SA in computer simulations as accurately as possible. Target of the present Chapter
is to give an overview of the three channel models used in the simulations in this thesis. To
this end, theoretical aspects of mobile radio propagation relevant to the radio transmissions in a
SA-based air interface architecture are first briefly treated with.
2.2 Theory of mobile radio propagation
In a wireless transmission in a mobile radio system, signals emitted by a transmitter reach
the receiver not only via direct line of sight (LOS) paths between transmitter and receiver.
Transmitted signals often impinge at the antennas of each receiver after reflection, scattering or
diffraction on physical obstacles. Only seldom does a direct LOS path exist [Par92, BARY95,
FL96], especially in dense urban areas. Given the usually large number of surfaces interacting
with the emitted electromagnetic waves, a multitude of paths exist along which indirect wireless
transmissions take place. It follows that a multitude of signals with different amplitudes, phases
and delays superimpose at the receiver.
In a static environment the mobile radio channel is described in the equivalent lowpass domain
as a linear time invariant filter having the complex transfer function H(f). The superposition of
the signals which reach the receiver each with a different delay τ [BBS97], varies for different
frequencies f from destructive to constructive. Therefore, the mobile radio channel is said to be
frequency selective, i.e., its transfer function H(f) fluctuates throughout the bandwidth B used
for the wireless transmission. On the other hand, if the mobile radio channel has one dominant
path and negligible signal energy is received via multipath propagation, then it is said to be
frequency nonselective or flat fading channel and the corresponding transfer function H(f) is
considered to be constant throughout the entire bandwidth B.
In a dynamic environment in which the movement of the MT and of its surroundings is taken
into account, the way the signals from multiple paths superpose at the receiver is time variant.
Depending on the relation of the movement of the MT to the system wavelength λ, it can be
discerned between small- and large scale movement [BARY95, FL96].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-30-320.jpg)
![2.3 Channel models used in the thesis 21
If the MT covers a distance of fractions of λ, then small but rapid variations of the amplitude
of the received signal occur. In particular, the small scale movement of the MT has a rather
negligible effect on the attenuation but a large impact on the phase of each of the superposed
signals. Therefore, the superposition of a large number of signals each with a rapidly changing
phase results in an also rapidly varying envelope of the total received signal and the effect is
called fast fading [Par92]. Large scale movement of the MT occurs if the movement of the MT
is in the order of magnitude of tens of λ. In such a case, the dominant effect is shadowing, i.e.,
the limited lifetime of the individual paths. As the MT moves, some paths disappear and new
paths are created. The resulting variation of the amplitude of the received signal is slow relative
to the case of small scale movement, and is called slow fading [Par92]. However, the variation
of the amplitude of the received signal caused by slow fading has a larger dynamic range as
compared to the case of fast fading [BARY95]. Hence, in the case of the dynamic propagation
environment, the time-variant transfer function H(f, t) is used to describe the mobile radio
channel [BBS97, Par92].
2.3 Channel models used in the thesis
2.3.1 COST 207 channel models
The most widely used channel models are stochastic channel models, i.e., models in which the
mobile radio channel is modelled as a bandlimited stochastic process. In the modelling proce-
dure it is assumed that the stochastic process describing the channel is stationary in the wide
sense at least in a small area and that the modelled wireless channel exhibits uncorrelated dis-
persiveness in time delays τw, w = 1 . . . W, and Doppler shifts fD,w, w = 1 . . .W, of the
W superposed paths, i.e., in stochastic models radio channels are modelled as wide sense sta-
tionary uncorrelated scattering (WSSUS) channels [Bel63, Sch88a, Hoe92]. Hence, in WSSUS
channels, the scattering function S (τ, fD) can be expressed as the product of the Doppler power
spectrum Sc (0, fD) and the power delay spectrum ρT(τ, 0) as
S (τ, fD) = Sc (0, fD) ρT(τ, 0). (2.1)
The most widely used stochastic channel models are the channel models of the COST 207 study
[COS88]. According to the COST 207 channel modelling, the mobile radio channel consists
of a superposition of a number W of uncorrelated paths, which have uniformly distributed null
phases θw, w = 1 . . . W, Doppler shifts fD,w, w = 1 . . .W, and unit amplitude.
The delays τw for each path w are taken from an interval [τw,min, τw,max] according to an
exponential-type power delay spectrum a exp (−bτw) , a, b ∈ R+
. For different values of](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-31-320.jpg)
![22 Chapter 2: Channel modelling
τw,min, τw,max, a and b four different propagation conditions are modelled, bad urban (BU), hilly
terrain (HT), rural area (RA) and typical urban (TU), as Table 2.1 shows.
Table 2.1. Parameters for the channel models of the four different propagation conditions of the
COST 207 study
environment τ/µs ρT(τ)
bad urban (BU) [0, 5] ∝ exp (−τ)
[5, 10] ∝ 0.5 exp (5 − τ)
hilly terrain (HT) [0, 2] ∝ exp (−3.5τ)
[15, 20] ∝ 0.1 exp (15 − τ)
rural area (RU) [0, 0.7] ∝ exp (−9.2τ)
typical urban (TU) [0, 7] ∝ exp (−τ)
If the motion of the MTs is not taken into account, i.e., if for each path w, w = 1 . . .W, the
Doppler shift fD,w is not taken into account, with the uniformly distributed null phase θw and
the delay τw taken from Table 2.1, the channel transfer function
H(f) =
1
√
W
W
w=1
exp (jθw) exp (−j2πfτw) (2.2)
of the mobile radio channel according to the COST 207 channel models is derived. In the
simulation of SA-based mobile radio systems, (2.2) is used KKB times to get the transfer
functions H(k,kB)
(f) of the wireless channels between each pair of MT k, k = 1 . . .K, and AP
kB, kB = 1 . . . KB.
2.3.2 Indoor geometric channel model
In order to perform simulations of a SA-based system in which OFDM is used, for each channel
snapshot KKB transfer functions H(k,kB)
(f), for the KKB channels between each MT and each
AP have to be generated by means of a channel model. In order to take into account interde-
pendencies between the wireless channels of the SA resulting from the geometrical structure of
the SA, a geometric MIMO indoor channel model is developed specifically for the simulation
needs of the thesis and it is described in the present Section. In contrast to the COST 207 chan-
nel models, which generate transfer functions H(k,kB)
(f) as samples of a stochastic process, the
geometric indoor channel model described in this Section is deterministic, i.e., the same transfer
functions H(k,kB)
(f) are generated given fixed positions of the MTs and geometry of the SA.
In the geometric channel model, the SA is a rectangular room of dimensions xmax ×ymax, as Fig.
2.1 shows. In the SA, a single CU, K MTs and KB APs exist, each equipped with single element](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-32-320.jpg)
![25
3 Modelling of OFDM-based MIMO systems
3.1 Introduction
Until now, OFDM-based systems are described by the use of a model based on IFFT, FFT, cyclic
prefix addition and cyclic prefix removal operations [vNP00, FK03]. However, such approaches
fail to address the fact that OFDM-based systems are just special cases of a more general class
of multiuser systems in which a time-continuous signature is assigned to each discrete transmit
value, i.e., of multiuser systems employing linear modulation.
Target of this Chapter is the development of a novel model for the data transmission in an
OFDM-based system employing transmission over a MIMO channel with KI inputs and KO
outputs. In a first step data transmission in a general multiuser system employing transmission
over a time-continuous KO × KI MIMO channel is modelled and then the data transmission
model for OFDM-based MIMO systems is derived as a special case.
Bandpass signal transmissions in multiuser systems can be efficiently described by the use of the
equivalent low pass domain representation of signals, in which signals are represented by their
complex envelopes [Pro95]. Moreover, the model for the data transmission can be decomposed
into
• a physical transmission model and
• pre- and post-processing stages,
as Fig. 3.1 shows.
It is assumed that L bits u
(k)
l , l = 1 . . . L, compiled into the bit vector
u(k)
= u
(k)
1 . . . u
(k)
L
T
, (3.1)
are transmitted per MT k, k = 1 . . .K. As shown in Fig. 3.1, the KI transmit vectors
s(kI)
= s(kI,1,1)
. . . s(kI,nF,nS)
. . . s(kI,NF,NS) T
, kI = 1 . . . KI, (3.2)
of dimension NFNS are generated from the K vectors u(k)
, k = 1 . . . K, of (3.1) by the pre-
processing stage.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-35-320.jpg)
![26 Chapter 3: Modelling of OFDM-based MIMO systems
physical
transmission
model
pre-processing
post-processing
u(1)
u(k)
u(K)
ˆu(1)
ˆu(k)
ˆu(K)
s(1)
s(kI)
s(KI)
e(1)
e(kO)
e(KO)
Figure 3.1. Model of the data transmission in a multiuser system with K MTs, in which the
physical transmission takes place over a time-continuous MIMO channel with KI inputs and
KO outputs, consisting of a model for the physical transmission with KI vector inputs and KO
vector outputs, complemented with pre- and post- processing stages
The physical transmission model of the investigated multiuser system is used to describe each
of the KO received vectors
e(kO)
= e(kO,1,1)
. . . e(kO,nF,nS)
. . . e(kO,NF,NS) T
, kO = 1 . . .KO, (3.3)
of dimension NFNS as a function of the KI transmit vectors s(kI)
, kI = 1 . . . KI, of (3.2). As
the mobile radio channel itself is time-continuous the physical transmission model consists of
an inner time-continuous part and an outer part which describes the synthesis and analysis of
the time-continuous transmit and received signals, respectively.
At the receiver side, a post-processing of each received vector e(kO)
of (3.3) is performed, in
order to yield the estimates
ˆu(k)
= ˆu
(k)
1 . . . ˆu
(k)
L
T
, k = 1 . . .K, (3.4)
of the bit vectors u(k)
, k = 1 . . . K, of (3.1).
Due to the fact that the investigation of the impact of synchronization errors on the performance
of OFDM-based MIMO systems is beyond the scope of this thesis, it is assumed hereafter
that the investigated OFDM system is perfectly synchronized in the time and in the frequency
domain [vSB97, HE97, BR98].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-36-320.jpg)
![28 Chapter 3: Modelling of OFDM-based MIMO systems
3.2.2 Transmitter
The task of the synthesis filter bank in Fig. 3.2 is the synthesis of each time-continuous transmit
signal s(kI)
(t) from the transmit vector s(kI)
. The signature ct,nF,nS
(t) is weighted by the transmit
value s(kI,nF,nS)
to produce the transmit-value-specific partial transmit signal
s(kI)
nF,nS
(t) = s(kI,nF,nS)
ct,nF,nS
(t). (3.5)
With the transmit-value-specific partial transmit signals s
(kI)
nF,nS(t), nF = 1 . . . NF, nS = 1 . . .NS,
of (3.5), the transmit signal
s(kI)
(t) =
NF
nF=1
NS
nS=1
s(kI)
nF,nS
(t) (3.6)
is calculated which is fed in the input kI of the time-continuous KO × KI MIMO channel.
In the following multicarrier systems are considered [vNP00, FK03], in which each signature
ct,nF,nS
(t) is a time- and frequency shifted replica of a basic transmit signature ct (t). With the
symbol slot duration Ts and the subcarrier spacing F, the input-specific signature ct,nF,nS
(t) at
subcarrier nF and symbol slot nS is expressed as
ct,nF,nS
(t) = ct (t − (nS − 1)Ts) exp (j2π(nF − 1)Ft) . (3.7)
In the following the symbol slot duration Ts is chosen to be larger than the impulse response
duration Th, i.e., Ts > Th holds. In the specific case of OFDM systems the subcarrier spacing
F =
1
Ts − Th
(3.8)
and the basic transmit signature
ct (t) =
1
√
Ts
rect
t
Ts
−
1
2
(3.9)
are used and with the basic transmit signature ct(t) of (3.9), (3.7) becomes
ct,nF,nS
(t) =
1
√
Ts
rect
t − (nS − 1)Ts
Ts
−
1
2
exp j2π
nF − 1
Ts − Th
t . (3.10)
Due to (3.5), (3.6) and (3.10), in a specific OFDM symbol slot nS the weighted sum of NF sinu-
soidal signals ct,nF,nS
(t), nF = 1 . . . NF, of (3.10) is fed in the input KI of the time-continuous
MIMO channel. The transmitter defined by (3.5), (3.6) and (3.10) corresponds to a conventional
OFDM transmitter [vNP00].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-38-320.jpg)
![3.2 Physical transmission model 31
holds. In (3.21)
n(kO,nF,nS)
=
∞
−∞
n(kO)
(t)cr,nF,nS
(−t)dt, nF = 1 . . . NF, nS = 1 . . . NS, (3.22)
are the NFNS noise values n(kO,nF,nS)
, nF = 1 . . . NF, nS = 1 . . . NS, at vector output kO of the
physical transmission model, which follow after filtering and sampling of the noise n(kO)
(t) of
the output kO of the time-continuous MIMO channel.
From (3.12), for the combined impulse response b
(kI,kO)
nF,nS
(t) in (3.21), follows
b
(kI,kO)
nF,nS
(t) = 0, for t /∈ [(nS − 1)Ts, nSTs + Th] . (3.23)
Moreover, in the case of OFDM follows for the impulse response cr,nF,nS
(t) of (3.18)
cr,nF,nS
(t) = 0, for t /∈ [−(nS − 1)Ts − Th, −nSTs] . (3.24)
Hence, as a consequence of (3.23) and (3.24),
∞
−∞
b
(kI,kO)
nF,nS
(t)cr,nF,nS
(−t)dt = 0, for nS = nS, (3.25)
i.e., the received value e(kO,nF,nS)
has no contributions from the transmit value s(kI,nF,nS)
for
nS = nS, which means that transmissions in different symbol slots in OFDM-based MIMO
systems are totally independent.
With the matrix H(kI,kO)
(f) being the result of the Fourier transformation of the impulse re-
sponse h(kI,kO)
(t), the discrete transfer coefficients
h(kI,kO,nF)
=
∞
−∞
b(kI,kO)
nF,nS
(t)cr,nF,nS
(−t)dt
=
Ts − Th
Ts
Th
0
exp (−j2π(nF − 1)Fτ) h(kI,kO)
(τ)dτ,
=
Ts − Th
Ts
H(kI,kO)
((nF − 1)F) . (3.26)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-41-320.jpg)
![3.2 Physical transmission model 33
Moreover, with (3.22), the noise values n(kO,nF,nS)
of (3.28) have the correlation
E n(kO,nF,nS)
n∗(kO,nF,nS)
= E
⎧
⎨
⎩
∞
−∞
n(kO)
(t1)cr,nF,nS
(−t1)dt1
∞
−∞
n∗(kO)
(t2)cr,nF,nS
(−t2)dt2
⎫
⎬
⎭
=
∞
−∞
∞
−∞
E n(kO)
(t1)n∗(kO)
(t2) cr,nF,nS
(−t1)cr,nF,nS
(−t2)dt1dt2
= N0
∞
−∞
cr,nF,nS
(t)cr,nF,nS
(t)dt
=
⎧
⎨
⎩
N0 kO = kO, nF = nF, nS = nS
0 else
. (3.30)
The receiver described by (3.18) and (3.21) corresponds to a conventional OFDM receiver
[vNP00].
3.2.5 Matrix-vector transmission model
Due to the independence of transmissions at different subcarriers and symbol slots, a compact
subcarrier- and symbol slot wise discrete physical transmission model for OFDM-based MIMO
systems is derived. Due to the subcarrier- and symbol slot wise investigation, the transmission
over each of the NFNS independent KO × KI discrete MIMO channels is modelled separately.
To this end, the transmit vector
s(nF,nS)
= s(1,nF,nS)
. . . s(KI,nF,nS) T
(3.31)
of dimension KI is formed, containing the KI transmit values s(kI,nF,nS)
, kI = 1 . . .KI. More-
over, the received vector
e(nF,nS)
= e(1,nF,nS)
. . . e(KO,nF,nS) T
(3.32)
of dimension KO, and the noise vector
n(nF,nS)
= n(1,nF,nS)
. . . n(KO,nF,nS) T
(3.33)
of dimension KO, with the autocorrelation matrix
Rn = E n(nF,nS)
n(nF,nS)∗T
= N0 IKO
(3.34)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-43-320.jpg)
![34 Chapter 3: Modelling of OFDM-based MIMO systems
are defined, containing the KO received values e(kO,nF,nS)
, kO = 1 . . .KO, and the KO noise
values n(kO,nF,nS)
, kO = 1 . . .KO, at subcarrier nF and symbol slot nS, respectively. Moreover,
the KIKO transfer coefficients h(kI,kO,nF)
, kI = 1 . . . KI, kO = 1 . . . KO, of (3.26) are compiled
in the KO × KI channel matrix
H(nS,nF)
=
⎛
⎜
⎜
⎜
⎝
h(1,1,nF)
. . . h(KI,1,nF)
h(1,2,nF)
. . . h(KI,2,nF)
...
...
...
h(1,KO,nF)
. . . h(KI,KO,nF)
⎞
⎟
⎟
⎟
⎠
. (3.35)
With e(nF,nS)
of (3.32), H(nF)
of (3.35), s(nF,nS)
of (3.31) and n(nF,nS)
of (3.33), the transmission
model
e(nF,nS)
= H(nF)
s(nF,nS)
+ n(nF,nS)
(3.36)
for subcarrier nF and symbol slot nS for OFDM-based MIMO systems is derived.
3.3 Pre- and post-processing stages
3.3.1 Optimum and suboptimum approaches
In what follows, transmissions at an isolated OFDM symbol slot nS are considered, i.e.,
NS = 1 (3.37)
holds and consequently the index nS is hereafter dropped for the sake of simplicity.
In terms of the probability of erroneous detection of u(k)
, the optimum strategy regarding pre-
and post-processing in Fig. 3.1, is the generation of s(kI)
directly from all u(k)
, k = 1 . . .K,
and the detection of u(k)
from all e(kO)
, kO = 1 . . . KO, in one step, respectively [Mas02].
However, such a strategy may not be followed for reasons such as the high complexity. One
important class of suboptimum approaches for the pre-processing stages is characterized by a
two-step approach. In a first step, after FEC coding and modulation of the bit vectors u(k)
of
(3.1), the complex data symbols
d(k,nF)
∈ D, nF = 1 . . .NF, k = 1 . . . K, (3.38)
taken from the data symbol alphabet
D = {d1, . . . , dD} (3.39)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-44-320.jpg)
![3.3 Pre- and post-processing stages 35
of cardinality D result. The K data symbols d(k,nF)
, k = 1 . . . K, of (3.38) corresponding to a
single subcarrier nF are compiled into the data vector
d(nF)
= d(1,nF)
. . . d(K,nF)
T
(3.40)
of dimension K, and the NF data vectors d(nF)
, nF = 1 . . .NF, of (3.40) are stacked to form
the total data vector
d = d(1)T
. . . d(NF)T T
. (3.41)
In a second step, the transmit vectors s(nF)
, nF = 1 . . . NF, of (3.31) are generated from the
total data vector d of (3.41). In the corresponding class of suboptimum post-processing stages,
the estimates
ˆd
(nF)
= ˆd
(1,nF)
. . . ˆd
(K,nF) T
, nF = 1 . . . NF, (3.42)
of the data vectors d(nF)
, nF = 1 . . . NF, of (3.40), which can be compiled to the total estimated
data vector
ˆd = ˆd
(1)T
. . . ˆd
(NF)T T
, (3.43)
are obtained from the received vectors e(nF)
, nF = 1 . . .NF, of (3.32). In a second step the
estimated data symbols ˆd
(k,nF)
, k = 1 . . .K, nF = 1 . . . NF, contained in the estimated data
vectors ˆd
(nF)
, nF = 1 . . . NF, of (3.42) are demodulated and FEC decoded to yield the estimated
bit vectors ˆu(k)
, k = 1 . . .K, of (3.4).
3.3.2 Subcarrierwise pre- and post-processing
In Section 3.2 it is shown that a subcarrierwise model can be used to model the physical trans-
mission in an OFDM-based MIMO system. As transmissions at different subcarriers are inde-
pendent of each other [vNP00], the subcarrierwise investigation followed in the physical trans-
mission model, under certain circumstances can be extended to the pre- and post processing
stages. In particular, if the post-processing stage in an OFDM-based MIMO system operates in
a subcarrierwise fashion, then also the pre-processing stage can be implemented in a subcarri-
erwise manner, without loss of performance. Equivalently, if subcarrierwise pre-processing is
applied at the pre-processing stage then the post-processing stage can operate in a subcarrier-
wise fashion.
In the case that both pre- and post-processing can be performed in a subcarrierwise fashion, an
OFDM-based MIMO system employing transmission over NF subcarriers can be considered as
NF independent smaller multiuser OFDM-based MIMO systems. Moreover, given the usually
large number of subcarriers to be used in future mobile radio systems [vNP00], subcarrierwise
pre- and post-processing techniques, if applicable, prove to be especially attractive in terms of
computational complexity [SWBC02].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-45-320.jpg)
![38 Chapter 4: Uplink transmission in the service area concept
As can be seen from (4.5) and (4.10), each received value e(kB,nF)
contains contributions from
all K data symbols d(k,nF)
, k = 1 . . . K, sent at the corresponding subcarrier nF. In SA-
based systems, JD is the post-processing algorithm in the CU and the task of JD is to obtain an
estimate ˆd
(k,nF)
for each data symbol d(k,nF)
. From the viewpoint of JD, (4.10) represents NF
independent linear systems of equations, each with KB equations and K unknowns. In other
words, in each of the NF linear equation systems, K data symbols d(k,nF)
, k = 1 . . .K, have
to be jointly detected from the KB received values e(kB,nF)
, kB = 1 . . .KB, of (4.5) available to
the CU. Such a detection becomes feasible only if
KB ≥ K (4.11)
holds, i.e., only if each of the NF systems of equations is not underdetermined.
In the following algorithms for JD are presented, with the aid of which the spatial receive
diversity inherent in the UL transmission of SA-based systems is exploited, i.e., the signals
received at the KB APs are combined targeting at the suppression of the interference between
the useful received signals of the active MTs.
4.2 Optimum joint detection
4.2.1 Approaches to optimum post-processing
The approach regarding the post-processing stage at the CU which is optimum with respect to
the erroneous decision for the bit u
(k)
l , is a JD algorithm which, given the total received vector e
of (4.10), yields the estimate ˆu
(k)
l with the maximum a posteriori probability P ˆu
(k)
l |e under
consideration of the modulation constellation D and the FEC code, i.e.,
ˆu
(k)
l = arg max
ˆu
(k)
l ∈{+1,−1}
P ˆu
(k)
l |e , k = 1 . . .K, l = 1 . . . L, (4.12)
holds [Ver86a, Ver86b, Ver98]. However, given practical parametrization of multiuser mobile
radio systems, the detector described by (4.12) is not realizable in multiuser scenarios due the
high complexity.
In what follows, only JD algorithms are considered which correspond to suboptimum, relative
to (4.12), approaches, in which estimates ˆd
(k,nF)
of the data symbols d(k,nF)
are obtained in an
intermediate step in the JD process, as described in Section 3.3.1. Hence, the term optimum JD
is used hereafter to refer to JD algorithms which are optimum with respect to the probability
of erroneous detection of the total data vector d of (3.41). As described in Section 3.2, each](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-48-320.jpg)
![4.2 Optimum joint detection 39
received value e(kB,nF)
contains no contributions from data symbols d(k,nF)
sent at subcarrier
nF = nF, and therefore optimum JD in a SA-based system can be performed in a subcarrierwise
fashion, i.e., optimum JD of the data vector d(nF)
of (3.40) from the received vector e(nF)
of
(3.32) can be performed for each subcarrier nF, nF = 1 . . . NF, separately [SWBC02].
4.2.2 Maximum a posteriori joint detection
The optimum approach for JD with respect to the probability of erroneous detection of the data
vector d(nF)
of (3.40) is JD performed according to the MAP principle [Ver86a]. Given the
received vector e(nF)
of (4.5) and the cardinality D of the data symbol alphabet D of (3.39),
from the DK
possible data vectors ˆd
(nF)
∈ DK
the data vector ˆd
(nF)
yielding the maximum a
posteriori probability P ˆd
(nF)
|e(nF)
is chosen as the estimate
ˆd
(nF)
= arg max
ˆd
(nF)
∈DK
P ˆd
(nF)
|e(nF)
(4.13)
according to optimum JD.
4.2.3 Maximum likelihood joint detection
With the conditional probability density function p e(nF)
| ˆd
(nF)
of the received vector e(nF)
of (4.5), the probability density function p e(nF)
of the received vector e(nF)
of (4.5) and the a
priori probability P ˆd
(nF)
of the data vector ˆd
(nF)
, the Bayes rule [Pap00] can be applied on
the a posteriori probability P ˆd
(nF)
|e(nF)
of the data vector ˆd
(nF)
of (3.40), to yield
P ˆd
(nF)
|e(nF)
=
1
p (e(nF))
p e(nF)
| ˆd
(nF)
P ˆd
(nF)
. (4.14)
If the data vectors ˆd
(nF)
in (4.14) are equiprobable, the probability P ˆd
(nF)
plays no role in
the maximization process of (4.13). Moreover, the probability density function p e(nF)
of the
received vector e(nF)
in (4.14) is independent of the considered vector d(nF)
and can therefore
be omitted in the maximization process. Hence, in the case of equiprobable data vectors ˆd
(nF)
the maximization of the a posteriori probability P ˆd
(nF)
|e(nF)
in (4.13) is equivalent with the
maximization of the likelihood function p e(nF)
| ˆd
(nF)
due to (4.14), and the MAP detector
of (4.13) becomes the ML detector [Ver98]
ˆd
(nF)
= arg max
ˆd
(nF)
∈DK
p e(nF)
| ˆd
(nF)
. (4.15)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-49-320.jpg)
![4.3 Linear joint detection 41
the estimate ˆd
(nF)
of d(nF)
through a linear transformation of the received vector e(nF)
. There-
fore, linear JD algorithms can be described by a K × KB demodulator matrix D(nF)
as
ˆd
(nF)
= D(nF)
e(nF)
. (4.19)
As (4.19) shows, in contrast to MAP JD of (4.13) and ML JD of (4.15) in linear JD the knowl-
edge concerning the modulation constellation D is not exploited, i.e., ˆd
(nF)
∈ CK
follows for
the estimated data vector ˆd
(nF)
obtained by linear JD as shown in (4.19).
Depending on the criterion which ˆd
(nF)
of (4.19) should satisfy, there exist numerous possibili-
ties for the choice of the demodulator matrix D(nF)
. In the following, the cases of RxZF JD and
MMSE JD are considered.
4.3.2 Receive zero-forcing joint detection
According to the RxZF criterion, with the received vector e(nF)
of (3.36) and the transfer matrix
H(nF)
of (3.35), the estimate ˆd
(nF)
of the data vector d(nF)
minimizes the Euclidean distance
e(nF)
− H(nF)ˆd
(nF) 2
, or in other words, the estimated data vector ˆd
(nF)
is chosen, from
which the reconstructed received vector H(nF)ˆd
(nF)
with the minimum Euclidean distance to
the received vector e(nF)
results. The criterion of RxZF JD is expressed as [KB92, KB93,
Kle96, BFKM93, FKB94, LV90]
ˆd
(nF)
= arg min
ˆd
(nF)
∈CK
e(nF)
− H(nF)ˆd
(nF) 2
. (4.20)
Comparing (4.17) and (4.20) it follows that in the case of zero-mean Gaussian noise, ML JD
and the RxZF JD have similar criteria. The difference between ML JD and the RxZF JD is that
the estimated data symbols ˆd
(k,nF)
, k = 1 . . .K, of (4.20) of RxZF JD can take any continuous
value from C, whereas the estimates ˆd
(k,nF)
, k = 1 . . . K, of ML JD of (4.17) can only take the
D discrete values of D.
With the received vector e(nF)
of (3.36), the transfer matrix H(nF)
of (3.35), the expression
ˆd
(nF)
= H(nF)∗T
H(nF)
−1
H(nF)∗T
D
(nF)
RxZF
e(nF)
(4.21)
for the estimated data vector ˆd
(nF)
of RxZF JD follows from (4.20). As (4.21) shows, D
(nF)
RxZF is
the left side pseudoinverse of the channel matrix H(nF)
. Moreover, for deterministic H(nF)
and
random n(nF)
, the estimated data vector ˆd
(nF)
of (4.21) of RxZF JD satisfies
E ˆd
(nF)
= d(nF)
, (4.22)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-51-320.jpg)
![42 Chapter 4: Uplink transmission in the service area concept
i.e., RxZF JD delivers unbiased estimates ˆd
(k,nF)
, k = 1 . . .K, of the data symbols d(k,nF)
, k =
1 . . .K, eliminating all intra-SA interference.
As opposed to RxZF JD for CDMA systems [KB92, KB93, Kle96, BFKM93] by which MTs
in a cell are separated based on their channel signatures and CDMA codes, RxZF JD in SA-
based systems eliminates intra-SA interference using only the channel signatures of the K MTs
inherent in the transfer matrix H(nF)
. Due to the spatial separation of the APs the transfer matrix
H(nF)
has, if special cases are not considered, full rank and can be used for the spatial separation
of the MTs.
4.3.3 Minimum mean square error joint detection
The criterion which the estimated data vector ˆd
(nF)
of MMSE JD satisfies is the MMSE error
min E d(nF)
− ˆd
(nF) 2
, hence for deterministic H(nF)
and random n(nF)
, the MMSE
JD criterion is expressed as [MH94, Gra81, LV89, XSR90, LV90, BFKM93, KKKB94, KKKB96]
ˆd
(nF)
= arg min
ˆd
(nF)
∈CK
E d(nF)
− ˆd
(nF) 2
. (4.23)
With the correlation matrix
R
(nF)
dd = E d(nF)
d(nF)∗T
(4.24)
of the data vector d(nF)
, the received vector e(nF)
of (3.36), the transfer matrix H(nF)
of (3.35)
and the variance σ2
of real and imaginary parts of the noise values n(kB,nF)
, kB = 1 . . .KB,
MMSE JD is expressed as
ˆd
(nF)
= H(nF)∗T
H(nF)
+ σ2
R
(nF)
dd
−1 −1
H(nF)∗T
D
(nF)
MMSE
e(nF)
. (4.25)
From (4.25) it can be seen that MMSE JD of (4.25), unlike RxZF JD of (4.21), does not deliver
unbiased estimates. Instead, in the case of the the MMSE JD, as compared to RxZF JD, infor-
mation concerning the reliability of the estimated data symbols ˆd
(k,nF)
is additionally taken into
account. In particular, for a low noise power σ2
, the MMSE JD demodulator matrix D
(nF)
MMSE
of (4.25) converges towards the demodulator matrix D
(nF)
RxZF of (4.21) of RxZF JD but for high
noise levels an all-zero estimated vector ˆd
(nF)
is obtained.
In comparison to MMSE JD for CDMA systems [MH94, Gra81, LV89, XSR90, LV90, BFKM93,
KKKB94, KKKB96], in which the MMSE criterion of (4.23) is applied in each cell using the
channel matrix and the CDMA component, in the case of MMSE JD for SA-based systems only
the transfer matrix H(nF)
is used to suppress the intra-SA interference.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-52-320.jpg)
![4.4 Iterative joint detection 43
4.4 Iterative joint detection
4.4.1 General model of iterative joint detection
JD can also be realized in an iterative fashion [Lam00b, Lam00a, DSR98, PH94, Var95, KIHP90].
The data detection model according to iterative JD is illustrated in Fig. 4.2. As shown in Fig. 4.2,
MF
bank
data estimate
refinement
and decoding
e r ˆd(p)
ˆˆd(p)ˆˆd(p − 1) ˆu(p)
F
R
Figure 4.2. Iterative JD model with data estimate refinement
in iterative JD the estimate ˆu(p) of the bit vector u is the output of each iteration p, p = 1 . . . P.
In order to yield the estimated bit vector ˆu(p) in each iteration p, a refined version
ˆˆd(p − 1) of
the total estimated data vector ˆd(p − 1) of iteration p − 1 is used to reconstruct the intra-SA
interference by the aid of the reverse path matrix R. The reconstructed intra-SA interference
R
ˆˆd(p − 1) is then subtracted from the output
r = H∗T
e (4.26)
of a MF bank, and after multiplication with the forward path matrix F, the total data vector es-
timate
ˆˆd(p) results from which the estimated bit vector ˆu(p) follows by means of demodulation
and FEC decoding.
Due to the iterative character of JD, intra-SA interference is removed by means of subtraction
rather than by exhaustive search as in optimum JD in Section 4.2, or by matrix inversion as in
linear JD in Section 4.3. As no significant advantage regarding complexity is gained by per-
forming iterative JD in a subcarrierwise fashion, nonsubcarrierwise iterative JD is considered.
The forward path matrix F and reverse path matrix R used in iterative JD are chosen based on
the criteria described in Section 4.4.2. For given forward path matrix F and reverse path matrix](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-53-320.jpg)
![4.4 Iterative joint detection 45
ˆd demod. FEC
ˆˆd
ˆu
Figure 4.3. Data estimate refinement and decoding block of iterative JD with transparent data
estimate refinement
Until now, the limiting value of iterative JD with transparent data estimate refinement is dealt
with. Regarding the criterion of convergence, the spectral radius [Sch88b] λmax (X) of a com-
plex matrix X with Q eigenvalues λq, q = 1 . . . Q, is introduced. The spectral radius λmax (X)
of X is defined as [Sch88b]
λmax (X) = max |λ1|, . . ., |λQ| . (4.32)
With the KNF × KNF product F R of the forward path matrix R and reverse path matrix F, it
has been shown [TR00] that iterative JD with transparent data estimate refinement converges if
λmax (F R) ≤ 1 (4.33)
holds, i.e., if all Q eigenvalues λq, q = 1 . . .Q, of F R lie within the bounds of the unity circle
around the origin of the complex plane.
4.4.3 Data estimate refinement by hard quantization
A first step towards the refinement of the total estimated data vector ˆd is to exploit the knowl-
edge of the modulation constellation DKNF
in the data estimate refinement process, as Fig. 4.4
shows.
In this case, data estimate refinement consists in quantizing the continuous valued elements
ˆd
(k,nF)
of the total estimated data vector ˆd with respect to the modulation constellation D, to
yield the total refined estimate
ˆˆd = arg min
d∈DKNF
ˆd − d
2
. (4.34)
of the data vector d.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-55-320.jpg)
![46 Chapter 4: Uplink transmission in the service area concept
ˆd demod. FEC
ˆˆd
ˆu
Figure 4.4. Data estimate refinement and decoding block of iterative JD with data estimate
refinement by hard quantization
4.4.4 Data estimate refinement by soft quantization
Data estimate refinement by soft quantization is an improvement of the data estimate refine-
ment by hard quantization, in which the reliability of each estimated coded bit ˆd
(k)
m is taken
into account. Fig. 4.5 shows the model for iterative JD with data estimate refinement by soft
quantization.
ˆd
2
ˆσd
2
σ2
d
estimation
sign(·)
tanh(·/2) mod.
demod. FEC
ˆˆd
ˆu
Lˆd|d
ˆd
(k)
m
Figure 4.5. Data estimate refinement and decoding block of iterative JD with data estimate
refinement by soft quantization
Soft quantization is the data estimate refinement technique which minimizes the error [MH97,
Lam00b, INF01, WOWB02, MW03]
E
ˆˆd(k)
m − d(k)
m
2
ˆd(k)
m =
ˆˆd(k)
m − E d(k)
m | ˆd(k)
m
2
+ var d(k)
m | ˆd(k)
m . (4.35)
The error E
ˆˆd
(k)
m − d
(k)
m
2
ˆd
(k)
m of (4.35) becomes minimal if the refined estimate
ˆˆd(k)
m = E d(k)
m | ˆd(k)
m (4.36)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-56-320.jpg)
![4.4 Iterative joint detection 47
is chosen. In the case of BPSK, the log-likelihood ratio [Hag97]
Ld|ˆd
ˆd(k)
m = ln
⎛
⎝
P d
(k)
m = +1| ˆd
(k)
m
P d
(k)
m = −1| ˆd
(k)
m
⎞
⎠ (4.37)
of the a posteriori probabilities P d
(k)
m = ±1| ˆd
(k)
m of the coded bit d
(k)
m is used to complement
the hard decision for d
(k)
m , expressed by the sign of Ld|ˆd
ˆd
(k)
m with reliability information
expressed by the magnitude of Ld|ˆd
ˆd
(k)
m [Hag97].
The log-likelihood ratio Ld|ˆd
ˆd
(k)
m of (4.37) can be expressed depending on the conditional
probabilities P ˆd
(k)
m |d
(k)
m ± 1 of the estimated coded bit ˆd
(k)
m and on the a priori probabilities
P d
(k)
m = ±1 of the coded bit d
(k)
m as
Ld|ˆd
ˆd(k)
m = ln
⎛
⎝
P ˆd
(k)
m |d
(k)
m = +1
P ˆd
(k)
m |d
(k)
m = −1
⎞
⎠
Lˆd|d
ˆd(k)
m
+ ln
⎛
⎝
P d
(k)
m = +1
P d
(k)
m = −1
⎞
⎠ . (4.38)
With (4.37), and assuming that all coded bits d
(k)
m , k = 1 . . . K, m = 1 . . . M, are equiprobable,
i.e.
ln
⎛
⎝
P d
(k)
m = +1
P d
(k)
m = −1
⎞
⎠ = 0, k = 1 . . .K, m = 1 . . . M, (4.39)
holds,
P ˆd(k)
m |d(k)
m = +1 =
exp Lˆd|d
ˆd(k)
m 2
exp Lˆd|d
ˆd(k)
m 2 + exp − Lˆd|d
ˆd(k)
m 2
(4.40)
and
P ˆd(k)
m |d(k)
m = −1 =
exp − Lˆd|d
ˆd(k)
m 2
exp Lˆd|d
ˆd(k)
m 2 + exp − Lˆd|d
ˆd(k)
m 2
(4.41)
follow and using (4.40) and (4.41), (4.36) becomes
ˆˆd(k)
m = tanh
⎛
⎝
Lˆd|d
ˆd
(k)
m
2
⎞
⎠. (4.42)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-57-320.jpg)
![4.4 Iterative joint detection 49
ˆd
2
ˆσd
2
σ2
d
estimation
sign(·)
tanh(·/2) mod.
MAP
demod. FEC
ˆˆd
ˆu
Lˆd|d
ˆd
(k)
m Ld|ˆd
ˆd(k)
Lu|ˆd
ˆd(k)
Figure 4.6. Data estimate refinement and decoding block of iterative JD with optimum data
estimate refinement
The criterion of optimum data estimate refinement is similar to the criterion of (4.35) of data
estimate refinement with soft quantization. In particular, using the estimate
ˆd(k)
= ˆd
(k)
1 . . . ˆd
(k)
M
T
, (4.47)
of the coded bit vector d(k)
of (4.3), the exploitation of the FEC code knowledge in the case of
optimum data estimate refinement alters (4.35) to the criterion [WOWB02]
E
ˆˆd(k)
m − d(k)
m
2
ˆd(k)
=
ˆˆd(k)
m − E d(k)
m |ˆd(k)
2
+ var d(k)
m |ˆd(k)
(4.48)
of optimum data estimate refinement. By exploiting knowledge concerning FEC coding, not
just a single estimated coded bit ˆd
(k)
m as in (4.35), but the whole coded estimated bit vector ˆd(k)
of (4.47) is taken into account. The error E
ˆˆd
(k)
m − d
(k)
m
2
ˆd(k)
of (4.48) becomes minimum
if the refined estimates
ˆˆd(k)
m = E d(k)
m |ˆd(k)
, k = 1 . . . K, m = 1 . . . M, (4.49)
of the coded bits
ˆˆd
(k)
m , k = 1 . . .K, m = 1 . . . M, are chosen by the refinement procedure. If
BPSK is used, the log-likelihood ratio
Ld|ˆd
ˆd(k)
= ln
⎛
⎝
P d
(k)
m = +1|ˆd(k)
P d
(k)
m = −1|ˆd(k)
⎞
⎠ (4.50)
of the a posteriori probabilities
P d(k)
m = ±1|ˆd(k)
=
d(k)|d(k)∈DK∧d
(k)
m =±1
P ˆd(k)
|d(k)
(4.51)
can be used, from which with (4.50), the refined estimate
ˆˆd(k)
m = tanh
⎛
⎝
Ld|ˆd
ˆd(k)
2
⎞
⎠ (4.52)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-59-320.jpg)
![50 Chapter 4: Uplink transmission in the service area concept
of each coded bit d
(k)
m can be calculated.
An algorithm with the aid of which the log-likelihood ratios Ld|ˆd
ˆd(k)
, k = 1 . . . K, m =
1 . . .M, of (4.50) can be calculated is the Bahl Cocke Jelinek Raviv (BCJR) algorithm [BCJR74].
The BCJR algorithm is a soft-input-soft-output MAP symbol by symbol detector, which takes
the log-likelihood ratios Lˆd|d
ˆd
(k)
m , k = 1 . . .K, m = 1 . . .M, as inputs. At its output the
BCJR algorithm provides the log-likelihood ratios Ld|ˆd
ˆd(k)
, k = 1 . . . K, m = 1 . . .M,
of (4.50) from which the refined estimates
ˆˆd
(k)
m , k = 1 . . . K, m = 1 . . . M, of the coded bits
d
(k)
m , m = 1 . . . M, k = 1 . . .K, can be calculated according to (4.52), and Lu|ˆd
ˆd(k)
, k =
1 . . .K, from which the estimates
ˆu
(k)
l = sign Lu|ˆd
ˆd(k)
, l = 1 . . .L, k = 1 . . . K, (4.53)
of the bits u
(k)
l , l = 1 . . . L, k = 1 . . . K, can be calculated by means of hard quantization as
Fig. 4.6 shows, i.e., the BCJR algorithm also performs FEC decoding [BCJR74].
With a closer look at Figs. 4.2 and 4.6, one can see that the iterative JD detector with optimum
data estimate refinement by means of FEC coding evaluation is comprised of two parts. The part
evaluating the FEC code, see Fig. 4.6, and the remaining part performing multiuser detection,
see Fig. 4.2. In contrast to serial multiuser detection schemes, the two parts of the iterative JD
detector of 4.2 and Fig. 4.6 exchange soft information. Hence, iterative JD with optimum data
estimate refinement by means of FEC coding evaluation is a multiuser detector following the
turbo principle [Hag97, Poo00].
It is therefore shown how turbo multiuser detection [Hag97, Poo00] can be used as an iterative
JD algorithm in the CU in SA-based systems. From the said employment of iterative JD with
optimum data estimate refinement, knowledge concerning the FEC code additionally to the
knowledge of the spatial signatures of the MTs, contained in the total transfer matrix H, is
exploited to combat intra-SA interference in an efficient way and to provide a high spectrum
capacity ηc of (1.1) in SA-based systems.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-60-320.jpg)
![5.2 Optimum joint transmission 53
holds, i.e., each of the NF systems of equations for determining the KB transmit values s(kB,nF)
, kB =
1 . . .KB, from the K data symbols d(k,nF)
, k = 1 . . . K, is underdetermined.
By the employment of the JT algorithms presented in the following, the spatial transmit diversity
in the DL transmission of SA-based systems is exploited and such transmit signals are generated
by JT by the transmission of which interference between the active MTs is suppressed.
5.2 Optimum joint transmission
5.2.1 Introduction
In the present Section, a novel nonlinear JT scheme is presented, which is optimum with re-
spect to the average bit error probability P
(nF)
b at the MTs. In contrast to approaches to a
minimum BER transmission for the DL of state-of-the-art CDMA mobile radio systems, see,
e.g., [IRF03], a flexible and compact model characterizes the optimum nonlinear JT scheme for
SA-based systems, due to the fact that optimum JT can be performed in a subcarrierwise fash-
ion. In what follows, the term optimum JT is used to denote JT which is optimum in the sense
of the average bit error probability P
(nF)
b at the MTs. For the sake of simplicity, investigations
are carried out using real signals. The extension to complex valued signals is straightforward
and can be performed by considering the real valued equivalent isomorphic form of the complex
signals [ZF86].
With respect to the average bit error probability P
(nF)
b the transmission of data vectors
d(nF)
, d(nF)
∈ DK
, where the data vector d(nF)
is a rotated version of the data vector d(nF)
,
is equivalent, which means that the investigation of both data vectors d(nF)
and d(nF)
in terms
of the average bit error probabilityP
(nF)
b is redundant. Equivalently, the set DK
of the data
vectors contains V effective data vectors d(nF)
v , v = 1 . . .V , which contribute to the average bit
error probability P
(nF)
b and DK
− V data vectors which result from the V effective data vectors
d(nF)
v , v = 1 . . .V , by means of a rotation operation and do not contribute to the average
bit error probability P
(nF)
b . Hence, for the purposes of investigation of the average bit error
probability P
(nF)
b , it suffices to consider the set
DK
eff = d
(nF)
1 , . . . , d
(nF)
V ⊂ DK
(5.9)
of effective data vectors d(nF)
v , v = 1 . . . V , of cardinality V instead of the set DK
of cardinality
DK
. For a given modulation scheme the choice of the effective data vectors d(nF)
v ∈ DK
eff is not
unique, whereas the cardinality V of the set DK
eff of (5.9) of effective data vectors is fixed. In
this thesis, optimum JT with BPSK is investigated, i.e.,
D = {+1, −1} (5.10)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-63-320.jpg)
![56 Chapter 5: Downlink transmission in the service area concept
of dimension KB, which is normalized as
1
2
s
(nF)
0,v
∗T
s
(nF)
0,v = KT, (5.18)
and with the energy factor t
(nF)
v , the effective transmit vector s
(nF)
v is expressed as
s(nF)
v = t(nF)
v s
(nF)
0,v . (5.19)
Using (5.14) and (5.18), it can be seen from (5.19) that the energy
T
(nF)
tot,v = t(nF)
v
2
KT (5.20)
of each effective transmit vector s
(nF)
v , v = 1 . . . V , is completely determined by the energy
factor t
(nF)
v . For example, it can be deduced from (5.16) and (5.20) that the fixed transmit
energy strategy can be realized by setting
t(nF)
v = 1, v = 1 . . .V. (5.21)
5.2.3 Parameterized representation of JT transmit signals
The crux of the parameterized representation of JT signals consists in the expression of the
vector s
(nF)
0,v of (5.17) and the energy factor t
(nF)
v in a coordinate system, which is an extension of
the spherical coordinate system in multidimensional spaces. The used coordinates are denoted
as generalized spherical coordinates.
With the KB − 1 angles ϕ
(kB,nF)
v ∈ [−π, π], kB = 1 . . .KB − 1, and with the dummy angle
ϕ(KB,nF)
v = 0, (5.22)
the KB elements s
(kB,nF)
0,v , kB = 1 . . .KB, of the vector s
(nF)
0,v of (5.17) can be expressed with the
aid of generalized spherical coordinates as
s
(kB,nF)
0,v =
√
2KT
kB−1
kB=1
sin ϕ
(kB,nF)
v cos ϕ(kB,nF)
v , kB = 1 . . . KB. (5.23)
Moreover, with the V − 1 angles ϑ
(nF)
v ∈ [0, π/2], v = 1 . . . V − 1, and the dummy angle
ϑ
(nF)
V = 0, (5.24)
follows for the energy factor
t(nF)
v =
√
V
v−1
v =1
sin ϑ
(nF)
v cos ϑ(nF)
v . (5.25)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-66-320.jpg)
![60 Chapter 5: Downlink transmission in the service area concept
Various numerical minimization algorithms can be applied in order to yield the effective trans-
mit vectors s
(nF)
v,opt of optimum JT. A first approach is the use of methods based on gradient
approaches, such as Newton methods [Sto83]. Such minimization algorithms use information
concerning the gradient of the objective function to be minimized, and in each iteration the
direction of steepest descent is followed to locate the minimum of the objective function. The
inverse of the Hessian matrix, needed for the location of the minimum of the objective function,
is numerically calculated by Newton methods. In order to avoid the large number of computa-
tions involved in the direct numerical calculation of the Hessian matrix, quasi-Newton methods
[Bro70, Fle70, Gol70, Sha70] use the observed behavior of the objective function and of its
gradient to make an approximation to the Hessian matrix using an appropriate updating tech-
nique such as the formula of Broyden [Bro70], Fletcher [Fle70], Goldfarb [Gol70], and Shanno
[Sha70] (BFGS). Instead of approximating the Hessian matrix and performing the inversion in
a second step, the inverse of the Hessian matrix can be approximated using the formula from
Davidon [Dav59], Fletcher and Powell [FP63] (DFP).
5.3 Transmit zero-forcing joint transmission
In this Section, TxZF JT is dealt with. With regard to the considerations of Section 5.2, in the
case of linear JT the mapping function f(nF)
of (5.13) is linear and can be therefore described by
a KB × K modulator matrix M(nF)
. According to TxZF JT for SA-based systems, the transmit
vector s(nF)
of dimension KB is generated from the data vector d(nF)
of dimension K under
consideration of the structure of the K MTs given by (5.7), through a linear transformation
[MBW+
00, Fis02]
s(nF)
= M(nF)
d(nF)
. (5.36)
In the present thesis, linear JT in the sense of TxZF JT [WMS+
02, MBW+
00, WSLW03] is
considered. By TxZF JT, intra-SA interference in the DL of SA-based systems is completely
eliminated, i.e., using (5.7), in the absence of noise the requirement of an interference free
estimate reads
ˆd
(nF)
= d(nF)
(5.37)
and with (5.6) follows
H(nF)T
s = d(nF)
. (5.38)
By posing the requirement of (5.38) on the transmit vector s(nF)
of (5.36), given that KB ≥ K,
an underdetermined system of K equations and KB unknowns results, which means that there
exist infinitely many transmit vectors s(nF)
which fulfill the requirement of (5.38), and that an
additional requirement should be posed on the transmit vector s(nF)
.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-70-320.jpg)
![5.4 Iterative joint transmission 61
With respect to the inter-SA interference in the DL, it is desirable to minimize the total transmit
energy
T
(nF)
tot =
1
2
s(nF)∗T
s(nF)
, (5.39)
which is radiated from the investigated SA. Therefore, among all transmit vectors s(nF)
which
fulfill (5.38), the transmit vector [MBW+
00, WMS+
02]
s(nF)
= H(nF)∗
H(nF)T
H(nF)∗ −1
M
(nF)
TxZF
d(nF)
(5.40)
is used in TxZF JT, which has the least energy T
(nF)
tot of (5.39) and consequently causes the
minimum possible inter-SA interference.
As is the case with RxZF JD in the UL transmission, see Section 4.3.2, by TxZF JT intra-SA
interference in the DL transmission of SA-based systems is eliminated using only the chan-
nel signatures of the MTs in the transfer matrix H(nF)T
of the DL transmission, as compared
to TxZF JT in CDMA systems by which also the CDMA components are used to eliminate
interference in each cell [MBW+
00, WMS+
02].
5.4 Iterative joint transmission
Drawing an analogy to iterative JD of Section 4.4, in this Section an iterative JT algorithm is
presented. Unlike TxZF JT of Section 5.3, in iterative JT intra-SA interference is mitigated in
an iterative fashion, rather than with a direct matrix inversion. Fig. 5.5 shows the model for
iterative JT.
As shown in Fig. 5.5, using the KNF × KNF forward path matrix F and the KNF × KNF
reverse path matrix R, the data vector d of dimension KNF is pre-processed in an iterative
way. With the initial value
t(0) = 0, (5.41)
in each iteration p, p = 1 . . . P, the transformed total data vector
t(p) = F (d − R t(p − 1)) (5.42)
of dimension KNF is produced, from which the total transmit vector
s(p) = H∗
t(p) (5.43)
of dimension KBNF is generated.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-71-320.jpg)
![62 Chapter 5: Downlink transmission in the service area concept
H∗
d s(p)t(p)
t(p − 1)
F
R
Figure 5.5. Iterative JT model
If iterative JT converges, then for the limiting value of the transformed data vector
t(∞) = F (d − R t(∞))
= F−1
+ R
−1
d. (5.44)
holds. Comparing the expression for the convergence value of the transformed data vector t(∞)
of (5.44) to the expression (4.28) for the limiting value of the estimated data vector ˆd(∞) of
iterative JD, it can be deduced that iterative JT and iterative JD with transparent data estimate
refinement are described by the formally equivalent expressions (4.28) and (5.44). Hence, using
the results of 4.4.2, with the the forward path matrix F and the reverse path matrix R, it follows
that iterative JT converges if and only if for the spectral radius [Sch88b] λmax (F R) of the
matrix product F R of dimension KNF × KNF
λmax (F R) ≤ 1 (5.45)
holds. In the case of convergence, with t(∞) of (5.44) and with the matrix
M∞ = H∗
F−1
+ R
−1
(5.46)
of dimension KBNF × KNF, the limiting value of the total transmit vector
s(∞) = H∗
F−1
+ R
−1
d (5.47)
is equal to the total transmit vector
s = M∞ d (5.48)
of a linear JT scheme characterized by the total modulator matrix M∞ of (5.46). For example,
choosing
F = diag HT
H∗ −1
(5.49)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-72-320.jpg)
![64 Chapter 6: Performance investigation of uplink transmission
6 Performance investigation of uplink transmission
6.1 Preliminary remarks
In Chapter 4 the transmission and detection model for the UL in SA-based air interface archi-
tectures employing OFDM is presented. The present Chapter deals with the assessment of the
performance of the various JD algorithms which are described in Chapter 4. In particular, per-
formance measures for JD are introduced and on the basis of these measures, the performance
of the various JD algorithms is assessed in a number of different scenarios.
In a first step, assumptions are introduced which significantly simplify the expressions that
follow. Aspects concerning the performance comparison of SA-based systems employing dif-
ferent modulation schemes are not dealt with in the present thesis. Therefore, without loss
of generality it is assumed that QPSK modulation is employed. Furthermore, the data symbols
d(k,nF)
, k = 1 . . .K, transmitted at a specific subcarrier nF in the UL are assumed to be uncorre-
lated. With the data vector d(nF)
of (3.40) and the K×K identity matrix IK, the aforementioned
assumption is expressed by the data correlation matrix
R
(nF)
dd = E d(nF)
d(nF)∗T
= 2 IK (6.1)
of dimension K × K. Finally, Gaussian distributed noise values n(kB,nF)
, kB = 1 . . . KB, are
assumed and with the variance σ2
of the real and imaginary part of each noise value n(kB,nF)
and the KB × KB identity matrix IKB
, the noise vector n(nF)
of (3.33) is characterized by the
noise correlation matrix
R(nF)
nn = E n(nF)
n(nF)∗T
= 2σ2
IKB
(6.2)
of dimension KB × KB.
Target of JD in the UL of SA-based systems is the suppression of the interference between the
received signals from the K MTs active in the SA. As far as the detection of the data symbol
d(k,nF)
is concerned, using (6.1), the transfer matrix H(nF)
of (3.35), and introducing the operator
[·]k,k which is used on a quadratic matrix returning the k-th element of its main diagonal, the
price to be paid for the suppression of the intra-SA interference disturbing the partial received
signal from MT k at subcarrier nF, is the suboptimum use of the receive energy
R(k,nF)
=
1
2
E |d(k,nF)
|2
H(nF)∗T
H(nF)
k,k
= H(nF)∗T
H(nF)
k,k
, (6.3)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-74-320.jpg)
![6.1 Preliminary remarks 65
resulting from the transmission of data symbol d(k,nF)
, when compared to an optimum single
user reference system based on matched filtering, in which only the data symbol d(k,nF)
is
transmitted and hence no need for interference suppression is present.
Common to all performance measures for JD introduced in this thesis is the assessment of the
said suboptimum use of the receive energy R(k,nF)
of (6.3). In particular, with the performance
measures for JD introduced in the present Chapter, the use of the receive energy R(k,nF)
of (6.3)
by JD is assessed on the basis of the SNR of the estimate ˆd
(k,nF)
of the data symbol d(k,nF)
and
of the achieved bit error probability P
(k,nF)
b .
Using the matrix operator [·]k which returns the k-th column of its argument as a column vector,
in the reference system in which only the data symbol d(k,nF)
is transmitted, transmission takes
place over the mobile radio channel described by the transfer vector H(nF)
k
thus yielding the
received vector
e(nF)
= H(nF)
k
d(k,nF)
+ n(nF)
. (6.4)
In terms of the use of the receive energy R(k,nF)
of (6.3), in the reference system the optimum
approach concerning data estimation is employed, being the use of a filter matched to the chan-
nel H(nF)
k
by which the estimated data symbol
ˆd
(k,nF)
= H(nF)
k
∗T
e(nF)
(6.5)
is obtained from the received vector e(nF)
of (6.4). In this case, with the variance σ2
of real and
imaginary parts of each noise value n(kB,nF)
, the maximum possible SNR
γ
(k,nF)
ref =
E d(nF)
2
E ˆd
(nF)
− d(nF)
2
=
1
σ2
H(nF)∗T
H(nF)
k,k
(6.6)
and the minimum possible bit error probability P
(k,nF)
b,ref for given receive energy R(k,nF)
of (6.3)
is obtained, which in the case of QPSK reads
P
(k,nF)
b,ref =
1
2
erfc
1
2σ2
H(nF)∗T
H(nF)
k,k
. (6.7)
Due to the fact that in the reference system a single data symbol d(k,nF)
is considered, the
performance of the reference system in terms of the bit error probability P
(k,nF)
b is also referred
to as single user bound.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-75-320.jpg)
![66 Chapter 6: Performance investigation of uplink transmission
6.2 Bit error probability
6.2.1 The bit error probability as performance measure
In this thesis, the main performance measure used to assess the efficiency with which the re-
ceive energy R(k,nF)
of (6.3) is used in JD is the bit error probability P
(k,nF)
b . In particular,
using the receive energy R(k,nF)
, the receive energy per bit E
(k,nF)
b corresponding to each of the
information bits contained in the QPSK data symbol d(k,nF)
is determined and, using the two-
sided power spectral density N0/2 of the noise, the corresponding bit error probability P
(k,nF)
b
is simulated for various values of E
(k,nF)
b /N0. In the case that the performance of JD averaged
over a large number of realizations of the mobile radio channel is investigated, the average bit
error probability P b is simulated for various values of Eb/N0.
The suboptimum use of the receive energy R(k,nF)
of (6.3) is expressed using simulations of
the bit error probability P
(k,nF)
b versus E
(k,nF)
b /N0 through the fact that for a given E
(k,nF)
b /N0
JD produces a bit error probability P
(k,nF)
b larger than the bit error probability P
(k,nF)
b,ref of the
reference system. Equivalently, in order to achieve a given bit error probability P
(k,nF)
b , JD
needs a larger E
(k,nF)
b /N0 as compared to the single user reference system.
In the simulation results for the bit error probability P
(k,nF)
b of JD presented in this Section, also
the bit error probability P
(k,nF)
b resulting from single user estimation in the sense of MF [Ver98]
is included for reasons of comparison. With MF, the estimated data symbols
ˆd
(nF)
= diag H(nF)∗T
H(nF)
−1
H(nF)∗T
e(nF)
(6.8)
are obtained from the received vector e(nF)
of (4.5). In the case of single user estimation by MF,
the estimated data symbols ˆd
(nF)
of (6.8) contain intra-SA interference. As intra-SA interfer-
ence is a systematic estimation error present even at high E
(k,nF)
b /N0, the bit error probability
P
(k,nF)
b of MF single user estimation of (6.8) converges, in the majority of cases, to an error
floor.
6.2.2 Bit error probability of optimum versus linear joint detection
As explained in Section 4.2, the fact that optimum JD can be performed in a subcarrierwise
fashion in SA-based OFDM systems, makes the application of optimum JD feasible. Target of
the present Section is to investigate the gains achievable with optimum JD as compared to linear
JD in SA-based systems quantitatively, in terms of the average bit error probability Pb.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-76-320.jpg)
![6.3 Asymptotic multiuser efficiency 77
6.3 Asymptotic multiuser efficiency
6.3.1 The asymptotic multiuser efficiency as performance measure
The fact that JD needs a higher E
(k,nF)
b /N0
JD
at its input than the E
(k,nF)
b /N0
ref
required by
the reference system in order to achieve a given target bit error probability P
(k,nF)
b is expressed
by the multiuser efficiency [Ver98, LV89]
η(k,nF)
e (σ2
) =
E
(k,nF)
b /N0
ref
E
(k,nF)
b /N0
JD P
(k,nF)
b,JD = P
(k,nF)
b,ref
∈ [0, 1] (6.24)
of JD. The asymptotic value of the multiuser efficiency η
(k,nF)
e (σ2
) of (6.24) for vanishing power
σ2
of the noise is termed asymptotic multiuser efficiency [Ver98, LV89]
η(k,nF)
= lim
σ2→0
η(k,nF)
e (σ2
). (6.25)
The use of the asymptotic multiuser efficiency η(k,nF)
of (6.25) instead of the multiuser effi-
ciency η
(k,nF)
e (σ2
) of (6.24) is advantageous when the description of the performance of JD by
a single scalar value is desired. In the present thesis, the asymptotic multiuser efficiency η(k,nF)
of (6.25) is used to assess linear JD in the sense of RxZF JD without FEC coding.
Using (6.1), the variance σ2
of real and imaginary parts of each noise value n(kB,nF)
and with
the KB × K transfer matrix H(nF)
, the SNR
γ
(k,nF)
RxZF =
E d(nF)
d(nF)∗T
k,k
E ˆd
(nF)
− d(nF) ˆd
(nF)
− d(nF)
∗T
k,k
=
1
σ2 H(nF)∗T
H(nF)
−1
k,k
(6.26)
of the estimated data symbol ˆd
(k,nF)
of RxZF JD according to (4.21) is calculated. Due to the fact
that the estimated data symbol ˆd
(k,nF)
of (4.21) is unbiased, the estimation error ˆd
(nF)
− d(nF)
is Gaussian [XSR90, Ver98, LV89] and with the output SNR γ
(k,nF)
RxZF of (6.26), the bit error
probability
P
(k,nF)
b,RxZF =
1
2
erfc
⎛
⎝ γ
(k,nF)
RxZF
2
⎞
⎠ (6.27)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-87-320.jpg)
![78 Chapter 6: Performance investigation of uplink transmission
of each bit in the QPSK data symbol d(k,nF)
results. Setting out from the fact that the bit error
probability P
(k,nF)
b,RxZF of (6.27) is a bijective and strictly monotonically decreasing function of the
output SNR γ
(k,nF)
RxZF of (6.26), η
(k,nF)
e (σ2
) of (6.24) becomes
η(k,nF)
e (σ2
) =
E
(k,nF)
b /N0
ref
E
(k,nF)
b /N0
JD γ
(k,nF)
RxZF = γ
(k,nF)
ref
∈ [0, 1]. (6.28)
It can be shown with the receive energy R(k,nF)
of (6.3) and with σ2
of (3.14) that in SA-based
systems in the absence of FEC coding
E
(k,nF)
b
N0
=
E
(k,nF)
b
N0
ref
=
E
(k,nF)
b
N0
JD
=
1
2
R(k,nF)
N0
=
1
2σ2
H(nF)∗T
H(nF)
k,k
(6.29)
holds. Further, using (6.26) and (6.29), the SNR
γ
(k,nF)
RxZF = 2 H(nF)∗T
H(nF)
−1
k,k
H(nF)∗T
H(nF)
k,k
−1
E
(k,nF)
b
N0
(6.30)
of the estimate of the data symbol d(k,nF)
by RxZF JD and with (6.6) and (6.29), the SNR
γ
(k,nF)
ref = 2
E
(k,nF)
b
N0
(6.31)
of the estimate of the data symbol d(k,nF)
by the reference system are calculated. As (6.30) and
(6.31) show, both γ
(k,nF)
RxZF and γ
(k,nF)
ref are linear functions of E
(k,nF)
b /N0 of (6.29) and therefore
the expression of the multiuser efficiency η
(k,nF)
e (σ2
) of (6.28) is further simplified to
η
(k,nF)
e,RxZF(σ2
) =
γ
(k,nF)
RxZF
γ
(k,nF)
ref
= H(nF)∗T
H(nF)
−1
k,k
H(nF)∗T
H(nF)
k,k
−1
(6.32)
According to (6.32), the multiuser efficiency η
(k,nF)
e,RxZF(σ2
) of RxZF JD in SA-based systems does
not depend on E
(k,nF)
b /N0 and hence, with (6.25) a compact expression also for the asymptotic
multiuser efficiency
η
(k,nF)
RxZF =
γ
(k,nF)
RxZF
γ
(k,nF)
ref
= H(nF)∗T
H(nF)
−1
k,k
H(nF)∗T
H(nF)
k,k
−1
(6.33)
of RxZF JD without FEC coding is derived.
For the case of QPSK using the asymptotic multiuser efficiency η
(k,nF)
RxZF of (6.33), for the bit
error probability P
(k,nF)
b,RxZF of (6.27)
P
(k,nF)
b,RxZF =
1
2
erfc
⎛
⎝ η
(k,nF)
RxZF
γ
(k,nF)
ref
2
⎞
⎠ (6.34)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-88-320.jpg)
![6.3 Asymptotic multiuser efficiency 79
follows.
Closely related to the asymptotic multiuser efficiency η
(k,nF)
RxZF of (6.33) is the SNR degradation
[Kle96, SWC+
02]
δ
(k,nF)
RxZF =
γ
(k,nF)
ref
γ
(k,nF)
RxZF
= H(nF)∗T
H(nF)
−1
k,k
H(nF)∗T
H(nF)
k,k
(6.35)
of RxZF JD. From the comparison of (6.35) and (6.33) follows that in the case of RxZF JD of
the data symbol d(k,nF)
the SNR degradation δ
(k,nF)
RxZF is the inverse of the asymptotic multiuser
efficiency η
(k,nF)
RxZF and quantifies the decreased SNR γ
(k,nF)
RxZF of RxZF JD as compared to the
SNR γ
(k,nF)
ref of the reference system. The said decrease of the SNR is the price to be paid for
the elimination of intra-SA interference by RxZF JD. Moreover, in the case of RxZF JD, the
SNR degradation δ
(k,nF)
RxZF of (6.35) and the asymptotic multiuser efficiency η
(k,nF)
RxZF of (6.33) both
express the fact that only the component of the useful received signal of MT k is used which
is orthogonal to the received signals corresponding to the other K − 1 MTs of the SA due to
the need for elimination of the intra-SA interference. Hence, the SNR degradation δ
(k,nF)
RxZF of
(6.35), and equivalently the inverse of the asymptotic multiuser efficiency η
(k,nF)
RxZF of (6.33) are
a measure for the amount of intra-SA interference disturbing the estimation of data symbol
d(k,nF)
.
6.3.2 Statistics of the asymptotic multiuser efficiency of receive zero-forcing
joint detection
Following the argumentation of Section 6.3.1, according to which the asymptotic multiuser ef-
ficiency η
(k,nF)
RxZF of (6.33) of RxZF JD is a measure for the intra-SA interference, in the present
Section the asymptotic multiuser efficiency η
(k,nF)
RxZF is investigated by the aid of the indoor geo-
metric channel model at a single subcarrier nF in order to provide insight into characteristics of
the intra-SA interference.
Using the indoor geometric channel model described in Section 2.3.2, with the distance r(k,kB)
between MT k and AP kB and the wavelength λ, follows from (2.4) for the corresponding
channel coefficient
h(k,kB,nF)
=
1
r(k,kB)
exp −j
2π
λ
r(k,kB)
. (6.36)
In the considered scenario
K = 2 (6.37)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-89-320.jpg)
![80 Chapter 6: Performance investigation of uplink transmission
MTs and
KB = 2 (6.38)
APs are considered. If (6.38) holds, then the SA structure resulting from the geometric channel
model of Section 2.3.2 is symmetrical. Due to the symmetry of the scenario, it suffices to con-
sider only the space defined by x ∈ [0, xmax/2] and y ∈ [0, ymax/2]. Without loss of generality,
MT 1 is placed at the origin, i.e.,
r(1,1)
= r(1,2)
= rB (6.39)
holds. MT 2 is randomly positioned in the considered scenario and the variable α ∈ R is
introduced to quantize the difference between r(2,1)
and r(2,2)
as
r(2,2)
= r(2,1)
+ α. (6.40)
With the coefficients h(k,kB,nF)
, k = 1 . . . K, kB = 1 . . .KB, of (6.36) and with the distances
r(k,kB)
, k = 1 . . . K, kB = 1 . . .KB, according to (6.39) and (6.40), the asymptotic multiuser
efficiency
η
(nF)
RxZF =
1
2
−
(α + r(2,1)
) cos
2π
λ
α
2 r(2,1)2
+ 2α r(2,1) + α2
(6.41)
averaged over the K data symbols d(k,nF)
, k = 1 . . .K, can be calculated from (6.33). As can
be seen from (6.41), the average asymptotic multiuser efficiency η
(nF)
RxZF depends on r(2,1)
and
α, or equivalently, η
(nF)
RxZF of (6.41) is a scalar function of the coordinates x
(2)
MT, y
(2)
MT of MT
2. Hence, η
(nF)
RxZF of (6.41) at the considered scenario can be visualized with the aid of a three-
dimensional plot of η
(nF)
RxZF of (6.41) with respect to the coordinates x
(2)
MT, y
(2)
MT of MT 2. Fig.
6.9 contains the aforementioned three-dimensional plot.
As Fig. 6.9 shows, the spatial distribution of η
(nF)
RxZF is characterized by a periodical succession
of maxima and minima. The expression of (6.41) for η
(nF)
RxZF can be rewritten as
η
(nF)
RxZF =
1
2
−
α
r(2,1)
+ 1 cos
2π
λ
α
2 + 2
α
r(2,1)
+
α
r(2,1)
2 . (6.42)
Given a fixed distance r(2,1)
and if α/r(2,1)
1, which holds, e.g., if the distances r(2,kB)
, kB =
1 . . .KB, of MT 2 to the APs of the SA are in the order of magnitude of tens of λ, the terms
α/r(2,1)
in (6.42) vanish and the variation of η
(nF)
RxZF of (6.42) is dominated by the variation of
the term cos
2π
λ
α . Hence, it follows from (6.42) that η
(nF)
RxZF of (6.42) has
• minima η
(nF)
RxZF = 0 at α = κλ, κ ∈ N, and](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-90-320.jpg)
![86 Chapter 7: Performance investigation of downlink transmission
The reference system is the system which optimally uses the transmit energy T (k,nF)
. With
the transfer matrix H(nF)T
valid for the DL in a SA-based system, in the reference system a
single data symbol d(k,nF)
is transmitted from the core network over the mobile radio channel
characterized by the row transfer vector H(nF)
k
T
. To this end the TxMF transmit vector
[JKG+
02]
s(nF)
= H(nF)
k
∗
d(k,nF)
(7.3)
is used, the choice of which is optimum in terms of use of the corresponding transmit energy
T
(k,nF)
ref =
1
2
E s(nF)∗T
s(nF)
=
1
2
E |d(k,nF)
|2
H(nF)
k
T
H(nF)
k
∗
= H(nF)T
H(nF)∗
k,k
. (7.4)
Given the transmit energy T
(k,nF)
ref of (7.4), using (7.1), and with the transmit vector s(nF)
of
(7.3), the received value
e(k,nF)
= H(nF)
k
T
s(nF)
+ n(k,nF)
(7.5)
with the maximum possible receive energy
R
(k,nF)
ref =
1
2
E e(k,nF) 2
=
1
2
E H(nF)
k
T
s(nF)
∗T
H(nF)
k
T
s(nF)
= H(nF)T
H(nF)∗
k,k
2
(7.6)
is produced. Due to the fact that, given the transmit energy T
(k,nF)
ref of (7.4), the received energy
R
(k,nF)
ref of (7.6) is maximum, the reference system achieves also the minimum possible bit error
probability P
(k,nF)
b,ref [Pro95].
The resulting bit error probability P
(k,nF)
b,ref of the reference system can be computed for the case
of QPSK using the received energy R
(k,nF)
ref of (7.6) and the variance σ2
or the real and imaginary
parts of each noise value n(k,nF)
, as
P
(k,nF)
b,ref =
1
2
erfc
1
2σ2
H(nF)T
H(nF)∗
k,k
. (7.7)
As only the transmission of d(k,nF)
is considered, the optimum performance of the reference
system in terms of the considered performance measures is also referred to as single user bound.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-96-320.jpg)
![7.2 Bit error probability 91
• extended MIMO parametric model,
• BPSK modulation,
• fixed transmit energy strategy,
• v = 1, with d
(nF)
v = [1 . . . 1]T
, and
• T/σ2
= 1.
In Fig. 7.3 the bit error probabilities P
(k,nF)
b,v , k = 1 . . .K, and the average bit error probability
P
(nF)
b,v for the case of
K = 2 (7.8)
as a function of ϕ
(1,nF)
v are depicted. As can be seen from Fig. 7.3, there are intervals in which
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
1
P
(1,nF)
b,v
P
(2,nF)
b,v
P
(nF)
b,v
ϕ
(1,nF)
v,TxZF
ϕ
(1,nF)
v,opt
ϕ
(1,nF)
v
Pb
Figure 7.3. Bit error probabilities P
(k,nF)
b,v , k = 1 . . . K, and average bit error probability P
(nF)
b,v ,
as a function of ϕ
(1,nF)
v ; Parameters: K = 2, KB = 2, T/σ2
= 1, v = 1, d
(nF)
v = [1 1]T
,
extended MIMO parametric channel model, ρ12 = 0.81, ρ21 = 0.01.
the bit error probabilities P
(k,nF)
b,v , k = 1 . . .K, are greater than 0.5. This happens due to the fact
that in the said intervals the corresponding transmit signals are not suited for the transmission
of the data vector d
(nF)
v = [1 1]T
. As an example, for the considered
d(nF)
v = [1 1]T
, (7.9)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-101-320.jpg)
![7.2 Bit error probability 93
−2
0
2
−3
−2
−1
0
1
2
3
0
0.2
0.4
0.6
0.8
1
ϕ
(1,nF)
v
ϕ
(2,nF)
v
P
(nF)
b,v
ϕ
(1,nF)
v,TxZF, ϕ
(2,nF)
v,TxZF
ϕ
(1,nF)
v,opt , ϕ
(2,nF)
v,opt
Figure 7.4. Average bit error probability P
(nF)
b,v , as a function of ϕ
(kB,nF)
v , kB = 1 . . .KB − 1;
Parameters: K = 3, KB = 3, v = 1, d
(nF)
v = [1 1 1]T
, T/σ2
= 1, extended MIMO parametric
channel model, ρ12 = 0.15, ρ13 = 0.70, ρ21 = 0.38, ρ23 = 0.86, ρ31 = 0.85, ρ32 = 0.59.
whereas the solution for optimum JT
ϕ
(1,nF)
v,opt , ϕ
(2,nF)
v,opt = (0.86, 0.57) (7.19)
yields the minimum possible bit error probability
P
(nF)
b,v,opt = 0.001. (7.20)
Comparing (7.17) and (7.19) to (7.12) and (7.14), it can be seen that the TxZF JT solution of
(7.17) and the optimum JT solution of (7.19) have a larger Euclidean distance than the TxZF
JT solution of (7.12) and the optimum JT solution of (7.15). Moreover, from the comparison of
(7.18) and (7.20) to (7.13) and (7.15) follows that larger gains in terms of P
(nF)
b,v are achievable
in the case of higher K in the considered channel snapshots. In particular, optimum JT achieves](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-103-320.jpg)
![98 Chapter 7: Performance investigation of downlink transmission
Taking advantage of the duality between iterative JT and iterative JD with transparent data
estimate refinement outlined in Section 5.4, the results concerning convergence of iterative JD
can be directly applied to iterative JT. In particular, it can be shown that the matrix product F R
of dimension KNF × KNF has the spectral radius
λmax (F R) = (K − 1)
2ρ + (K − 2)ρ2
1 + (K − 1)ρ2
, (7.23)
with which it can be shown that iterative JT in the case of the MIMO parametric channel model
converges if
ρ <
1
K − 3
2
K − 2
K − 1
− 1 (7.24)
holds. In the specific case of
K = 4 (7.25)
(7.24) yields
ρ < 0.155. (7.26)
7.3 Transmission efficiency
7.3.1 The transmission efficiency as performance measure
With the aid of the transmission efficiency, the efficiency by which JT in the DL of SA-based
systems converts the available transmit energy T (k,nF)
into receive energy R(k,nF)
is assessed.
The assessment of the said efficiency is based on a comparison of R(k,nF)
/T(k,nF)
JT
with the
maximum possible ratio R(k,nF)
/T(k,nF)
ref
corresponding to the reference system, i.e., the
transmission efficiency of JT is defined as [TWMB01]
t(k,nF)
=
R(k,nF)
T(k,nF)
JT
(R(k,nF) /T(k,nF) )ref
. (7.27)
Due to the suboptimum conversion of the transmit energy T (k,nF)
into receive energy R(k,nF)
,
the transmission efficiency t(k,nF)
of (7.27) takes the values t(k,nF)
∈ [0, 1].](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-108-320.jpg)
![106 Chapter 8: Performance assessment of service area based systems
8.2.2 Energy efficiency
As shown by the simulation results of Chapters 6 and 7, RxZF JD and TxZF JT are characterized
by the same energy loss with respect to the corresponding reference system. In this Section, a
performance measure is derived, quantifying the common energy loss in UL and DL by RxZF
JD and TxZF JT, respectively.
In a first step, the reference system is defined, in which only a single data symbol d(k,nF)
is
transmitted. However, unlike the reference systems used for the investigations in Chapters 6 and
7, the chosen reference system for the generalized unbiased linear data transmission utilizes all
KI inputs and all KO outputs due to the need for application on both UL and DL. The reference
system is optimum with respect to the use of the transmit energy
T(k,nF)
=
1
2
s(nF)∗T
s(nF)
(8.5)
per data symbol. In order to achieve the said optimum use, the transmit vector s(nF)
in the
reference system is the eigenvector corresponding to the eigenvalue of H(nF)∗T
H(nF)
with the
largest magnitude. With the spectral radius λmax H(nF)∗T
H(nF)
of H(nF)∗T
H(nF)
[Sch88b],
the maximum possible receive energy
E
(k,nF)
b,opt =
1
2
T(k,nF)
λmax H(nF)∗T
H(nF)
(8.6)
and the minimum possible bit error probability
P
(k,nF)
b,opt =
1
2
erfc
1
2σ2
T(k,nF)λmax H(nF)∗T
H(nF)
(8.7)
for each bit in the QPSK data symbol d(k,nF)
are obtained [Pro95] given the transmit energy
T(k,nF)
of (8.5).
SA-based systems with linear pre- and post-processing are suboptimum with respect to the use
of the transmit energy T (k,nF)
, due to the following two reasons:
• Due to the spatial separation of the MTs, the eigenvector corresponding to the eigenvalue
of H(nF)∗T
H(nF)
with the largest magnitude cannot be used as the transmit vector, which
means that the transmit energy T (k,nF)
cannot be converted in receive energy R(k,nF)
as
efficiently as in the reference system and
• only a part of the receive energy R(k,nF)
is used, in contrast to the reference system.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-116-320.jpg)
![8.2 Dualities between uplink and downlink 107
The above mentioned reasons hold due to the multiuser nature of the SA-based system. In
contrast to the reference system, more than one data symbols have to be transmitted and the
eigenvector corresponding to the maximum eigenvalue of H(nF)∗T
H(nF)
cannot be used for all
the data symbols d(k,nF)
, k = 1 . . . K. The corresponding suboptimum conversion of T (k,nF)
into R(k,nF)
is quantified by the transmission efficiency [WSLW03, TWMB01]
t(k,nF)
=
M(nF)∗T
H(nF)∗T
H(nF)
M(nF)
k,k
λmax H(nF)∗T
H(nF)
M(nF)∗T
M(nF)
k,k
(8.8)
of generalized unbiased linear data transmission.
At the receiver side, in contrast to the reference system, in which the whole E
(k,nF)
b is used, only
a part of the receive energy R(k,nF)
and thus of the receive energy E
(k,nF)
b per bit in the QPSK
data symbol d(k,nF)
is used, due to the need for the elimination of intra-SA interference. The
said suboptimum use of E
(k,nF)
b is measured by the asymptotic multiuser efficiency [WSLW03,
Ver98]
η(k,nF)
=
1
M(nF)∗T
H(nF)∗T
H(nF)
M(nF)
k,k
D(nF)
D(nF)∗T
k,k
(8.9)
of generalized unbiased linear data transmission.
Both the transmission efficiency t(k,nF)
of (8.8) and the asymptotic multiuser efficiency η(k,nF)
of (8.9) are heavily influenced by the spatial separation of the MTs in the SA which is expressed
in a diagonal form of the modulator matrix M(nF)
or the demodulator matrix D(nF)
in the UL
or the DL transmission, respectively. Moreover, as t(k,nF)
of (8.8) measures the suboptimum
conversion of the transmit energy T (k,nF)
to receive energy R(k,nF)
and η(k,nF)
of (8.9) the sub-
optimum use of the available receive energy R(k,nF)
, the energy efficiency
ε(k,nF)
= t(k,nF)
η(k,nF)
=
1
λmax H(nF)∗T
H(nF)
M(nF)∗T
M(nF)
k,k
D(nF)
D(nF)∗T
k,k
(8.10)
collectively expresses the suboptimum use of the transmit energy T (k,nF)
by both transmitter
and receiver sides together. With ε(k,nF)
of (8.10), and using (8.8) and (8.9), and with E
(k,nF)
b,opt of
(8.6), the bit error probability
P
(k,nF)
b =
1
2
erfc
⎛
⎝
E
(k,nF)
b,opt ε(k,nF)
σ2
⎞
⎠
=
1
2
erfc
⎛
⎜
⎝
T(k,nF)
2σ2 M(nF)∗T
M(nF)
k,k
D(nF)
D(nF)∗T
k,k
⎞
⎟
⎠ (8.11)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-117-320.jpg)
![108 Chapter 8: Performance assessment of service area based systems
of each bit in the QPSK data symbol d(k,nF)
is calculated [Pro95]. As (8.11) shows, P
(k,nF)
b
depends on the matrices M(nF)
and D(nF)
, i.e., on the linear processing in the transmitter and
receiver side, and implicitly also on the transfer matrix H(nF)
due to the requirement for unbi-
ased linear data transmission of (8.4).
Hence, in the case of unbiased linear data transmission in SA-based systems, independently of
whether UL or DL is considered, the energy efficiency ε(k,nF)
of (8.10) expresses the subopti-
mum use of the transmit energy T (k,nF)
by the transmitter and receiver sides in the generalized
unbiased linear data transmission, as compared to the reference system. In particular, if a certain
transmit energy is required by the reference system in order to achieve a given a target bit error
probability P
(k,nF)
b , a SA-based system employing unbiased linear data transmission requires an
transmit energy T (k,nF)
increased by the factor 1 ε(k,nF)
to obtain the same bit error probability
P
(k,nF)
b as compared to the reference system, and this increase of the required transmit energy
T(k,nF)
is the price to be paid for the elimination of the intra-SA interference in the generalized
unbiased linear transmission. In what follows, ε(k,nF)
of (8.10) is determined for UL and DL of
SA-based systems.
In the UL transmission of SA-based systems, the spatial separation of the MTs results in the
modulator matrix
M
(nF)
UL = IK. (8.12)
Due to the said spatial separation of the MTs, the K inputs to the KB ×K MIMO channel of the
SA are not jointly available as it is the case in the reference system. With the modulator matrix
M
(nF)
UL according to (8.12) and the transfer matrix H
(nF)
UL valid for the UL, the aforementioned
fact results in a decreased transmission efficiency
t
(k,nF)
UL =
H
(nF)
UL H
(nF)
UL
∗T
k,k
λmax H
(nF)
UL
∗T
H
(nF)
UL
. (8.13)
Linear post-processing is performed by the CU at the receiver side. With the use of the demod-
ulator matrix
D
(nF)
UL = H
(nF)
UL
∗T
H
(nF)
UL
−1
H
(nF)
UL
∗T
(8.14)
according to the RxZF principle [Kle96, SWC+
02, WMS+
02], all intra-SA interference is can-
celled. Due to the need for intra-SA interference elimination, only the orthogonal parts of the
partial received signals are used. With (8.9) and using the demodulator matrix D
(nF)
UL of (8.14)
and the transfer matrix H
(nF)
UL , the said suboptimum use of the available receive energy R(k,nF)
in the UL is quantified by the asymptotic multiuser efficiency
η
(k,nF)
UL =
1
H
(nF)
UL
∗T
H
(nF)
UL
−1
k,k
H
(nF)
UL
∗T
H
(nF)
UL
k,k
. (8.15)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-118-320.jpg)
![8.2 Dualities between uplink and downlink 109
With t
(k,nF)
UL of (8.13) and η
(k,nF)
UL of (8.15) follows from (8.10) the energy efficiency
ε
(k,nF)
UL =
1
λmax H
(nF)
UL
∗T
H
(nF)
UL H
(nF)
UL
∗T
H
(nF)
UL
−1
k,k
(8.16)
of the UL transmission.
In the DL transmission of SA-based systems, he spatial separation of the MTs in the DL is
expressed by the diagonal demodulator matrix
D
(nF)
DL = IK. (8.17)
Because each MT uses the whole available received energy R(k,nF)
, an asymptotic multiuser
efficiency
η
(k,nF)
DL = 1 (8.18)
follows from (8.9) for the DL transmission.
At the transmitter side, the modulator matrix
M
(nF)
DL = H
(nF)
DL
∗T
H
(nF)
DL H
(nF)
DL
∗T −1
(8.19)
is used according to the TxZF principle [MBW+
00, WMS+
02]. Because a part of the avail-
able transmit energy T (k,nF)
is devoted to eliminate intra-SA interference, from (8.8) and using
M
(nF)
DL of (8.19) and the transfer matrix H
(nF)
UL , the suboptimum use of T (k,nF)
in the DL trans-
mission is is quantified by the transmission efficiency
t
(k,nF)
DL =
1
λmax H
(nF)
DL H
(nF)
DL
∗T
H
(nF)
DL H
(nF)
DL
∗T −1
k,k
. (8.20)
With t
(k,nF)
DL of (8.20) and η
(k,nF)
DL of (8.18), follows from (8.10) for the DL transmission the
energy efficiency
ε
(k,nF)
DL =
1
λmax H
(nF)
DL H
(nF)
DL
∗T
H
(nF)
DL H
(nF)
DL
∗T −1
k,k
. (8.21)
Given that TDD is employed and that the channels of UL and DL are reciprocal,
H
(nF)
DL = H
(nF)
UL
T
(8.22)](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-119-320.jpg)
![110 Chapter 8: Performance assessment of service area based systems
holds for the transfer matrices of UL and DL. Moreover, for a square matrix X
λmax XT
= λmax (X) (8.23)
holds [ZF86].
Using (8.22) and (8.23), the comparison of ε
(k,nF)
UL of (8.16) and ε
(k,nF)
DL of (8.21) yields
ε
(k,nF)
UL = ε
(k,nF)
DL (8.24)
and for the corresponding bit error probabilities
P
(k,nF)
b,UL = P
(k,nF)
b,DL (8.25)
holds.
(8.24) expresses an important characteristic of SA-based systems. According to (8.24), with the
transfer matrix H(nF)
valid for the UL transmission, UL and DL are characterized by the same
energy efficiency
ε(k,nF)
=
1
λmax H(nF)∗T
H(nF)
H(nF)∗T
H(nF)
−1
k,k
. (8.26)
In other words, the price to be paid for intra-SA interference elimination is the same for RxZF
JD and TxZF JT. Consequently, investigations regarding the energy efficiency ε(k,nF)
in the case
of unbiased linear data transmission in SA-based systems can be carried out jointly for UL and
DL.
8.3 System layer aspects
The energy efficiency ε(k,nF)
as defined in (8.24) is an energy related measure. As such, it is
useful also in investigations concerning the system layer of SA-based systems with unbiased
linear data transmission, in which not the structure of the signals, but the transmit and receive
energies play a role. For this reason, the energy efficiency ε(k,nF)
as defined in (8.24) is used in
this Section to provide an insight in issues regarding the system layer of SA-based systems, i.e.,
in issues related to inter-SA interference.
The energy efficiency ε(k,nF)
as defined in (8.24) quantifies the efficiency of the use of the
transmit energy T (k,nF)
. An energy efficiency ε(k,nF)
smaller than unity means that a higher
transmit energy T (k,nF)
is required by the SA-based system than by the reference system in](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-120-320.jpg)
![8.3 System layer aspects 111
order to achieve a given bit error probability P
(k,nF)
b , and that higher energy is radiated towards
the neighboring SAs causing inter-SA interference. Equivalently, for given transmit energy
T(k,nF)
lower receive energy R(k,nF)
is achieved relative to the reference system, which means
that the sensitivity of the receivers in a SA to noise, i.e., to inter-SA interference is increased.
Hence, the energy efficiency ε(k,nF)
of (8.24) is a measure for the inter-SA interference caused
from the transmitters of a SA to neighboring SAs or equivalently, for the sensitivity of the
receivers in a SA to inter-SA interference stemming from neighboring SAs.
An important aspect of interest to system level considerations is the dependence of the energy
efficiency ε(k,nF)
of (8.24) on the number K of MTs and the number KB of APs. Fig. 8.2 depicts
the average energy efficiency ε(nF)
of unbiased linear data transmission in a SA for fixed system
load K/KB. The transfer matrix H(nF)
used consists of independent and identically distributed
complex random variables, each having a magnitude following the Rayleigh distribution. As
1 3 5 7 9 11 13 15
0
0.2
0.4
0.6
0.8
1
K
ε(nF)
K/KB = 1
K/KB = 0.5
K/KB = 0.33
K/KB = 0.25
Figure 8.2. Average energy efficiency ε(nF)
of a SA employing unbiased linear data transmission
for Rayleigh fading
can be seen from Fig. 8.2, the energy efficiencies ε(nF)
are unity for K = 1 MT, for all sys-
tem loads K/KB, as expected from theory. The energy efficiency ε(nF)
initially decreases for
increasing number of MTs K, and for large K converges to a constant value. The said limiting
value of ε(nF)
could be computed analytically with the aid of random matrix theory [Meh91].
Ultimately, Fig. 8.2 shows that for a large number K of MTs, the energy efficiency ε(nF)
is a
function only of the system load K/KB and is independent of the number K of MTs.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-121-320.jpg)
![112 Chapter 8: Performance assessment of service area based systems
The transmit energy used by the reference system in which a single data symbol is transmitted
is antiproportional to the number KB of employed APs, i.e., of the number of antennas jointly
available in the SA [God97a, God97b]. Therefore, due to the fact that the average energy
efficiency ε(nF)
is a function of the system load K/KB only, the transmit energy used in a SA
for a single data symbol d(k,nF)
is also antiproportional to the number KB of APs for given
system load K/KB. From the latter observation follows directly that the total transmit power
in a SA is a function of the system load K/KB only and independent of the number K of
MTs. Hence, the inter-SA interference induced from a SA to its neighboring SAs in a SA-based
system for a given system load K/KB does not depend on the number K of MTs. Equivalently,
if the system load K/KB is kept constant, the number K of MTs in a SA of a SA-based system
employing unbiased linear data transmission can be increased without any increase in the inter-
SA interference.
With respect to the spectrum capacity ηc of (1.1), it follows that a decisive increase in the
spectrum capacity ηc is achievable in SA-based systems as compared to state-of-the-art mobile
radio systems based on the cellular air interface architecture. For this reason, the choice of the
SA air interface architecture is especially attractive for application on beyond 3G mobile radio
systems, on which the demand for high spectrum capacity ηc is posed.](https://image.slidesharecdn.com/3e860f0e-ec79-479c-a3b3-cd101420d1a1-160210224238/85/Dissertation-A-Sklavos-122-320.jpg)
![122 References
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Dissertation A. Sklavos
- 1. Alexandros Sklavos Service Area Based OFDM Air Interface for Beyond 3G Mobile Radio Systems Forschungsberichte Mobilkommunikation Band 15 Herausgegeben von Prof. Dr.-Ing. habil. Dr.-Ing. E.h. P.W. Baier
- 2. Bibliografische Information der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbiographie; detaillierte bibliografische Daten sind im Internet ¨uber http://dnb.ddb.de abrufbar. Herausgeber: Prof. Dr.–Ing. habil. Dr.–Ing. E. h. P. W. Baier Lehrstuhl f¨ur hochfrequente Signal¨ubertragung und –verarbeitung Technische Universit¨at Kaiserslautern Postfach 3049 67653 Kaiserslautern Verfasser: Alexandros Sklavos Verlag: Technische Universit¨at Kaiserslautern Druck: ZBT - Abteilung Foto-Repro-Druck der Technischen Universit¨at Kaiserslautern D 386 c Alexandros Sklavos · Kaiserslautern 2004 Alle Rechte vorbehalten, auch das des auszugsweisen Nachdrucks, der auszugsweisen oder vollst¨andi- gen Wiedergabe (Photographie, Mikrokopie), der Speicherung in Datenverarbeitungsanlagen und das der ¨Ubersetzung. Als Manuskript gedruckt. Printed in Germany. ISSN 1438–6720 ISBN 3–936890–47–1
- 3. Alexandros Sklavos Ifigeneias Str. 48 17672 Kallithea Griechenland Geburtsort: Griechenland Service Area Based OFDM Air Interface for Beyond 3G Mobile Radio Systems deutscher Titel: OFDM-Luftschnittstelle f¨ur Mobilfunksysteme jenseits der dritten Generation auf der Basis von Service Gebieten Vom Fachbereich Elektrotechnik und Informationstechnik der Technischen Universit¨at Kaiserslautern zur Verleihung des akademischen Grades Doktor der Ingenieurwissenschaften (Dr.–Ing.) genehmigte Dissertation von Dipl.–Ing. Alexandros Sklavos, D 386 Tag der Einreichung: 28. April 2004 Tag der m¨undlichen Pr¨ufung: 19. Juli 2004 Dekan des Fachbereichs Elektrotechnik: Prof. Dr.–Ing. G. Huth Vorsitzender der Pr¨ufungskommission: Prof. Dr.–Ing. habil. L. Litz 1. Berichterstatter: Dr.–Ing. habil. T. Weber 2. Berichterstatter: Prof. Dr. H. Rohling
- 5. V Vorwort Die vorliegende Arbeit entstand in der Zeit von Januar 2001 bis April 2004 im Rahmen meiner T¨atigkeit als wissenschaftlicher Mitarbeiter Prof. Dr.–Ing. habil. Dr.–Ing. E. h. P. W. Baiers am Lehrstuhl f¨ur hochfrequente Signal¨ubertragung und –verarbeitung der Technischen Univer- sit¨at Kaiserslautern. Ich m¨ochte all jenen danken, die mich bei der Entstehung dieser Arbeit unterst¨utzt haben. Mein besonderer Dank geht an Herrn Prof. Dr.–Ing. habil. Dr.–Ing. E.h. P. W. Baier f¨ur die Anregung und F¨orderung dieser Arbeit. Mit seiner steten Diskussions– und Hilfsbereitschaft hat er einen entscheidenden Beitrag zum Gelingen der Arbeit geleistet. Ein weiterer besonderer Dank ergeht an Herrn Dr.–Ing. habil. T. Weber f¨ur die Betreuung meiner Arbeit und f¨ur die enge und fruchtbare Zusammenarbeit w¨ahrend der gesamten Zeit meiner wissenschaftlichen T¨atigkeit. Durch seine Ratschl¨age und Hinweise trug er erheblich zur Steigerung der Qualit¨at der vorliegenden Dissertation bei. Herrn Prof. Dr. H. Rohling von der Technischen Universit¨at Hamburg-Harburg, danke ich f¨ur die freundliche ¨Ubernahme des Korreferats und f¨ur die im Rahmen unserer Kooperation in Verbundprojekten enstandenen Ideen und Anregungen. Weiterhin bedanke ich mich bei dem Vorsitzenden der Promotionskommis- sion, Herrn Prof. Dr.–Ing. habil. L. Litz. Bei der Technischen Universit¨at Kaiserslautern m¨ochte ich mich f¨ur die M¨oglichkeit der Be- nutzung der leistungsf¨ahigen Rechnersysteme des Regionalen Hochschulrechenzentrums Kai- serslautern (RHRK) bedanken. Den Mitarbeitern des RHRK danke ich auch f¨ur die Beratung und die Hilfestellung in Rechnerfragen. Die in der vorliegenden Arbeit enthaltenen Ergebnisse entstanden gr¨oßtenteils im Rahmen von Projekten, die durch die Fa. Siemens gef¨ordert wurden. F¨ur die finanzielle F¨orderung sowie f¨ur zahlreiche Anregungen aus der industriellen Praxis danke ich Herrn Dr.–Ing. E. Schulz, Frau Dr.–Ing. E. Costa, Herrn Dr.–Ing. M. Weckerle und Herrn Prof. Dr. H. Haas. Im Rahmen dieser Projekte ergab sich auch eine enge Zusammenarbeit mit den Lehrst¨uhlen Prof. Dr. H. Rohlings, Technische Universit¨at Hamburg-Harburg, und Prof. Dr.–Ing. M. Bosserts, Universit¨at Ulm, woraus wichtige Anregungen und Hinweise f¨ur meine Arbeit resultierten. Den jetzigen und den ehemaligen Kollegen am Lehrstuhl f¨ur hochfrequente Signal¨ubertragung und –verarbeitung danke ich f¨ur die stets angenehme Arbeitsatmosph¨are. Insbesondere danke ich den Herren Dr.–Ing. C. A. J¨otten, Dr.–Ing H. Tr¨oger und Dr.–Ing. M. Meurer f¨ur ihre Hilfe und f¨ur unsere viele fruchtbare Diskussionen. Ein weiterer Dank ergeht an alle Studenten, die im Rahmen von Studien–, Diplom– und Mas- terarbeiten unter meiner Anleitung Beitr¨age zu meiner Dissertation geleistet haben. Nicht zuletzt m¨ochte ich mich bei meiner Schwester und bei meinen Freunden bedanken, die mir immer ein großer R¨uckhalt waren. Ein ganz besonderer Dank gilt meinen Eltern. Sie haben mir das Studium der Elektrotechnik erm¨oglicht und mich immer nach besten Kr¨aften ununter- brochen und entscheidend unterst¨utzt. Ihnen ist diese Arbeit gewidmet. Kaiserslautern, im Juli 2004 Alexandros Sklavos
- 7. CONTENTS VII Contents 1 Introduction 1 1.1 Demands on future mobile radio systems . . . . . . . . . . . . . . . . . . . . . 1 1.2 Service area based architectures versus cellular architectures . . . . . . . . . . 5 1.3 OFDM transmission technique . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 State of the art and open questions . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 Channel modelling 20 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Theory of mobile radio propagation . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Channel models used in the thesis . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 COST 207 channel models . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Indoor geometric channel model . . . . . . . . . . . . . . . . . . . . . 22 2.3.3 Multiple-input-multiple-output parametric channel model . . . . . . . 24 3 Modelling of OFDM-based MIMO systems 25 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Physical transmission model . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 General description of the physical transmission . . . . . . . . . . . . 27 3.2.2 Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.3 MIMO channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.4 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.5 Matrix-vector transmission model . . . . . . . . . . . . . . . . . . . . 33 3.3 Pre- and post-processing stages . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.1 Optimum and suboptimum approaches . . . . . . . . . . . . . . . . . 34 3.3.2 Subcarrierwise pre- and post-processing . . . . . . . . . . . . . . . . . 35 4 Uplink transmission in the service area concept 36 4.1 Transmission model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Optimum joint detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2.1 Approaches to optimum post-processing . . . . . . . . . . . . . . . . . 38 4.2.2 Maximum a posteriori joint detection . . . . . . . . . . . . . . . . . . 39 4.2.3 Maximum likelihood joint detection . . . . . . . . . . . . . . . . . . . 39 4.2.4 Complexity of optimum joint detection . . . . . . . . . . . . . . . . . 40 4.3 Linear joint detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3.1 General model of linear joint detection . . . . . . . . . . . . . . . . . 40 4.3.2 Receive zero-forcing joint detection . . . . . . . . . . . . . . . . . . . 41 4.3.3 Minimum mean square error joint detection . . . . . . . . . . . . . . . 42
- 8. VIII CONTENTS 4.4 Iterative joint detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.4.1 General model of iterative joint detection . . . . . . . . . . . . . . . . 43 4.4.2 Transparent data estimate refinement . . . . . . . . . . . . . . . . . . 44 4.4.3 Data estimate refinement by hard quantization . . . . . . . . . . . . . . 45 4.4.4 Data estimate refinement by soft quantization . . . . . . . . . . . . . . 46 4.4.5 Optimum data estimate refinement — turbo multiuser data detection . . 48 5 Downlink transmission in the service area concept 51 5.1 Transmission model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Optimum joint transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2.2 Transmit energy strategies . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2.3 Parameterized representation of JT transmit signals . . . . . . . . . . . 56 5.2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.3 Transmit zero-forcing joint transmission . . . . . . . . . . . . . . . . . . . . . 60 5.4 Iterative joint transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6 Performance investigation of uplink transmission 64 6.1 Preliminary remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.2 Bit error probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.2.1 The bit error probability as performance measure . . . . . . . . . . . . 66 6.2.2 Bit error probability of optimum versus linear joint detection . . . . . . 66 6.2.3 Bit error probability of iterative joint detection . . . . . . . . . . . . . 69 6.3 Asymptotic multiuser efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.3.1 The asymptotic multiuser efficiency as performance measure . . . . . . 77 6.3.2 Statistics of the asymptotic multiuser efficiency of receive zero-forcing joint detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 7 Performance investigation of downlink transmission 85 7.1 Preliminary remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2 Bit error probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.2.1 The bit error probability as performance measure . . . . . . . . . . . . 87 7.2.2 Bit error probability of transmit zero-forcing joint transmission . . . . . 87 7.2.3 Bit error probability of optimum versus transmit zero-forcing joint trans- mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.2.4 Bit error probability of iterative joint transmission . . . . . . . . . . . 97 7.3 Transmission efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.3.1 The transmission efficiency as performance measure . . . . . . . . . . 98 7.3.2 Statistics of the transmission efficiency of transmit zero-forcing joint transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
- 9. CONTENTS IX 8 Performance assessment of service area based systems 103 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 8.2 Dualities between uplink and downlink . . . . . . . . . . . . . . . . . . . . . . 104 8.2.1 Model of general unbiased linear data transmission . . . . . . . . . . . 104 8.2.2 Energy efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 8.3 System layer aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 9 Summary 113 9.1 Summary in English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 9.2 Summary in German . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Appendix A Frequently used abbreviations and symbols 115 A.1 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 A.2 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 References 122
- 11. 1 1 Introduction 1.1 Demands on future mobile radio systems The target of a mobile radio system is the provision of communication services to multiple mobile terminals (MTs). Due to the demand for mobility of the MTs, each MT in a mobile radio system communicates with at least one fixed access point (AP) by means of transmission of electromagnetic waves with frequencies in the radio frequency band [Gib99, Ste92, DB96, Wes02]. Each AP communicates either directly or indirectly with other fixed entities of the mobile radio system such as mobile switching centers [GSM98], which perform tasks related to the proper forwarding of information to and from the APs. Such fixed entities are collectively described by the term core network of the mobile radio system. The wireless interface between the MTs and the fixed APs is called the air interface of the mobile radio system. Concerning the air interface one can discern between uplink (UL) and downlink (DL) transmission [Gib99, Ste92, DB96], depending on whether information is sent from the MTs to the APs or vice versa. Performance measures of high importance to mobile radio system operators such as the quality of service [Ste92, HT02] or the number of MTs which can be simultaneously supported in a given bandwidth B and area A [Lee89, Vit91, Ste92] are essentially determined by the air interface. Hence, the design of the air interface of future mobile radio systems is of paramount importance and forms the main focus of the present thesis. As the following considerations of this Section are valid for the UL as well as for the DL, the more general terms transmitters and receivers will be used in this Section instead of the terms MTs and APs in order to describe the air interface independently of the direction of information flow in the air interface, i.e., independently of whether the UL or the DL is considered. Setting out from a group of antennas which are jointly available, a transmitter in a mobile radio system is an entity generating transmit signals for a group of antennas and a receiver corresponds to an entity obtaining the signals received by a group of antennas. Hence, the MTs are the transmitters in the UL and the receivers in the DL. On the other hand, in the general case no direct relation between APs and receivers in the UL and between APs and transmitters in the DL can be postulated. However, in the special case that only the antennas of each AP are jointly available the APs correspond to the receivers in the UL and to the transmitters in the DL. If a linear transmission scheme is employed at each transmitter in the mobile radio system, then the signal at the location of each receiver consists of a superposition of a number of information bearing partial signals, each corresponding to a different MT, along with signals stemming from sources other than the transmitters of the considered mobile radio system, such as other mobile radio systems, or thermal and cosmic noise sources. Considering the detection of the infor- mation of a particular MT, the corresponding partial received signal is termed useful received
- 12. 2 Chapter 1: Introduction signal. The remaining partial received signals corresponding to other MTs disturb the useful received signal, and therefore act as multiple access interference [Gib99, Ste92, DB96, Wes02]. However, if nonlinear transmission schemes are employed, the signal at a specific receiver in general cannot be viewed as a superposition of partial received signals, each corresponding to an MT. For this reason, the definition of multiple access interference in the case of nonlinear transmission schemes is an open problem. Moreover, although the term interference is often used in a more general context to collectively describe all received signals not related to the detection of a particular data symbol, it is used in the following to denote only multiple access interference, which forms the main focus of the present thesis. In state-of-the-art mobile radio systems, which are characterized by a high density of transmit- ters and receivers and high transmit powers, interference dominates the nonuseful part of the received signal in such a way that the effect of other noise signal sources, such as thermal or cosmic noise, can be safely neglected in the design of a mobile radio system. Therefore, mobile radio systems are interference limited [Cal88, Lee82]. The number K of MTs which can be supported with a given quality of service [Ste92, HT02], normalized to the system bandwidth B and the area A which is covered by the mobile radio system, is the spectrum capacity ηc = K B A (1.1) of the mobile radio system [Lee89, Vit91, Ste92]. The spectrum capacity ηc of (1.1) is a measure for the efficiency of the use of the available frequency bandwidth B of a mobile radio system. An efficient use of the available frequency bandwidth B is of great importance to mobile radio system operators as it has been demonstrated above all by the outcome of auctions for the 3G mobile radio system spectrum, e.g., in Germany, where nearly 50 billion Euros were spent for the corresponding licenses by the mobile radio system operators [ntz00a, ntz00b]. In an interference limited system, the interference present at the antennas of the receivers limits the achievable spectrum capacity ηc of (1.1) [Sha48, CT91, Roh95]. Therefore, considering future mobile radio systems, an air interface should be developed, in which the adverse effects of the interfering signals are kept at a low level. In what follows the radio channel of the air interface of mobile radio systems is dealt with. Mobile radio system operators use multiple APs to support a large number of MTs. However, for the purpose of modelling the air interface of a mobile radio system, instead of the total air interface with the usually very large number of transmitters and receivers, an excerpt of the mo- bile radio system is considered containing transmitters and receivers of a cohesive geographical area. Moreover, the said excerpt is chosen to be self-contained, i.e., no wireless communication takes place across its borders. Therefore, all signals stemming from transmitters outside the considered excerpt act as interference and are modelled as additive noise to the received signals in the considered excerpt. Hence, due to the fact that the modelling of the interference, e.g., as
- 13. 1.1 Demands on future mobile radio systems 3 Gaussian noise, is merely an approximation, the larger the excerpt of the mobile radio system is chosen, the more precise the resulting air interface model is. In the considered excerpt of the mobile radio system, if special cases of obstructed radio chan- nels, e.g., due to physical obstacles are not considered, signals radiated from each of the transmit antennas impinge at all the receive antennas. Hence, the radio channel of the considered excerpt of a mobile radio system in the UL as well in the DL is modelled as a multiple-input-multiple- output (MIMO) channel [Fos96, FG98, Tel99], in which the inputs are the multiple transmit antennas in which the transmit signals are fed and the outputs are the multiple receive antennas from which the received signals are obtained. Moreover, systems in which the channel is mod- elled as a MIMO channel, such as the chosen excerpt of a mobile radio system, are known as MIMO systems [Ala98, DCGV02, CS00, Ahl73, CT91, FCG+ 03, GFVW98, GFVW99, Hug00, JVG01, JVG02, TSC98, VJG02, YC01, YRBC01]. If neighboring MIMO systems use the same frequency bands, then signals corresponding to MTs of neighboring MIMO systems are received by the receivers of a certain MIMO system and such signals act as interference to the useful received signals of the considered MIMO system. To mitigate the aforementioned performance degrading interference, the bandwidth B available to the mobile radio system op- erator is partitioned into disjoint frequency subbands and different subbands are allocated to neighboring MIMO systems. This way, transmissions in a MIMO system do not interfere with transmissions in directly neighboring MIMO systems. However, if the concept of bandwidth partitioning would be strictly applied as described, given the large number of MIMO systems in a mobile radio system, a very large system bandwidth B would be required to totally avoid interferences in a mobile radio system. Therefore, the subband allocated to a reference MIMO system is reused after a certain distance large enough so that the attenuation of the electromag- netic waves received in the reference MIMO system stemming from MIMO systems using the same frequency subband is sufficiently large and the induced interference by the reuse of the same frequency subband is acceptable [McD79]. The number of disjoint subbands in which the system bandwidth B is partitioned is called reuse factor of the mobile radio system [McD79]. In terms of achievable channel capacity [Sha48], the best case for a MIMO system is that all inputs and outputs of the MIMO channel are jointly available for joint processing and that perfect knowledge of the MIMO channel is present at both transmit and receive side [Tel99]. But in the case of the MIMO channel of the considered excerpt of a mobile radio system in general not all the inputs and outputs of the MIMO channel are jointly available, due to the spatial separation of the transmitters and receivers. For example, it is not possible to perform signal processing tasks jointly for different MTs, at least with a reasonable overhead, due to the fact that different MTs are spatially separated. Fig. 1.1 depicts the MIMO channel of a mobile radio system with N transmit and M receive antennas in total. Transmit and receive antennas of the MIMO channel in Fig. 1.1 form NB and MB groups corresponding to the NB and MB
- 14. 4 Chapter 1: Introduction transmitters and receivers, respectively, to indicate that only the antennas of each of the groups, i.e., of each of the transmitters or receivers, are jointly available. Transmitter 1 channel MIMO 1 Receiver 1 MN 1 Receiver MBTransmitter NB Figure 1.1. MIMO channel of an excerpt of a mobile radio system with NB transmitters and MB receivers Depending on the value of NB and MB, different special cases of MIMO channel structures can be distinguished, as Table 1.1 shows. Table 1.1. Classification of MIMO channel structures depending on the number NB of transmit antennas and the number MB of receive antennas case number NB MB MIMO structure 1 1 1 point-to-point channel 2 1 > 1 broadcast channel 3 > 1 1 multiple access channel 4 > 1 > 1 multipoint-to-multipoint channel The first case corresponds to a point-to-point MIMO channel which means that all N inputs and M outputs of the MIMO channel are jointly available. Pioneering work on the point-to- point MIMO channel in [Tel99, Fos96, FG98] shows that in the presence of rich scattering and if perfect channel knowledge is available at least at the receiver, impressive gains in terms of channel capacity [Sha48] and spectrum efficiency [BBS97, Bla98] are achievable as compared to single antenna systems using signals of the same transmit energy. These high gains, almost for free, only at the cost of some increased hardware complexity, initiated a worldwide research on MIMO systems [Ala98, DCGV02, CS00, Ahl73, CT91, FCG+ 03, GFVW98, GFVW99, Hug00, JVG01, JVG02, TSC98, VJG02, YC01, YRBC01]. The point-to-point MIMO channel corresponds to the case where the considered excerpt of the mobile radio system consists of a single transmitter communicating with a single receiver. In the MIMO channel structure of the second case of Table 1.1 all inputs of the MIMO chan-
- 15. 1.2 Service area based architectures versus cellular architectures 5 nel are jointly available whereas not all outputs are jointly available. This second case corre- sponds to the case where in the considered excerpt of the mobile radio system a single trans- mitter communicates with multiple receivers. In literature, such MIMO channels are known as broadcast channels [CS00, CT91]. Assuming that the transmitter disposes of channel knowl- edge a joint transmit signal processing could aim at reducing interference at the receivers [MBW+ 00, WMS+ 02]. The third case of Table 1.1 represents a MIMO channel structure, dual to the second case, where all outputs are jointly available whereas not all inputs of the MIMO channel are jointly avail- able. Such MIMO channels are known as multiple access channels. Multiple access channels correspond to the case where multiple transmitters communicate with a single receiver in the considered excerpt of the mobile radio system. A joint signal processing at the receiver could aim at reducing interferences among the multiple transmitters [Kle96, WMS+ 02]. In the most general last case of Table 1.1 of multipoint-to-multipoint MIMO channels, neither all the inputs nor all the outputs of the MIMO channel are jointly available. This corresponds to the case where multiple transmitters and multiple receivers exist in the considered excerpt of the mobile radio system. Due to the said dislocation between the transmitters and between the receivers interference suppression in multipoint-to-multipoint MIMO channels is a difficult task. According to the author, the research towards future mobile radio systems should aim at an efficient utilization of the available frequency bandwidth B, i.e., high spectrum capacities ηc should be strived for. As high system capacities can be achieved by mitigating the adverse effects of interference, the demand for the development of air interface architectures targeted at the suppression of the interference between the useful signals of the active MTs follows. Given the MIMO nature of the radio channel of an excerpt of a mobile radio system, shown in Fig. 1.1, it is shown that such a goal can be approached by employing an air interface in which all inputs to the MIMO channel in the DL and all outputs of the MIMO channel in the UL are jointly available. Hence, the cases of multiple access channels and broadcast channels shown in Table 1.1 are of special interest as far as the design of the air interface of future mobile radio systems is concerned. The present thesis deals with such an air interface proposal for future mobile radio systems. 1.2 Service area based architectures versus cellular architec- tures As demonstrated in the previous Section, there exists the demand for future mobile radio system air interfaces to yield high spectrum capacities ηc. The objective of this Section is to introduce a
- 16. 6 Chapter 1: Introduction novel air interface architecture by the employment of which the adverse effects of interference between the useful signals of the simultaneously active MTs in a MIMO system can be mitigated and therefore high spectral capacities ηc can be achieved. In order to better illuminate the basic characteristics of the novel air interface architecture, a brief overview of the characteristics of the cellular architecture, employed in state-of-the-art mobile radio systems, is performed. The cellular architecture [McD79] is employed in mobile radio systems of the first-, second- and third generation. The fundamental concept of cellular systems is the cell, which is the geographical area of responsibility of an AP, i.e., the area in which the MTs associated with the particular AP reside [McD79, Gib99, DB96, Wes02]. In a cellular mobile radio system, the association of MTs to APs is performed according to criteria such as the quality of the propagation conditions, and is based on the premise that from the viewpoint of a certain MT there exists typically one AP to which the propagation conditions are most favorable. Due to this association of MTs to APs a partitioning of the whole geographical area of the mobile radio system into cells follows naturally. In cellular mobile radio systems it can be discerned between two basic types of interference, depending on whether the signals of MTs of the same cell or of MTs of different cells interfere. In the case of interference between the signals of MTs of the same cell, the interference is called intracell interference. Intracell interference can be combated by techniques such as joint detection [Kle96, KB92] or joint transmission [MBW+ 00, TWMB01]. On the other hand, if the useful signals of MTs of neighboring cells interfere, the interference is called intercell interference. The effects of intercell interference are mitigated in 2G mobile radio systems by means of partitioning of the bandwidth B, as explained in Section 1.1. However, due to the said partitioning of the bandwidth B an inefficient use of the system bandwidth B results. Fig. 1.2 shows an excerpt of a mobile radio system based on the cellular concept consisting of twelve cells grouped in three clusters of four cells. As can be seen from Fig. 1.2, each cell has an AP. The APs in turn are connected to the core network of the mobile radio system which is the data source and data sink for the information sent to and received from the MTs, respectively. Following the argumentation of Section 1.1, higher spectral capacities ηc of (1.1) can be achieved if a larger number of inputs of the MIMO channel in the DL or of outputs of the MIMO channel at the UL at the fixed side of the wireless communication channel are jointly available than in cellular mobile radio systems. The transition from the cellular architecture to the novel air interface architecture can be visualized as the result of merging of a group of neighboring cells. The merging of the neighboring cells consists in establishing a communication link between each of the APs and a central unit (CU), which is in turn connected to the core network of the mobile radio system. Each such group of APs defines a service area (SA) and the resulting
- 17. 1.2 Service area based architectures versus cellular architectures 7 c o r e n e t w o r k c e l l B S M T Figure 1.2. Excerpt of a cellular mobile radio system, consisting of 12 cells C U C U c o r e n e t w o r k S A A P M T C U Figure 1.3. Excerpt of a mobile radio system employing the SA-based architecture, consisting of 3 SAs
- 18. 8 Chapter 1: Introduction mobile radio system air interface architecture is called service area based (SA-based) architec- ture [WMS+ 02, SWC+ 02, SWBC02, MWS+ 02]. The crux of the novel SA-based air interface architecture consists in the fact that as a result of the merge of a number of cells in a single SA, the intercell interference between the useful signals corresponding to the MTs active in the said cells becomes intra-SA interference in the case of SA-based systems and can be easily combated by interference suppression techniques [Kle96, MBW+ 00, WMS+ 02]. Fig. 1.3 illus- trates an excerpt from a mobile radio system employing the SA-based air interface architecture with three SAs, each consisting of four APs. Comparing Fig. 1.2 to Fig. 1.3, in the exemplary excerpt of the considered mobile radio system, each SA can be thought of as a union of four cells in terms of cellular architectures. In the UL transmission in a SA, the signals transmitted from each MT are received by all APs of the SA and fed to the CU, which performs the signal processing tasks. If the SA is chosen to be the MIMO system of Fig. 1.1, all the outputs of the SA MIMO wireless channel are jointly available to the CU and therefore the MIMO channel in the UL of a SA-based air interface architecture is modelled as a multiple access channel [Ahl73], in which the MTs are the multiple transmitters and the CU is the receiver. If not all the outputs of the MIMO channel were jointly available, i.e., if the signals received by each of the APs were considered separately, as it is the case in the APs in cellular architectures, the mitigation of the interference from the partial received signals stemming from the other MTs of the SA caused to the useful received signal of a specific MT would be possible only in a limited extent at a certain AP [Ost01]. However, as in the UL of SA-based architectures all outputs of the MIMO channel are jointly available and given that the CU disposes of knowledge concerning the transmission properties of the MIMO channel of the SA, which is the result of a channel estimation procedure in the UL [SMW+ 01, MWS+ 02], the structure of each of the partial received signals at the APs is known at the CU. In the exemplary case of linear JD, the CU has knowledge of the vector subspace to which each of the partial received signals belongs and can therefore minimize the interference caused to the partial received signal of a desired MT by the partial received signals correspond- ing to the other MTs of the SA. This means that the CU can combine the received signals from the APs in an optimum way in terms of suppression of interference between the various simul- taneously active MTs, i.e., the CU in the UL transmission in a SA-based architecture performs joint detection (JD) [WMS+ 02, Kle96, KB92, SWC+ 02, SWBC02]. In the DL transmission, information is sent from the core network to the MTs. For this purpose the CU generates AP-specific signals and each MT in the DL transmission receives the signals from all APs. Therefore, the channel valid for the DL in SA-based air interface architectures is modelled as a MIMO broadcast channel [CS00], in which the CU is the transmitter and the MTs are the multiple receivers. As it is the case with the UL transmission, if the transmit signals were
- 19. 1.2 Service area based architectures versus cellular architectures 9 generated independently for each of the MTs, as is the case in cellular mobile radio systems, then each MT would also receive signals intended for the other MTs of the SA, i.e., signals which cannot be constructively utilized and act as interference to each of the MTs. In SA-based architectures, the CU has knowledge concerning the MIMO broadcast channel valid for the DL transmission in the SA. Such a fact can hold, for example, if time division duplexing (TDD) [Pro95] is used and the time elapsing between UL and DL transmission is sufficiently smaller than the coherence time of the channel. In this case, channel knowledge re- sulting from a channel estimation process in the UL can be assumed to be valid also for the DL transmission. This reciprocity between UL and DL channels is known as channel reciprocity and given the parametrization of state-of-the-art mobile radio systems [ENS97, MBW+ 00], the said channel reciprocity is a major advantage of TDD systems as compared to frequency divi- sion duplexing (FDD) systems in which the coherence bandwidth of the mobile radio channel [Par92] is typically smaller than the bandwidth of the frequency bands of UL and DL transmis- sion. Additionally to the channel knowledge, the receiver algorithms employed in the MTs active in a SA are known to the CU and this knowledge is exploited for the generation of the AP-specific transmit signals in the DL transmission. Transmission schemes which utilize knowledge con- cerning the structure of the receiver and of the mobile radio channel in order to generate the transmit signals are known as receiver oriented schemes, in contrast to transmitter oriented schemes, which adjust the receiver according to the structure of the transmitter. The advantage of receiver oriented schemes if applied on the DL is that no resources have to be spent for chan- nel estimation in the DL and that a variety of MT structures, even very simple MTs, can be supported [MBW+ 00, TWMB01, WMS+ 02]. As all inputs to the MIMO broadcast channel are jointly available and the characteristics of the mobile radio channel valid for the DL transmission are known, the CU has a priori knowledge of the structure of the received signal at each MT for given transmit signals. Moreover, by exploiting the knowledge concerning the structure of the MTs, the CU can design transmit signals for the APs in such a way that the estimates of the sent data symbols at each of the MTs satisfy given criteria, e.g., are free from intra-SA interference. In a SA-based architecture the CU can design transmit signals jointly for all MTs of the SA in order to mitigate the effects of intra-SA interference, i.e., the CU in the DL transmission in a SA performs joint transmission (JT) [WMS+ 02, MBW+ 00, TWMB01, TWMB01]. It follows that the crux of the SA-based architectures consists in the availability of all the an- tennas of the APs to the CU, i.e., in the availability of all outputs to the multiple access channel in the UL and of all inputs of the broadcast channel in the DL. The CU can then employ JD and
- 20. 10 Chapter 1: Introduction JT in the UL and DL transmission, respectively, to minimize the interference between the MTs. Hence, in SA-based systems by means of JD and JT a significant portion of the intercell inter- ference, which would be present in a cellular system, is combated. In the present thesis a variety of algorithms for JD and JT is investigated, such as linear, nonlinear and iterative algorithms. 1.3 OFDM transmission technique At the transmitter side in a mobile radio system multiple data carrying signals are merged into a single transmit signal which is fed into one of the inputs of the time-continuous MIMO mobile radio channel. At the receiver side the multiple data carrying received signals are extracted from the received signal. The techniques of transmission of multiple data carrying signals us- ing a single signal for each input and output of the MIMO mobile radio channel are called multiplexing techniques, the choice of which is an important aspect in the design of a mobile radio system. Orthogonal frequency division multiplexing (OFDM) is a multiplexing technique gaining considerable interest the last years. Moreover, OFDM is applied in numerous com- munications systems over the world [ETS97a, ETS97b, RCLF89, RS95, TL97, Cim85, Bin91, CTC91, Jon95, IEE99, CWKS97, vNAM+ 99, ETS96, ETS99], is contained in a proposal for 3G systems in Europe [ETS98] and is considered to be the leading candidate multiplexing tech- nique for beyond 3G mobile radio systems [RGG01b, Roh00, RGG01a]. In what follows, after describing the principles of some basic multiplexing techniques, an outline of the characteristics of an OFDM system is performed. Blockwise transmission is assumed and each block is called symbol slot. A first choice regarding multiplexing is time division multiplexing where each symbol slot con- tains a serial concatenation in time of the data carrying signals. However, due to the multipath propagation in the wireless channel [Par92], in a mobile radio system employing time division multiplexing the part of the received signal corresponding to a particular data carrying signal contains apart from the desired data carrying signal signal portions caused by time delayed echoes of previously sent data carrying signals, an effect known as intersymbol interference. Future mobile radio systems are characterized by a demand for higher data rates, which trans- lates in the case of time division multiplexing systems into shorter time durations of the data carrying signals and therefore a larger impact of intersymbol interference. In time division mul- tiplexing systems a guard interval can be employed to combat intersymbol interference the use of which however introduces an overhead in the data transmission especially undesired in the case of high data rates. In a system in which frequency division multiplexing is employed, the data carrying signals are sent in parallel, i.e., each of the data carrying signals modulates a sinusoidal signal of a
- 21. 1.3 OFDM transmission technique 11 specific subcarrier frequency, called a subcarrier. Multiplexing techniques characterized by the modulation of multiple subcarriers with the data carrying signals are also known as multicarrier modulation techniques [GW00]. A decisive advantage offered by the frequency division mul- tiplexing techniques and by multicarrier modulation techniques in general is the possibility to accommodate high data rates, as higher data rates require solely a larger number of subcarriers [vNP00] and are not limited by the amount of time dispersiveness of the mobile radio channel. If subcarrier spacings are chosen to be large enough so that spectra of different subcarriers do not overlap significantly, the available frequency bandwidth B is inefficiently used in frequency division multiplexing systems. Hence, as far as multicarrier modulation techniques are con- cerned, it is imperative to realize a tight subcarrier spacing and at the same time mitigate the effects of the undesired crosstalk between different subcarriers. Much research has been conducted in the development of a multicarrier modulation system with a tight subcarrier spacing [FL61, Sal67]. OFDM [WE71, KZ89] is a multicarrier modulation technique in which the spectra of different subcarriers overlap without causing intercarrier in- terference. The interference free overlap of different subcarriers in OFDM systems is achieved by choosing subcarrier frequencies which satisfy an orthogonality relationship, thanks to which the signals corresponding to different subcarriers in an OFDM system are orthogonal to each other. The receiver in an OFDM system considers only a part of the total received signal, during which the aforementioned orthogonality of the signals is preserved. Hence, an OFDM system achieves an efficient use of the available bandwidth B, as a tight spacing of the subcarriers be- comes possible. The physical transmission model of OFDM-based MIMO systems is treated in detail in Chapter 3. The fundamentals of the OFDM technique are first presented in the paper of Weinstein and Er- bert in 1971 [WE71], where a DFT structure is presented to realize the OFDM technique. But it was not until the realization of an OFDM system by highly efficient FFT structures in combi- nation with its appealing simplicity when intensive research in OFDM was sparkled regarding, e.g., the application of different multiple access algorithms in OFDM systems [GRC+ 01, RG97, RGG01b, GRC+ 02], or the employment of adaptive modulation at each of the OFDM subcar- riers [HH, CCB95, FH96, GR00]. OFDM is part of the digital video broadcasting (DVB) and digital audio broadcasting (DAB) systems in Europe [ETS97a, ETS97b, RCLF89, RS95, TL97, Cim85] and is applied in the digital subscriber line (DSL) standards in the USA [Bin91, CTC91, Jon95]. Moreover, many wireless local area network (WLAN) systems are based on OFDM, such as the IEEE 802.11a [IEE99, CWKS97, vNAM+ 99], the IEEE 802.11g [IEE03] and the HIPERLAN and HIPER- LAN/2 systems [ETS96, ETS99].
- 22. 12 Chapter 1: Introduction 1.4 State of the art and open questions Two dominating characteristics of the SA-based air interface architecture are the MIMO nature of the wireless channel of the SA and the employment of the multiuser algorithms of JD and JT in order to mitigate the interference between MTs in the SA. Literature on mobile radio systems abides in investigations concerning MIMO channels and in multiuser algorithms. In particular, since the initial ground breaking discovery of the potential of MIMO systems, an explosion of the number of investigations on MIMO systems is observed. On the other hand, multiuser algorithms are continuously a topic of investigation since the early 80s and therefore a variety of relevant publications is available. In this Section, the most important, according to the author, literature citations on MIMO systems and on multiuser algorithms are listed and the citations relevant to the considerations in the present thesis are highlighted. At the end of this Section, open questions regarding the air interface of future mobile radio systems are pointed out. Table 1.2 lists the most important contributions in the field of MIMO systems, dealing with the achievable capacity of MIMO channels and with specific algorithms targeted at the achievement of significant portions of the available MIMO capacity. In order to provide a more comprehen- sive overview, the publications in Table 1.2 are grouped in the two categories: I: II: theoretical investigations on the capacity of MIMO systems, and near capacity-achieving MIMO algorithms for point-to-point MIMO channels. Category I contains publications regarding the derivation of the capacity formulas for the MIMO point-to-point wireless link, and for the MIMO multiple access channel and the MIMO broad- cast channel for various cases regarding, e.g., whether channel state information is available at the transmitter or at the receiver or neither at the receiver and the transmitter. Complemen- tary to the theoretical considerations concerning the capacity of MIMO channels of Category I, investigations of two practical algorithms for MIMO systems targeted at achieving at least a significant portion of the theoretically available capacity of the MIMO channel, space time coding and Bell Labs layered space time (BLAST), are listed in Category II. [Tel99] and [Fos96] are two seminal works on the capacity of point-to-point MIMO channels which unveil the large capacity potential of MIMO systems and sparkled a worldwide research activity. In [Tel99] and [Fos96] a N × M point-to-point MIMO channel is investigated. If a rich scattering environment provides independent channels between each pair of transmit and receive antennas and the channel can be accurately tracked at the receiver, it is shown in [Tel99] and [Fos96] that the use of a fraction of the total available transmit energy in each of the equivalent min{N, M} independent single-input-single-output channels is counterbalanced by the exploitation of the cross-couplings of the MIMO channel, resulting in a MIMO channel
- 23. 1.4 State of the art and open questions 13 Table 1.2. Contributions on MIMO systems category reference remarks I [Tel99],[Fos96],[FG98],[VM01], capacity of point-to-point [JVG01],[JG04],[MH99] MIMO channels [YRBC01],[Ahl73],[CT91], capacity of multiple access channels [VTA01],[JVG02] [CT91],[CS00],[YC01], capacity of broadcast channels [VT03],[VJG02],[JVG02] II [Wit93],[SW94],[TSC98], space time coding [Ala98],[TJC99] [Fos96],[FG98], D-BLAST, V-BLAST [GFVW98],[GFVW99] capacity which scales linearly with min{N, M}. However, it is not always possible to track the channel accurately, e.g., in the case that rapid motion of the receiver or the transmitter results in a fast variation of the channel. The case of partial channel state information is treated in [VM01, JVG01, JG04, MH99]. MIMO multiple access channels were first dealt with in [Ahl73] and in [CT91]. Considering the distributions of the input signals to the MIMO multiple access channel achieving the capacity regions, in [YRBC01] a modified iterative version of the waterfilling technique [CT91] is intro- duced and a numerical technique is employed to find the capacity region achieving covariance matrices of the input signals to the MIMO multiple access channel. Concerning the capacity regions of the MIMO broadcast channel, the work of Costa [Cos83] attracted a lot of attention. Given that the transmitter for a single-input-single-output channel has knowledge of the interference at the receiver, Costa in [Cos83] shows that the capacity of the point-to-point single-input-single-output channel with additive Gaussian interference is the same as if interference was not present. In [CT91] an initial work on the capacity regions of the broadcast channel for the case that the transmitter has a single antenna is carried out and in [CS00] some first results on the broadcast channel with multiple antennas at the transmitter are presented. Yu and Cioffi in [YC01] introduce the Trellis precoding scheme and extend the considerations on the broadcast channel to the multi-antenna receiver case. Despite of serious efforts, the derivation of a closed capacity formula directly for the generalized broadcast channel remained a complex problem, until Jafar and Goldsmith in [JG04] revealed a duality in the rate regions between the broadcast channel and the multiple access channel, by the use of which the optimum covariance matrices can be found for the multiple access channel case using standard optimization techniques and then can be transformed to obtain the optimum covariance matrices for the dual broadcast channel, according to [JG04].
- 24. 14 Chapter 1: Introduction The quality of the estimation of a particular data symbol in terms of signal to noise ratio (SNR), after transmission through a distorting wireless channel can be greatly improved by providing an additional replica of the transmitted signal to the receiver via another channel. A system providing more than one independent channel from the transmitter to the receiver is said to provide diversity. For instance, in a SA-based system spatial diversity is provided by the em- ployment of multiple APs in the SA. The transmit diversity scheme dominating in the literature is space time coding [Wit93, SW94, TSC98, Ala98], according to which each data symbol to be transmitted is encoded in time and in space, i.e., in time and along the various transmit an- tennas jointly available to the transmitter. Space time coding algorithms primarily focus on point-to-point MIMO channels as all inputs and outputs of the MIMO channel must be jointly available to implement joint space-time coding and decoding, respectively. The first space time coding proposal is considered to be from Winters [SW94], who was inspired by the multipath diversity scheme introduced by Wittneben in [Wit93]. The first decisive contribution however in the field of space time coding is considered to be the introduction of the space time trellis coding scheme by Tarokh et. al [TSC98], in which convolutional codes are employed for the temporal and spatial coding. Considering the application of block codes instead of convolu- tional codes, an important representative of the block space time coding approaches is the space time block coding algorithm by Alamouti [Ala98], which offers the same diversity benefit as space time trellis coding while having a decisively smaller decoding complexity. The space time block coding scheme by Alamouti has gained worldwide attention and is also adopted in the wideband CDMA and cdma2000 standards [w3G99, TIA00]. Instead of introducing redundancy, as it is the case in space time coding, in the case of the BLAST architecture [Fos96, FG98, GFVW98, GFVW99] independent data streams are trans- mitted from each transmit antenna. In this way, spatial diversity is sacrificed for an increased spectrum efficiency of the MIMO system. BLAST as well as space time coding, is an architec- ture for point-to-point MIMO channels as it requires joint availability of the inputs and outputs of the MIMO channel. The support of multiple MTs in a SA-based system is achieved by the application of JD [Kle96] in the UL and JT [MBW+ 00] in the DL, as described in Section 1.2. JD and JT are algorithms belonging to the category of multiuser algorithms, the most important literature for which is contained in Table 1.3. As can be seen from Table 1.3, literature on multiuser algorithms can be classified into two main Categories: I: II: transmitter oriented multiuser algorithms and receiver oriented multiuser algorithms. In wireless channels where transmitter oriented multiuser algorithms are applied, the receiver is designed according to the structure of the transmitter. Because literature on transmitter oriented
- 25. 1.4 State of the art and open questions 15 multiuser algorithms, which are also known as multiuser detection or multiuser estimation al- gorithms, is quite extensive, Category I contains only the most representative, according to the author, publications on transmitter oriented multiuser algorithms. Dual to transmitter oriented multiuser algorithms, in receiver oriented multiuser algorithms the transmitter adapts itself to the receiver, as for example in JT. In Category II the most important publications related to receiver oriented multiuser algorithms are listed. Table 1.3. Contributions on multiuser systems category reference remarks Ia [Ver98],[Ver86a],[Ver86b] optimum multiuser detection Ib [LV89],[XSR90],[LV90], linear multiuser estimation [KB92],[KB93],[Kle96], - RxZF JD [Mil88],[BFKM93],[FKB94],[KKKB94], - MMSE [KKKB96],[MH94],[Gra81] [VA90],[PH94],[VA91], iterative multiuser detection [Var95],[Lam00b],[Lam00a], - multistage detection [YKI93],[KIHP90],[HL98], - parallel interference cancellation [DSR98] [Hag97],[BG96],[BM96], turbo multiuser detection [HOP96],[BDMP98],[BGT93], [ARAS99],[Moh98],[RSAA98], [Hag96],[AGR98],[VW98] II [Fis02],[WR01],[Bar02], receiver oriented algorithms [VJ98],[MBW+ 00],[KM00], - Joint precoding/Joint Predistortion [BOS98],[JKG+ 02] - TxZF JT - transmit Wiener Filter Concerning transmitter oriented multiuser algorithms, it can be discerned among two main groups of algorithms: • multiuser detection algorithms, producing discrete output values belonging to a prede- fined alphabet, and • multiuser estimation algorithms, producing continuous output values, which are quan- tized with respect to the predefined alphabet in a separate step. It follows that the concatenation of a multiuser estimator with the quantizer can be also seen as a multiuser detector. The optimum multiuser detector in terms of the probability of erroneous detection is described in [Ver86a, Ver86b, Ver98]. Such an optimum detector yields estimates of the transmitted data
- 26. 16 Chapter 1: Introduction symbols in a nonlinear fashion, according to the maximum a posteriori (MAP) or maximum likelihood (ML) criterion using a priori knowledge concerning the transmitted data symbols. However, given the parametrization of state-of-the-art multiuser mobile radio systems, the op- timum multiuser detector is highly complex and hence not realizable. Suboptimum multiuser detectors present a tradeoff between performance in terms of erroneous decision and implemen- tation complexity and yield the estimates of the transmitted data symbols either linearly or in an iterative fashion. Linear multiuser estimators yield continuous valued estimates of the transmitted data symbols by performing a linear operation on the received signal. Various linear multiuser estimators exist, which differ in the performance criterion which the estimates of the data symbols satisfy. In [KB92, KB93, Kle96, BFKM93, FKB94, LV90] receive zero-forcing JD (RxZF JD) is in- vestigated, which delivers interference free estimates of the sent data symbols. The estimator applying the minimum mean square error (MMSE) principle investigated in [MH94, Gra81, LV89, XSR90, LV90, BFKM93, KKKB94, KKKB96] trades off interference suppression for an improved SNR of the estimated data symbols as compared to RxZF JD. Alternatively to linear estimation, detection of the multiple transmitted data symbols can be performed in an iterative fashion. If convergent, iterative multiuser algorithms yield estimates of the transmitted data symbols in multiple iterations or stages, being at the same time less complex than linear multiuser algorithms. To the category of iterative multiuser detection al- gorithms belong multistage detection [VA90, VA91, YKI93, HL98] and parallel interference cancellation [Lam00b, Lam00a, DSR98, PH94, Var95, KIHP90], which are governed by the same general principles. An iterative data detection algorithm gaining considerable attention is turbo multiuser detection [DJB+ 95, Moh98, RSAA98, WP99], which is based on the turbo prin- ciple [Hag96, Hag97, BG96, BGT93] originally designed for decoding concatenated forward error correcting (FEC) codes. In receiver oriented multiuser algorithms, the transmitter generates transmit signals based on the knowledge of the structure of the receiver and of the wireless MIMO channel. The pro- cess of generation of transmit signals in receiver oriented algorithms is known as precoding or predistortion [Fis02, Bar02, YC01, Tom71, HM72]. A special case of predcoding algorithms are algorithms in which the transmit signals are generated by performing a linear operation on the data symbols [MBW+ 00, TWMB01, KM00, JUN01, JKG+ 02, VJ98]. Common to all precoding and predistortion algorithms is that the wireless channel is pre-equalized at the trans- mitter side. As in receiver oriented multiuser algorithms the signal processing tasks related to channel equalization are performed by the transmitter, multiuser precoding and predistortion algorithms are especially attractive for the application in the broadcast channel where multiple low complexity MTs are served.
- 27. 1.4 State of the art and open questions 17 The first precoding algorithm is considered to be the Tomlinson-Harashima precoding algorithm [Tom71, HM72]. According to the Tomlinson-Harashima precoding algorithm, the channel is pre-equalized at the transmitter by means of an inversion of the channel matrix and in order to avoid the peaks in the transmit power which would result at frequencies coinciding with channel fades, the amplitude of the transmit signal is restricted to a specific interval by means of a modulo-2 addition of the data symbols with a precoding sequence, which depends on the modulation used. Though the Tomlinson-Harashima precoding algorithm as described in [Tom71, HM72] is not a multiuser algorithm in its nature, Yu and Cioffi in [YC01] extend the Tomlinson-Harashima algorithm to the broadcast channel. Linear predistortion and precoding algorithms differ in the way the linear transformation ma- trix is applied to the data symbols to be transmitted. In the predistortion method proposed for CDMA systems by Vojˇci´c and Jang [VJ98], the linearly transformed data symbols are spread and then fed into the channel, whereas in the Joint Predistortion algorithm proposed by Kowalewski and Mangold [KM00, BOS98], the linear transformation is applied on the spread signals. On the other hand, in the case of JT [MBW+ 00], the spreading process in the trans- mitter is not performed separately from the linear transformation. Given the structure of the receiver and of the wireless MIMO channel, the linear transformation matrix in JT is chosen in such a way that interference free estimates of the data symbols are obtained at the receivers and that the transmit signals are of minimum energy. Due to the interference free transmission, linear JT is also known as transmit ZF JT (TxZF JT) demonstrating the duality to RxZF JD in transmitter oriented multiuser algorithms. The search for the analogon of MMSE for the case of receiver oriented multiuser algorithms led to the derivation of the transmit Wiener filter by Joham et al. in [JKG+ 02], which represents a trade-off between receive energy exploitation and interference suppression achieved by the transmit matched filtering (TxMF) and the TxZF JT algorithms, respectively, just as MMSE JD represents a trade-off between matched filter (MF) and RxZF JD in transmitter oriented multiuser algorithms. As stated in Section 1.1, high spectrum capacities ηc should characterize future mobile radio systems. Due to the fact that mobile radio systems are interference limited, the high spectrum capacities can be achieved mainly by combatting interference. However, in cellular architec- tures intercell interference limits the achievable spectrum capacity ηc. According to the knowl- edge of the author, proposals regarding future mobile radio systems [AMAS02, WWR], as well as the contributions in Tables 1.2 and 1.3, refer to cell-based architectures. As such, they fail to address the issue of the suppression of interference, as shown in Section 1.2, and are thus inherently suboptimum with respect to the provision of high spectrum capacities ηc. Hence, the need for the development of an alternative air interface architecture for future mobile radio systems is evident. The design of such an air interface architecture should be aimed at the
- 28. 18 Chapter 1: Introduction provision of high spectrum capacities, i.e., interference suppression should be the main focus of the novel air interface architecture. The SA-based air interface architecture described in Section 1.2 fulfills the aforementioned requirement as the suppression of interference between the simultaneously active MTs is the crux of the SA-base air interface architecture proposal. The investigation of a SA-based air interface architecture combined with the OFDM transmission technique is the topic of the present thesis. 1.5 Structure of the thesis Apart from the Introduction, the present thesis is comprised of eight chapters, the contents of which are outlined in this Section. For the purposes of the design and of the performance assessment of a mobile radio system, assumptions have to be made regarding the underlying wireless channel. In Chapter 2 the fundamental principles of mobile radio propagation are briefly recapitulated and the channel models used in the thesis are described. In Chapter 3 a novel approach for the modelling of the data transmission in OFDM-based MIMO systems is performed. The novelty of the model for the data transmission in OFDM- based MIMO systems presented in Chapter 3 consists in taking into account the time-continuous nature of the MIMO channel. The developed model consists of a physical transmission model complemented with pre- and post-processing stages. The mathematical modelling of the UL with JD in SA-based systems is performed in Chapter 4. For a single SA, the transmission model is derived, i.e., the mathematical expression of the received signals at the antennas of the APs as a function of the transmitted signals and of the channel matrix is derived. It is shown how JD is employed in SA-based systems to mitigate intra-SA interference by the joint detection of data symbols sent by each of the MTs, which are active simultaneously in the SA and in the same frequency band. Regarding JD algorithms for the UL, the cases of optimum nonlinear JD in the sense of MAP and ML JD, linear JD in the sense of RxZF JD and MMSE JD, and iterative JD with transparent, hard, soft and optimum data estimate refinement are investigated. The DL with JT in a SA-based system is the topic of Chapter 5. First, the transmission model for the DL is derived, i.e., the complex amplitudes of the signals received by the MTs are expressed using matrix-vector notation as a function of the transmitted signals and of the channel matrix of the SA. The crux of Chapter 5 consists in showing how, with the aid of JT, interference between multiple MTs is suppressed and the need for channel estimation at the MTs is eliminated in
- 29. 1.5 Structure of the thesis 19 the DL of SA-based systems. With regard to JT schemes, a novel JT scheme optimum with respect to the average bit error probability is firstly investigated. Moreover, the application of TxZF JT is investigated, with the aid of which interference free estimates of the data symbols are available at the active MTs. Chapter 5 is concluded with the introduction of an iterative JT scheme, according to which the total transmit vector is designed in an iterative fashion in a way analog to iterative JD with transparent data estimate refinement presented in Chapter 4. Chapter 6 covers the performance investigation of JD in the UL. In a first step, the performance measures asymptotic multiuser efficiency and bit error probability are defined, which are used in the context of UL transmission in SA-based systems to assess the efficiency with which JD uses the receive energy. Using the defined performance measures, the performance of optimum JD is analyzed. As the superior performance of optimum JD in comparison to linear JD is trivial, the target of the simulations is to quantify the performance gains achievable with optimum JD in comparison to linear JD in a SA-based system. Furthermore, using the geometric indoor channel model, RxZF JD is investigated by means of the calculation of the spatial distribution and of statistical results for the asymptotic multiuser efficiency. Finally, iterative JD with transparent, hard, soft and optimum data estimate refinement is investigated. Performance investigations for the DL of SA-based systems with JT are the topic of Chapter 7. Two performance measures for JT, namely transmission efficiency and bit error probability are introduced. In the case of optimum JT, the average bit error probability at the MTs is determined for fixed and variable energy transmit signal vectors. Finally, TxZF JT and iterative JT are investigated in terms of transmission efficiency and bit error probability. Chapter 8 presents an approach for the unified investigation of UL and DL in SA-based systems for the case of linear pre- and post processing. Moreover, the energy efficiency of a SA-based mobile radio system is defined as a performance measure. Chapter 8 is concluded with system level investigations of a SA-based mobile radio system. Chapter 9 concludes the thesis by summarizing the results of Chapters 2 to 8 in English and in German.
- 30. 20 Chapter 2: Channel modelling 2 Channel modelling 2.1 Introduction The design of a SA-based air interface architecture, as of any air interface architecture, is con- siderably aided by computer simulations. Profound knowledge concerning the characteristics of the mobile radio channel of the SA is essential in order to be able to model the wireless chan- nel of the SA in computer simulations as accurately as possible. Target of the present Chapter is to give an overview of the three channel models used in the simulations in this thesis. To this end, theoretical aspects of mobile radio propagation relevant to the radio transmissions in a SA-based air interface architecture are first briefly treated with. 2.2 Theory of mobile radio propagation In a wireless transmission in a mobile radio system, signals emitted by a transmitter reach the receiver not only via direct line of sight (LOS) paths between transmitter and receiver. Transmitted signals often impinge at the antennas of each receiver after reflection, scattering or diffraction on physical obstacles. Only seldom does a direct LOS path exist [Par92, BARY95, FL96], especially in dense urban areas. Given the usually large number of surfaces interacting with the emitted electromagnetic waves, a multitude of paths exist along which indirect wireless transmissions take place. It follows that a multitude of signals with different amplitudes, phases and delays superimpose at the receiver. In a static environment the mobile radio channel is described in the equivalent lowpass domain as a linear time invariant filter having the complex transfer function H(f). The superposition of the signals which reach the receiver each with a different delay τ [BBS97], varies for different frequencies f from destructive to constructive. Therefore, the mobile radio channel is said to be frequency selective, i.e., its transfer function H(f) fluctuates throughout the bandwidth B used for the wireless transmission. On the other hand, if the mobile radio channel has one dominant path and negligible signal energy is received via multipath propagation, then it is said to be frequency nonselective or flat fading channel and the corresponding transfer function H(f) is considered to be constant throughout the entire bandwidth B. In a dynamic environment in which the movement of the MT and of its surroundings is taken into account, the way the signals from multiple paths superpose at the receiver is time variant. Depending on the relation of the movement of the MT to the system wavelength λ, it can be discerned between small- and large scale movement [BARY95, FL96].
- 31. 2.3 Channel models used in the thesis 21 If the MT covers a distance of fractions of λ, then small but rapid variations of the amplitude of the received signal occur. In particular, the small scale movement of the MT has a rather negligible effect on the attenuation but a large impact on the phase of each of the superposed signals. Therefore, the superposition of a large number of signals each with a rapidly changing phase results in an also rapidly varying envelope of the total received signal and the effect is called fast fading [Par92]. Large scale movement of the MT occurs if the movement of the MT is in the order of magnitude of tens of λ. In such a case, the dominant effect is shadowing, i.e., the limited lifetime of the individual paths. As the MT moves, some paths disappear and new paths are created. The resulting variation of the amplitude of the received signal is slow relative to the case of small scale movement, and is called slow fading [Par92]. However, the variation of the amplitude of the received signal caused by slow fading has a larger dynamic range as compared to the case of fast fading [BARY95]. Hence, in the case of the dynamic propagation environment, the time-variant transfer function H(f, t) is used to describe the mobile radio channel [BBS97, Par92]. 2.3 Channel models used in the thesis 2.3.1 COST 207 channel models The most widely used channel models are stochastic channel models, i.e., models in which the mobile radio channel is modelled as a bandlimited stochastic process. In the modelling proce- dure it is assumed that the stochastic process describing the channel is stationary in the wide sense at least in a small area and that the modelled wireless channel exhibits uncorrelated dis- persiveness in time delays τw, w = 1 . . . W, and Doppler shifts fD,w, w = 1 . . .W, of the W superposed paths, i.e., in stochastic models radio channels are modelled as wide sense sta- tionary uncorrelated scattering (WSSUS) channels [Bel63, Sch88a, Hoe92]. Hence, in WSSUS channels, the scattering function S (τ, fD) can be expressed as the product of the Doppler power spectrum Sc (0, fD) and the power delay spectrum ρT(τ, 0) as S (τ, fD) = Sc (0, fD) ρT(τ, 0). (2.1) The most widely used stochastic channel models are the channel models of the COST 207 study [COS88]. According to the COST 207 channel modelling, the mobile radio channel consists of a superposition of a number W of uncorrelated paths, which have uniformly distributed null phases θw, w = 1 . . . W, Doppler shifts fD,w, w = 1 . . .W, and unit amplitude. The delays τw for each path w are taken from an interval [τw,min, τw,max] according to an exponential-type power delay spectrum a exp (−bτw) , a, b ∈ R+ . For different values of
- 32. 22 Chapter 2: Channel modelling τw,min, τw,max, a and b four different propagation conditions are modelled, bad urban (BU), hilly terrain (HT), rural area (RA) and typical urban (TU), as Table 2.1 shows. Table 2.1. Parameters for the channel models of the four different propagation conditions of the COST 207 study environment τ/µs ρT(τ) bad urban (BU) [0, 5] ∝ exp (−τ) [5, 10] ∝ 0.5 exp (5 − τ) hilly terrain (HT) [0, 2] ∝ exp (−3.5τ) [15, 20] ∝ 0.1 exp (15 − τ) rural area (RU) [0, 0.7] ∝ exp (−9.2τ) typical urban (TU) [0, 7] ∝ exp (−τ) If the motion of the MTs is not taken into account, i.e., if for each path w, w = 1 . . .W, the Doppler shift fD,w is not taken into account, with the uniformly distributed null phase θw and the delay τw taken from Table 2.1, the channel transfer function H(f) = 1 √ W W w=1 exp (jθw) exp (−j2πfτw) (2.2) of the mobile radio channel according to the COST 207 channel models is derived. In the simulation of SA-based mobile radio systems, (2.2) is used KKB times to get the transfer functions H(k,kB) (f) of the wireless channels between each pair of MT k, k = 1 . . .K, and AP kB, kB = 1 . . . KB. 2.3.2 Indoor geometric channel model In order to perform simulations of a SA-based system in which OFDM is used, for each channel snapshot KKB transfer functions H(k,kB) (f), for the KKB channels between each MT and each AP have to be generated by means of a channel model. In order to take into account interde- pendencies between the wireless channels of the SA resulting from the geometrical structure of the SA, a geometric MIMO indoor channel model is developed specifically for the simulation needs of the thesis and it is described in the present Section. In contrast to the COST 207 chan- nel models, which generate transfer functions H(k,kB) (f) as samples of a stochastic process, the geometric indoor channel model described in this Section is deterministic, i.e., the same transfer functions H(k,kB) (f) are generated given fixed positions of the MTs and geometry of the SA. In the geometric channel model, the SA is a rectangular room of dimensions xmax ×ymax, as Fig. 2.1 shows. In the SA, a single CU, K MTs and KB APs exist, each equipped with single element
- 33. 2.3 Channel models used in the thesis 23 antennas. The K MTs with coordinates (x (k) MT, y (k) MT), k = 1 . . . K, are randomly positioned in the room and their positions are kept fixed once chosen. The KB APs are uniformly deployed on a circular periphery of radius rB, having its center at the origin of the cartesian coordinate system, which coincides with the center of the rectangular room of the SA. Their coordinates in the chosen system will be denoted by (x (kB) AP , y (kB) AP ), kB = 1 . . .KB. −xmax/2 −ymax/2 ymax/2 xmax/2 y x AP 1 AP 2 AP 3 AP KB MT 1 MT 2 MT K rB Figure 2.1. SA of dimensions xmax × ymax with K MTs with coordinates (x (k) MT, y (k) MT), ran- domly positioned in the SA and KB APs with coordinates (x (kB) AP , y (kB) AP ), deployed on a circular periphery of radius rB Reflection on the walls forming the borders of the SA is not taken into account. It is assumed that each wireless link between an AP kB and an MT k consists approximately of one path, the one corresponding to the direct LOS transmission, and that such a LOS connection exists between all pairs of APs and MTs. Usually radio wave propagation in real life environments cannot be approximated with a LOS channel model. Nevertheless, the use of the geometric channel model permits the efficient study of special characteristics of SA-based systems, as it is shown in Chapter 6, and does not target at the modelling of a real life scenario.
- 34. 24 Chapter 2: Channel modelling With the distance r(k,kB) = y (k) MT − y (kB) AP 2 + x (kB) AP − x (k) MT 2 (2.3) between MT k and AP kB, for the considered subcarrier nF and frequency f and the speed c0 of propagation of electromagnetic waves in vacuum, the attenuation factor 1 r(k,kB)2 , and the phase rotation factor exp −j2πfr(k,kB) /c0 of the direct path from MT k to AP kB is calculated. Hence, the transfer function H(k,kB) (f) between MT k, AP kB at frequency f can be expressed as H(k,kB) (f) = 1 r(k,kB) exp −j2πf r(k,kB) c0 . (2.4) 2.3.3 Multiple-input-multiple-output parametric channel model In the SA-based air interface architecture the system performance is in many cases a function of the degree by which channels of different MTs are correlated, as will be shown in Chapter 6. For this reason, a deterministic MIMO parametric channel model is developed with which the degree of correlation between the channels of the various MTs is parameterized. Given full system load, i.e., KB = K, (2.5) and with the variable ρ ∈ C, the output of the MIMO parametric channel model are the transfer functions H(k,kB) (f) = 1 k = kB, ρ else, k = 1 . . .K, kB = 1 . . . KB, (2.6) which are frequency nonselective. Using the variables ρkkB ∈ C, k = 1 . . .K, kB = 1 . . .KB, the MIMO parametric channel model can be extended to include more degrees of freedom, yielding the transfer functions H(k,kB) (f) = 1 k = kB, ρkkB else, k = 1 . . . K, kB = 1 . . . KB, (2.7) as output.
- 35. 25 3 Modelling of OFDM-based MIMO systems 3.1 Introduction Until now, OFDM-based systems are described by the use of a model based on IFFT, FFT, cyclic prefix addition and cyclic prefix removal operations [vNP00, FK03]. However, such approaches fail to address the fact that OFDM-based systems are just special cases of a more general class of multiuser systems in which a time-continuous signature is assigned to each discrete transmit value, i.e., of multiuser systems employing linear modulation. Target of this Chapter is the development of a novel model for the data transmission in an OFDM-based system employing transmission over a MIMO channel with KI inputs and KO outputs. In a first step data transmission in a general multiuser system employing transmission over a time-continuous KO × KI MIMO channel is modelled and then the data transmission model for OFDM-based MIMO systems is derived as a special case. Bandpass signal transmissions in multiuser systems can be efficiently described by the use of the equivalent low pass domain representation of signals, in which signals are represented by their complex envelopes [Pro95]. Moreover, the model for the data transmission can be decomposed into • a physical transmission model and • pre- and post-processing stages, as Fig. 3.1 shows. It is assumed that L bits u (k) l , l = 1 . . . L, compiled into the bit vector u(k) = u (k) 1 . . . u (k) L T , (3.1) are transmitted per MT k, k = 1 . . .K. As shown in Fig. 3.1, the KI transmit vectors s(kI) = s(kI,1,1) . . . s(kI,nF,nS) . . . s(kI,NF,NS) T , kI = 1 . . . KI, (3.2) of dimension NFNS are generated from the K vectors u(k) , k = 1 . . . K, of (3.1) by the pre- processing stage.
- 36. 26 Chapter 3: Modelling of OFDM-based MIMO systems physical transmission model pre-processing post-processing u(1) u(k) u(K) ˆu(1) ˆu(k) ˆu(K) s(1) s(kI) s(KI) e(1) e(kO) e(KO) Figure 3.1. Model of the data transmission in a multiuser system with K MTs, in which the physical transmission takes place over a time-continuous MIMO channel with KI inputs and KO outputs, consisting of a model for the physical transmission with KI vector inputs and KO vector outputs, complemented with pre- and post- processing stages The physical transmission model of the investigated multiuser system is used to describe each of the KO received vectors e(kO) = e(kO,1,1) . . . e(kO,nF,nS) . . . e(kO,NF,NS) T , kO = 1 . . .KO, (3.3) of dimension NFNS as a function of the KI transmit vectors s(kI) , kI = 1 . . . KI, of (3.2). As the mobile radio channel itself is time-continuous the physical transmission model consists of an inner time-continuous part and an outer part which describes the synthesis and analysis of the time-continuous transmit and received signals, respectively. At the receiver side, a post-processing of each received vector e(kO) of (3.3) is performed, in order to yield the estimates ˆu(k) = ˆu (k) 1 . . . ˆu (k) L T , k = 1 . . .K, (3.4) of the bit vectors u(k) , k = 1 . . . K, of (3.1). Due to the fact that the investigation of the impact of synchronization errors on the performance of OFDM-based MIMO systems is beyond the scope of this thesis, it is assumed hereafter that the investigated OFDM system is perfectly synchronized in the time and in the frequency domain [vSB97, HE97, BR98].
- 37. 3.2 Physical transmission model 27 synthesisfilterbank analysisfilterbank time- continuous MIMO KO × KI channel h(kI,kO) (t) discrete MIMO channel with KI vector inputs and KO vector outputs s(1) s(kI) s(KI) s(1) (t) s(kI) (t) s(KI) (t) e(1) (t) e(kO) (t) e(KO) (t) e(1) e(kO) e(KO) n(1) (t) n(kO) (t) n(KO) (t) Figure 3.2. Physical transmission model with KI vector inputs and KO vector outputs of a mul- tiuser system employing transmission over a time-continuous MIMO channel with KI inputs and KO outputs 3.2 Physical transmission model 3.2.1 General description of the physical transmission Fig. 3.2 shows the physical transmission model of the considered multiuser system. The KI transmit vectors s(kI) , kI = 1 . . .KI, of (3.2) are processed by the synthesis filter bank to pro- duce the KI corresponding time-continuous signals s(kI) (t), kI = 1 . . .KI, which are transmit- ted through the time-continuous KO × KI MIMO channel, characterized by the KIKO impulse responses h(kI,kO) (t), kI = 1 . . . KI, kO = 1 . . . KO. It is assumed that each impulse response h(kI,kO) (t) has a maximum duration of Th. The KO time-continuous received signals e(kO) (t), kO = 1 . . . KO, containing also noise n(kO) (t), kO = 1 . . .KO, are processed by the analysis filter bank to yield the KO received vectors e(kO) , kO = 1 . . .KO, of (3.3). Due to the application of the synthesis and analysis filter banks, the KO × KI time-continuous MIMO channel is transformed into a discrete MIMO channel with KI vector inputs and KO vector outputs, as Fig. 3.2 shows.
- 38. 28 Chapter 3: Modelling of OFDM-based MIMO systems 3.2.2 Transmitter The task of the synthesis filter bank in Fig. 3.2 is the synthesis of each time-continuous transmit signal s(kI) (t) from the transmit vector s(kI) . The signature ct,nF,nS (t) is weighted by the transmit value s(kI,nF,nS) to produce the transmit-value-specific partial transmit signal s(kI) nF,nS (t) = s(kI,nF,nS) ct,nF,nS (t). (3.5) With the transmit-value-specific partial transmit signals s (kI) nF,nS(t), nF = 1 . . . NF, nS = 1 . . .NS, of (3.5), the transmit signal s(kI) (t) = NF nF=1 NS nS=1 s(kI) nF,nS (t) (3.6) is calculated which is fed in the input kI of the time-continuous KO × KI MIMO channel. In the following multicarrier systems are considered [vNP00, FK03], in which each signature ct,nF,nS (t) is a time- and frequency shifted replica of a basic transmit signature ct (t). With the symbol slot duration Ts and the subcarrier spacing F, the input-specific signature ct,nF,nS (t) at subcarrier nF and symbol slot nS is expressed as ct,nF,nS (t) = ct (t − (nS − 1)Ts) exp (j2π(nF − 1)Ft) . (3.7) In the following the symbol slot duration Ts is chosen to be larger than the impulse response duration Th, i.e., Ts > Th holds. In the specific case of OFDM systems the subcarrier spacing F = 1 Ts − Th (3.8) and the basic transmit signature ct (t) = 1 √ Ts rect t Ts − 1 2 (3.9) are used and with the basic transmit signature ct(t) of (3.9), (3.7) becomes ct,nF,nS (t) = 1 √ Ts rect t − (nS − 1)Ts Ts − 1 2 exp j2π nF − 1 Ts − Th t . (3.10) Due to (3.5), (3.6) and (3.10), in a specific OFDM symbol slot nS the weighted sum of NF sinu- soidal signals ct,nF,nS (t), nF = 1 . . . NF, of (3.10) is fed in the input KI of the time-continuous MIMO channel. The transmitter defined by (3.5), (3.6) and (3.10) corresponds to a conventional OFDM transmitter [vNP00].
- 39. 3.2 Physical transmission model 29 3.2.3 MIMO channel Each time-continuous transmit signal s(kI) (t) of (3.6) passes through the time-continuous KO × KI MIMO channel, characterized by the impulse responses h(kI,kO) (t), kI = 1 . . .KI, kO = 1 . . .KO. Hence, with the KI time-continuous transmit signals s(kI) (t), kI = 1 . . .KI, of (3.6), the KI impulse responses h(kI,kO) (t), kI = 1 . . .KI, and the additive noise n(kO) (t), for the time-continuous received signal e(kO) (t) at output kO of the time-continuous MIMO channel e(kO) (t) = KI kI=1 ∞ −∞ s(kI) (t − τ)h(kI,kO) (τ)dτ + n(kO) (t) = KI kI=1 NF nF=1 NS nS=1 Th 0 s(kI,nF,nS) ct,nF,nS (t − τ)h(kI,kO) (τ)dτ + n(kO) (t) (3.11) holds. From (3.11) it can be seen that the combined effect of the input-specific signature ct,nF,nS (t) and of the impulse response h(kI,kO) (t) on each transmit value s(kI,nF,nS) is charac- terized by the combined impulse response b(kI,kO) nF,nS (t) = Th 0 ct,nF,nS (t − τ)h(kI,kO) (τ)dτ, (3.12) with which the expression (3.11) for the time-continuous received signal e(kO) (t) becomes e(kO) (t) = KI kI=1 NF nF=1 NS nS=1 s(kI,nF,nS) b(kI,kO) nF,nS (t) + n(kO) (t). (3.13) The additive noise n(kO) (t) in (3.13) is considered to be zero-mean white noise with the two- sided spectral power density N0/2, i.e., the variance σ2 = N0 (3.14) characterizes each of the real and imaginary parts of the noise n(kO) (t) in the following. More- over, it is assumed that the noise n(kO) (t) and n(kO) (t) at different outputs kO = kO of the time-continuous MIMO channel is uncorrelated, i.e., E n(kO) (t + τ)n∗(kO) (t) = ⎧ ⎨ ⎩ N0δ(τ) kO = kO, 0 else, (3.15) holds.
- 40. 30 Chapter 3: Modelling of OFDM-based MIMO systems 3.2.4 Receiver At the receiver side of the considered multiuser system, an analysis filter bank is employed, as shown in Fig. 3.2. The task of the analysis filter bank is the filtering of each time-continuous re- ceived signal e(kO) (t) in order to yield the NFNS received values e(kO,nF,nS) , nF = 1 . . . NF, nS = 1 . . .NS. To perform this task, a bank of KO filters is employed in the analysis filter bank. Each filter in the analysis filter bank has the impulse response cr,nF,nS (t) and its output is sampled. In multicarrier systems, with a basic receive signature cr(t), each impulse response cr,nF,nS (t) is chosen as cr,nF,nS (t) = cr (t − (nS − 1)Ts) exp (j2π (nF − 1) Ft) , (3.16) in analogy to (3.7). In the special case of OFDM cr(t) = 1 √ Ts − Th rect −t − Th Ts − Th − 1 2 (3.17) holds. With the basic receive signature cr(t) of (3.17) and the subcarrier spacing F of (3.8), (3.16) becomes cr,nF,nS (t) = 1 √ Ts − Th rect −t − Th − (nS − 1)Ts Ts − Th − 1 2 exp j2π nF − 1 Ts − Th t . (3.18) In OFDM systems each impulse response cr,nF,nS (t) of (3.18) is matched to the part (nS − 1)Ts − Th ≤ t ≤ nSTs of the combined impulse response b(kI,kO) nF,nS of (3.12) of duration Ts − Th. As it will be shown in what follows, during the aforementioned time interval, for a given input kI, the combined impulse responses b(kI,kO) nF,nS , nF = 1 . . .NF, nS = 1 . . . NS, of (3.18) are orthogonal. With the time-continuous received signal e(kO) (t) of (3.13), the impulse responses cr,nF,nS (t), nF = 1 . . . NF, nS = 1 . . . NS, (3.19) of (3.16) and the combined impulse responses b(kI,kO) nF,nS (t), nF = 1 . . . NF, nS = 1 . . . NS, kI = 1 . . . KI, (3.20) of (3.12), for the vector output kO of the analysis filter bank e(kO,nF,nS) = ∞ −∞ e(kO) (t)cr,nF,nS (−t)dt = KI kI=1 NF nF=1 NS nS=1 s(kI,nF,nS) ∞ −∞ b (kI,kO) nF,nS (t)cr,nF,nS (−t)dt + n(kO,nF,nS) , nF = 1 . . .NF, nS = 1 . . .NS, (3.21)
- 41. 3.2 Physical transmission model 31 holds. In (3.21) n(kO,nF,nS) = ∞ −∞ n(kO) (t)cr,nF,nS (−t)dt, nF = 1 . . . NF, nS = 1 . . . NS, (3.22) are the NFNS noise values n(kO,nF,nS) , nF = 1 . . . NF, nS = 1 . . . NS, at vector output kO of the physical transmission model, which follow after filtering and sampling of the noise n(kO) (t) of the output kO of the time-continuous MIMO channel. From (3.12), for the combined impulse response b (kI,kO) nF,nS (t) in (3.21), follows b (kI,kO) nF,nS (t) = 0, for t /∈ [(nS − 1)Ts, nSTs + Th] . (3.23) Moreover, in the case of OFDM follows for the impulse response cr,nF,nS (t) of (3.18) cr,nF,nS (t) = 0, for t /∈ [−(nS − 1)Ts − Th, −nSTs] . (3.24) Hence, as a consequence of (3.23) and (3.24), ∞ −∞ b (kI,kO) nF,nS (t)cr,nF,nS (−t)dt = 0, for nS = nS, (3.25) i.e., the received value e(kO,nF,nS) has no contributions from the transmit value s(kI,nF,nS) for nS = nS, which means that transmissions in different symbol slots in OFDM-based MIMO systems are totally independent. With the matrix H(kI,kO) (f) being the result of the Fourier transformation of the impulse re- sponse h(kI,kO) (t), the discrete transfer coefficients h(kI,kO,nF) = ∞ −∞ b(kI,kO) nF,nS (t)cr,nF,nS (−t)dt = Ts − Th Ts Th 0 exp (−j2π(nF − 1)Fτ) h(kI,kO) (τ)dτ, = Ts − Th Ts H(kI,kO) ((nF − 1)F) . (3.26)
- 42. 32 Chapter 3: Modelling of OFDM-based MIMO systems are defined and using (3.8), (3.10), (3.12), (3.18) and (3.26), it follows ∞ −∞ b (kI,kO) nF,nS (t)cr,nF,nS (−t)dt = 1 √ Ts − Th √ Ts Ts Th Th 0 exp (j2π(nF − 1)F(t − τ)) h(kI,kO) (τ)dτ · exp (−j2π(nF − 1)Ft) dt = 1 √ Ts − Th √ Ts Ts Th exp j2π nF − nF Ts − Th t dt · Th 0 exp −j2π nF − 1 Ts − Th τ h(kI,kO) (τ)dτ = h(kI,kO,nF) nF = nF, 0 else, (3.27) i.e., the transmissions in different subcarriers nF and nF in OFDM-based MIMO systems are also totally independent. With the independence of transmissions in different symbol slots of (3.25) and different subcar- riers of (3.27), the expression of (3.21) for the received value e(kO,nF,nS) of the vector output kO of the discrete MIMO channel at subcarrier nF and symbol slot nS using the discrete transfer coefficients h(kI,kO,nF) , kI = 1 . . . KI, of (3.26) is simplified to e(kO,nF,nS) = KI kI=1 s(kI,nF,nS) ∞ −∞ b(kI,kO) nF,nS (t)cr,nF,nS (−t)dt + n(kO,nF,nS) , = KI kI=1 s(kI,nF,nS) h(kI,kO,nF) + n(kO,nF,nS) . (3.28) demonstrating that each received value e(kO,nF,nS) depends solely on the KI transmit values s(kI,nF,nS) , kI = 1 . . . KI, at the same subcarrier nF and symbol slot nS and the said dependence is quantified by the discrete transfer coefficients h(kI,kO,nF) of (3.26). Because at a specific OFDM symbol slot nS each impulse response cr,nF,nS (t) of (3.18) is matched to a section of the combined impulse response b(kI,kO) nF,nS of duration Ts − Th, rather than to the whole combined im- pulse response b(kI,kO) nF,nS of length Ts + Th, the operation of the analysis filter bank is suboptimum with respect to the exploitation of the energy of the time-continuous received signal e(kO) (t) of (3.13) at output kO. This suboptimality is quantified by the energy loss factor Ts − Th Ts < 1. (3.29)
- 43. 3.2 Physical transmission model 33 Moreover, with (3.22), the noise values n(kO,nF,nS) of (3.28) have the correlation E n(kO,nF,nS) n∗(kO,nF,nS) = E ⎧ ⎨ ⎩ ∞ −∞ n(kO) (t1)cr,nF,nS (−t1)dt1 ∞ −∞ n∗(kO) (t2)cr,nF,nS (−t2)dt2 ⎫ ⎬ ⎭ = ∞ −∞ ∞ −∞ E n(kO) (t1)n∗(kO) (t2) cr,nF,nS (−t1)cr,nF,nS (−t2)dt1dt2 = N0 ∞ −∞ cr,nF,nS (t)cr,nF,nS (t)dt = ⎧ ⎨ ⎩ N0 kO = kO, nF = nF, nS = nS 0 else . (3.30) The receiver described by (3.18) and (3.21) corresponds to a conventional OFDM receiver [vNP00]. 3.2.5 Matrix-vector transmission model Due to the independence of transmissions at different subcarriers and symbol slots, a compact subcarrier- and symbol slot wise discrete physical transmission model for OFDM-based MIMO systems is derived. Due to the subcarrier- and symbol slot wise investigation, the transmission over each of the NFNS independent KO × KI discrete MIMO channels is modelled separately. To this end, the transmit vector s(nF,nS) = s(1,nF,nS) . . . s(KI,nF,nS) T (3.31) of dimension KI is formed, containing the KI transmit values s(kI,nF,nS) , kI = 1 . . .KI. More- over, the received vector e(nF,nS) = e(1,nF,nS) . . . e(KO,nF,nS) T (3.32) of dimension KO, and the noise vector n(nF,nS) = n(1,nF,nS) . . . n(KO,nF,nS) T (3.33) of dimension KO, with the autocorrelation matrix Rn = E n(nF,nS) n(nF,nS)∗T = N0 IKO (3.34)
- 44. 34 Chapter 3: Modelling of OFDM-based MIMO systems are defined, containing the KO received values e(kO,nF,nS) , kO = 1 . . .KO, and the KO noise values n(kO,nF,nS) , kO = 1 . . .KO, at subcarrier nF and symbol slot nS, respectively. Moreover, the KIKO transfer coefficients h(kI,kO,nF) , kI = 1 . . . KI, kO = 1 . . . KO, of (3.26) are compiled in the KO × KI channel matrix H(nS,nF) = ⎛ ⎜ ⎜ ⎜ ⎝ h(1,1,nF) . . . h(KI,1,nF) h(1,2,nF) . . . h(KI,2,nF) ... ... ... h(1,KO,nF) . . . h(KI,KO,nF) ⎞ ⎟ ⎟ ⎟ ⎠ . (3.35) With e(nF,nS) of (3.32), H(nF) of (3.35), s(nF,nS) of (3.31) and n(nF,nS) of (3.33), the transmission model e(nF,nS) = H(nF) s(nF,nS) + n(nF,nS) (3.36) for subcarrier nF and symbol slot nS for OFDM-based MIMO systems is derived. 3.3 Pre- and post-processing stages 3.3.1 Optimum and suboptimum approaches In what follows, transmissions at an isolated OFDM symbol slot nS are considered, i.e., NS = 1 (3.37) holds and consequently the index nS is hereafter dropped for the sake of simplicity. In terms of the probability of erroneous detection of u(k) , the optimum strategy regarding pre- and post-processing in Fig. 3.1, is the generation of s(kI) directly from all u(k) , k = 1 . . .K, and the detection of u(k) from all e(kO) , kO = 1 . . . KO, in one step, respectively [Mas02]. However, such a strategy may not be followed for reasons such as the high complexity. One important class of suboptimum approaches for the pre-processing stages is characterized by a two-step approach. In a first step, after FEC coding and modulation of the bit vectors u(k) of (3.1), the complex data symbols d(k,nF) ∈ D, nF = 1 . . .NF, k = 1 . . . K, (3.38) taken from the data symbol alphabet D = {d1, . . . , dD} (3.39)
- 45. 3.3 Pre- and post-processing stages 35 of cardinality D result. The K data symbols d(k,nF) , k = 1 . . . K, of (3.38) corresponding to a single subcarrier nF are compiled into the data vector d(nF) = d(1,nF) . . . d(K,nF) T (3.40) of dimension K, and the NF data vectors d(nF) , nF = 1 . . .NF, of (3.40) are stacked to form the total data vector d = d(1)T . . . d(NF)T T . (3.41) In a second step, the transmit vectors s(nF) , nF = 1 . . . NF, of (3.31) are generated from the total data vector d of (3.41). In the corresponding class of suboptimum post-processing stages, the estimates ˆd (nF) = ˆd (1,nF) . . . ˆd (K,nF) T , nF = 1 . . . NF, (3.42) of the data vectors d(nF) , nF = 1 . . . NF, of (3.40), which can be compiled to the total estimated data vector ˆd = ˆd (1)T . . . ˆd (NF)T T , (3.43) are obtained from the received vectors e(nF) , nF = 1 . . .NF, of (3.32). In a second step the estimated data symbols ˆd (k,nF) , k = 1 . . .K, nF = 1 . . . NF, contained in the estimated data vectors ˆd (nF) , nF = 1 . . . NF, of (3.42) are demodulated and FEC decoded to yield the estimated bit vectors ˆu(k) , k = 1 . . .K, of (3.4). 3.3.2 Subcarrierwise pre- and post-processing In Section 3.2 it is shown that a subcarrierwise model can be used to model the physical trans- mission in an OFDM-based MIMO system. As transmissions at different subcarriers are inde- pendent of each other [vNP00], the subcarrierwise investigation followed in the physical trans- mission model, under certain circumstances can be extended to the pre- and post processing stages. In particular, if the post-processing stage in an OFDM-based MIMO system operates in a subcarrierwise fashion, then also the pre-processing stage can be implemented in a subcarri- erwise manner, without loss of performance. Equivalently, if subcarrierwise pre-processing is applied at the pre-processing stage then the post-processing stage can operate in a subcarrier- wise fashion. In the case that both pre- and post-processing can be performed in a subcarrierwise fashion, an OFDM-based MIMO system employing transmission over NF subcarriers can be considered as NF independent smaller multiuser OFDM-based MIMO systems. Moreover, given the usually large number of subcarriers to be used in future mobile radio systems [vNP00], subcarrierwise pre- and post-processing techniques, if applicable, prove to be especially attractive in terms of computational complexity [SWBC02].
- 46. 36 Chapter 4: Uplink transmission in the service area concept 4 Uplink transmission in the service area concept 4.1 Transmission model In this Chapter, the model of the UL with JD in a SA-based mobile radio system employing OFDM is described. Fig. 4.1 illustrates a SA in the UL transmission. CU AP 1 AP 2 AP KB MT 1 MT 2 MT K d(1,nF) d(2,nF) d(K,nF) ˆd (1,nF) ˆd (2,nF) ˆd (K,nF) Figure 4.1. SA in UL transmission at subcarrier nF, consisting of a CU, K MTs and KB APs The SA of Fig. 4.1 consists of K MTs, KB APs and one CU. The K MTs and the KB APs are equipped each with a single omnidirectional antenna. As stated in Chapter 3, a subcarrierwise physical transmission model can be used. At a certain subcarrier nF, UL transmission in a SA-based system takes place over a MIMO channel with KI = K (4.1) inputs and KO = KB (4.2)
- 47. 4.1 Transmission model 37 outputs. It is assumed that all transfer factors h(k,kB,nF) , k = 1 . . .K, kB = 1 . . .KB, and hence the KB × K transfer matrix H(nF) of (3.35), are exactly known at the CU. Each MT k applies FEC coding on the bit vector u(k) of (3.1) to yield the coded bit vector d(k) = d (k) 1 . . . d (k) M T (4.3) of dimension M. After modulation of the coded bit vector d(k) of (4.3), NF complex data symbols d(k,nF) , nF = 1 . . .NF, result per MT k. The K complex data symbols d(k,nF) , k = 1 . . .K, sent by all the K active MTs at the considered subcarrier nF, are compiled in the data vector d(nF) of (3.40) of dimension K. The MTs are simple OFDM transmitters, employing no pre-processing, i.e., s(nF) = d(nF) (4.4) holds for the transmit signal vector s(nF) of (3.31). With (4.4) and using the KB × K transfer matrix H(nF) of (3.35), the noise vector n(nF) of (3.33) of dimension KB representing inter-SA interference, the expression (3.36) for the received vector e(nF) of dimension KB containing the KB received values e(kB,nF) , kB = 1 . . .KB, at the KB APs at subcarrier nF, becomes e(nF) = H(nF) d(nF) + n(nF) (4.5) for the case of the UL in a SA-based system employing OFDM. With the total data vector d = d(1)T . . . d(NF)T T (4.6) of dimension KNF, the KBNF × KNF total transfer matrix H = ⎛ ⎜ ⎜ ⎜ ⎝ H(1) 0 . . . 0 0 H(2) . . . 0 ... ... . . . ... 0 0 . . . H(NF) ⎞ ⎟ ⎟ ⎟ ⎠ , (4.7) and the total noise vector n = n(1)T . . . n(NF)T T (4.8) of dimension KBNF, the expression for the total received vector e = e(1)T . . . e(NF)T T (4.9) of dimension KBNF becomes e = H d + n. (4.10) The expression of (4.10) represents the total transmission model for the UL in a SA-based system.
- 48. 38 Chapter 4: Uplink transmission in the service area concept As can be seen from (4.5) and (4.10), each received value e(kB,nF) contains contributions from all K data symbols d(k,nF) , k = 1 . . . K, sent at the corresponding subcarrier nF. In SA- based systems, JD is the post-processing algorithm in the CU and the task of JD is to obtain an estimate ˆd (k,nF) for each data symbol d(k,nF) . From the viewpoint of JD, (4.10) represents NF independent linear systems of equations, each with KB equations and K unknowns. In other words, in each of the NF linear equation systems, K data symbols d(k,nF) , k = 1 . . .K, have to be jointly detected from the KB received values e(kB,nF) , kB = 1 . . .KB, of (4.5) available to the CU. Such a detection becomes feasible only if KB ≥ K (4.11) holds, i.e., only if each of the NF systems of equations is not underdetermined. In the following algorithms for JD are presented, with the aid of which the spatial receive diversity inherent in the UL transmission of SA-based systems is exploited, i.e., the signals received at the KB APs are combined targeting at the suppression of the interference between the useful received signals of the active MTs. 4.2 Optimum joint detection 4.2.1 Approaches to optimum post-processing The approach regarding the post-processing stage at the CU which is optimum with respect to the erroneous decision for the bit u (k) l , is a JD algorithm which, given the total received vector e of (4.10), yields the estimate ˆu (k) l with the maximum a posteriori probability P ˆu (k) l |e under consideration of the modulation constellation D and the FEC code, i.e., ˆu (k) l = arg max ˆu (k) l ∈{+1,−1} P ˆu (k) l |e , k = 1 . . .K, l = 1 . . . L, (4.12) holds [Ver86a, Ver86b, Ver98]. However, given practical parametrization of multiuser mobile radio systems, the detector described by (4.12) is not realizable in multiuser scenarios due the high complexity. In what follows, only JD algorithms are considered which correspond to suboptimum, relative to (4.12), approaches, in which estimates ˆd (k,nF) of the data symbols d(k,nF) are obtained in an intermediate step in the JD process, as described in Section 3.3.1. Hence, the term optimum JD is used hereafter to refer to JD algorithms which are optimum with respect to the probability of erroneous detection of the total data vector d of (3.41). As described in Section 3.2, each
- 49. 4.2 Optimum joint detection 39 received value e(kB,nF) contains no contributions from data symbols d(k,nF) sent at subcarrier nF = nF, and therefore optimum JD in a SA-based system can be performed in a subcarrierwise fashion, i.e., optimum JD of the data vector d(nF) of (3.40) from the received vector e(nF) of (3.32) can be performed for each subcarrier nF, nF = 1 . . . NF, separately [SWBC02]. 4.2.2 Maximum a posteriori joint detection The optimum approach for JD with respect to the probability of erroneous detection of the data vector d(nF) of (3.40) is JD performed according to the MAP principle [Ver86a]. Given the received vector e(nF) of (4.5) and the cardinality D of the data symbol alphabet D of (3.39), from the DK possible data vectors ˆd (nF) ∈ DK the data vector ˆd (nF) yielding the maximum a posteriori probability P ˆd (nF) |e(nF) is chosen as the estimate ˆd (nF) = arg max ˆd (nF) ∈DK P ˆd (nF) |e(nF) (4.13) according to optimum JD. 4.2.3 Maximum likelihood joint detection With the conditional probability density function p e(nF) | ˆd (nF) of the received vector e(nF) of (4.5), the probability density function p e(nF) of the received vector e(nF) of (4.5) and the a priori probability P ˆd (nF) of the data vector ˆd (nF) , the Bayes rule [Pap00] can be applied on the a posteriori probability P ˆd (nF) |e(nF) of the data vector ˆd (nF) of (3.40), to yield P ˆd (nF) |e(nF) = 1 p (e(nF)) p e(nF) | ˆd (nF) P ˆd (nF) . (4.14) If the data vectors ˆd (nF) in (4.14) are equiprobable, the probability P ˆd (nF) plays no role in the maximization process of (4.13). Moreover, the probability density function p e(nF) of the received vector e(nF) in (4.14) is independent of the considered vector d(nF) and can therefore be omitted in the maximization process. Hence, in the case of equiprobable data vectors ˆd (nF) the maximization of the a posteriori probability P ˆd (nF) |e(nF) in (4.13) is equivalent with the maximization of the likelihood function p e(nF) | ˆd (nF) due to (4.14), and the MAP detector of (4.13) becomes the ML detector [Ver98] ˆd (nF) = arg max ˆd (nF) ∈DK p e(nF) | ˆd (nF) . (4.15)
- 50. 40 Chapter 4: Uplink transmission in the service area concept For the case of zero-mean, Gaussian distributed and uncorrelated noise values n(kB,nF) , kB = 1 . . .KB, with variance σ2 of real and imaginary parts, for the likelihood function p e(nF) |ˆd (nF) = 1 (πσ2)KB exp − 1 σ2 e(nF) − H(nF)ˆd (nF) 2 (4.16) follows and ML JD of (4.15) takes the simplified form ˆd (nF) = arg min ˆd (nF) ∈DK e(nF) − H(nF)ˆd (nF) 2 . (4.17) 4.2.4 Complexity of optimum joint detection In order to detect all NF data vectors d(nF) , nF = 1 . . .NF, both MAP JD of (4.13) and ML JD of (4.15) involve in total NF exhaustive search processes among the set DK of cardinality DK . As the aforementioned search is the complexity dominating process, the computational complexity of subcarrierwise optimum JD is O NF DK . If subcarrierwise optimum JD were not possible, exhaustive search among all elements of the set DKNF of cardinality DKNF would have to be performed in order to detect the total data vector d ∈ DKNF and the complexity of such a detection would be O DKNF . Hence, O NF DK O DKNF (4.18) readily holds. The decisive reduction in computational complexity needed to perform optimum JD in OFDM-based MIMO systems is clear. Hence, from (4.18), the application of optimum JD in the form of MAP or ML JD can be considered in OFDM-based MIMO systems, e.g., in SA-based systems. 4.3 Linear joint detection 4.3.1 General model of linear joint detection Despite of the reduction in the computational complexity of optimum JD achieved thanks to the subcarrierwise detection in SA-based systems, the computational complexity due to the exhaus- tive search involved in both MAP and ML JD may still be undesired. Representing a trade-off between probability of erroneous decision for d(nF) and complexity, linear JD algorithms yield
- 51. 4.3 Linear joint detection 41 the estimate ˆd (nF) of d(nF) through a linear transformation of the received vector e(nF) . There- fore, linear JD algorithms can be described by a K × KB demodulator matrix D(nF) as ˆd (nF) = D(nF) e(nF) . (4.19) As (4.19) shows, in contrast to MAP JD of (4.13) and ML JD of (4.15) in linear JD the knowl- edge concerning the modulation constellation D is not exploited, i.e., ˆd (nF) ∈ CK follows for the estimated data vector ˆd (nF) obtained by linear JD as shown in (4.19). Depending on the criterion which ˆd (nF) of (4.19) should satisfy, there exist numerous possibili- ties for the choice of the demodulator matrix D(nF) . In the following, the cases of RxZF JD and MMSE JD are considered. 4.3.2 Receive zero-forcing joint detection According to the RxZF criterion, with the received vector e(nF) of (3.36) and the transfer matrix H(nF) of (3.35), the estimate ˆd (nF) of the data vector d(nF) minimizes the Euclidean distance e(nF) − H(nF)ˆd (nF) 2 , or in other words, the estimated data vector ˆd (nF) is chosen, from which the reconstructed received vector H(nF)ˆd (nF) with the minimum Euclidean distance to the received vector e(nF) results. The criterion of RxZF JD is expressed as [KB92, KB93, Kle96, BFKM93, FKB94, LV90] ˆd (nF) = arg min ˆd (nF) ∈CK e(nF) − H(nF)ˆd (nF) 2 . (4.20) Comparing (4.17) and (4.20) it follows that in the case of zero-mean Gaussian noise, ML JD and the RxZF JD have similar criteria. The difference between ML JD and the RxZF JD is that the estimated data symbols ˆd (k,nF) , k = 1 . . .K, of (4.20) of RxZF JD can take any continuous value from C, whereas the estimates ˆd (k,nF) , k = 1 . . . K, of ML JD of (4.17) can only take the D discrete values of D. With the received vector e(nF) of (3.36), the transfer matrix H(nF) of (3.35), the expression ˆd (nF) = H(nF)∗T H(nF) −1 H(nF)∗T D (nF) RxZF e(nF) (4.21) for the estimated data vector ˆd (nF) of RxZF JD follows from (4.20). As (4.21) shows, D (nF) RxZF is the left side pseudoinverse of the channel matrix H(nF) . Moreover, for deterministic H(nF) and random n(nF) , the estimated data vector ˆd (nF) of (4.21) of RxZF JD satisfies E ˆd (nF) = d(nF) , (4.22)
- 52. 42 Chapter 4: Uplink transmission in the service area concept i.e., RxZF JD delivers unbiased estimates ˆd (k,nF) , k = 1 . . .K, of the data symbols d(k,nF) , k = 1 . . .K, eliminating all intra-SA interference. As opposed to RxZF JD for CDMA systems [KB92, KB93, Kle96, BFKM93] by which MTs in a cell are separated based on their channel signatures and CDMA codes, RxZF JD in SA- based systems eliminates intra-SA interference using only the channel signatures of the K MTs inherent in the transfer matrix H(nF) . Due to the spatial separation of the APs the transfer matrix H(nF) has, if special cases are not considered, full rank and can be used for the spatial separation of the MTs. 4.3.3 Minimum mean square error joint detection The criterion which the estimated data vector ˆd (nF) of MMSE JD satisfies is the MMSE error min E d(nF) − ˆd (nF) 2 , hence for deterministic H(nF) and random n(nF) , the MMSE JD criterion is expressed as [MH94, Gra81, LV89, XSR90, LV90, BFKM93, KKKB94, KKKB96] ˆd (nF) = arg min ˆd (nF) ∈CK E d(nF) − ˆd (nF) 2 . (4.23) With the correlation matrix R (nF) dd = E d(nF) d(nF)∗T (4.24) of the data vector d(nF) , the received vector e(nF) of (3.36), the transfer matrix H(nF) of (3.35) and the variance σ2 of real and imaginary parts of the noise values n(kB,nF) , kB = 1 . . .KB, MMSE JD is expressed as ˆd (nF) = H(nF)∗T H(nF) + σ2 R (nF) dd −1 −1 H(nF)∗T D (nF) MMSE e(nF) . (4.25) From (4.25) it can be seen that MMSE JD of (4.25), unlike RxZF JD of (4.21), does not deliver unbiased estimates. Instead, in the case of the the MMSE JD, as compared to RxZF JD, infor- mation concerning the reliability of the estimated data symbols ˆd (k,nF) is additionally taken into account. In particular, for a low noise power σ2 , the MMSE JD demodulator matrix D (nF) MMSE of (4.25) converges towards the demodulator matrix D (nF) RxZF of (4.21) of RxZF JD but for high noise levels an all-zero estimated vector ˆd (nF) is obtained. In comparison to MMSE JD for CDMA systems [MH94, Gra81, LV89, XSR90, LV90, BFKM93, KKKB94, KKKB96], in which the MMSE criterion of (4.23) is applied in each cell using the channel matrix and the CDMA component, in the case of MMSE JD for SA-based systems only the transfer matrix H(nF) is used to suppress the intra-SA interference.
- 53. 4.4 Iterative joint detection 43 4.4 Iterative joint detection 4.4.1 General model of iterative joint detection JD can also be realized in an iterative fashion [Lam00b, Lam00a, DSR98, PH94, Var95, KIHP90]. The data detection model according to iterative JD is illustrated in Fig. 4.2. As shown in Fig. 4.2, MF bank data estimate refinement and decoding e r ˆd(p) ˆˆd(p)ˆˆd(p − 1) ˆu(p) F R Figure 4.2. Iterative JD model with data estimate refinement in iterative JD the estimate ˆu(p) of the bit vector u is the output of each iteration p, p = 1 . . . P. In order to yield the estimated bit vector ˆu(p) in each iteration p, a refined version ˆˆd(p − 1) of the total estimated data vector ˆd(p − 1) of iteration p − 1 is used to reconstruct the intra-SA interference by the aid of the reverse path matrix R. The reconstructed intra-SA interference R ˆˆd(p − 1) is then subtracted from the output r = H∗T e (4.26) of a MF bank, and after multiplication with the forward path matrix F, the total data vector es- timate ˆˆd(p) results from which the estimated bit vector ˆu(p) follows by means of demodulation and FEC decoding. Due to the iterative character of JD, intra-SA interference is removed by means of subtraction rather than by exhaustive search as in optimum JD in Section 4.2, or by matrix inversion as in linear JD in Section 4.3. As no significant advantage regarding complexity is gained by per- forming iterative JD in a subcarrierwise fashion, nonsubcarrierwise iterative JD is considered. The forward path matrix F and reverse path matrix R used in iterative JD are chosen based on the criteria described in Section 4.4.2. For given forward path matrix F and reverse path matrix
- 54. 44 Chapter 4: Uplink transmission in the service area concept R, iterative JD variants differ in the choice of the data estimate refinement and decoding block. In what follows, four cases of data estimate refinement techniques, by which also decoding is performed, are considered. In cases in which the operation of the described block does not depend on the iteration index p, p is omitted for the sake of simplicity in the following. Finally, considerations are performed for the case of BPSK modulation and can also be directly extended to QPSK modulated data symbols. 4.4.2 Transparent data estimate refinement The most trivial data estimate refinement technique for iterative JD is to perform transparent data estimate refinement as Fig. 4.3 shows, i.e., ˆˆd = ˆd. (4.27) holds. In the case of transparent data estimate refinement, issues regarding the convergence of iterative JD can be analytically investigated. If iterative JD with transparent data estimate refinement converges, then after an infinitely large number of iterations the limiting value of the total estimated data vector ˆd(∞) is obtained. With the forward path matrix F and the reverse path matrix R follows for the limiting value ˆd(∞) of the total estimated data vector ˆd(∞) = F r − F R ˆd(∞) = F−1 + R −1 r. (4.28) Hence, if iterative JD with transparent data estimate refinement converges, then the limiting value ˆd(∞) of the total estimated data vector is equal to the total estimated data vector ˆd of a linear estimator characterized by the demodulator matrix D∞ = F−1 + R −1 H∗T . (4.29) From (4.29) it can be seen that depending on F and R the convergence of iterative JD with transparent data estimate refinement to any desired linear JD scheme can be achieved. For example, with the matrix operator diag (·) returning a matrix with the elements on the main diagonal of its matrix argument, and the operator diag (·) returning a matrix with the offdiagonal elements of its matrix argument, choosing F = diag H∗T H −1 (4.30) and R = diag H∗T H (4.31) it can be achieved that iterative JD with transparent data estimate refinement, if convergent, converges towards RxZF JD.
- 55. 4.4 Iterative joint detection 45 ˆd demod. FEC ˆˆd ˆu Figure 4.3. Data estimate refinement and decoding block of iterative JD with transparent data estimate refinement Until now, the limiting value of iterative JD with transparent data estimate refinement is dealt with. Regarding the criterion of convergence, the spectral radius [Sch88b] λmax (X) of a com- plex matrix X with Q eigenvalues λq, q = 1 . . . Q, is introduced. The spectral radius λmax (X) of X is defined as [Sch88b] λmax (X) = max |λ1|, . . ., |λQ| . (4.32) With the KNF × KNF product F R of the forward path matrix R and reverse path matrix F, it has been shown [TR00] that iterative JD with transparent data estimate refinement converges if λmax (F R) ≤ 1 (4.33) holds, i.e., if all Q eigenvalues λq, q = 1 . . .Q, of F R lie within the bounds of the unity circle around the origin of the complex plane. 4.4.3 Data estimate refinement by hard quantization A first step towards the refinement of the total estimated data vector ˆd is to exploit the knowl- edge of the modulation constellation DKNF in the data estimate refinement process, as Fig. 4.4 shows. In this case, data estimate refinement consists in quantizing the continuous valued elements ˆd (k,nF) of the total estimated data vector ˆd with respect to the modulation constellation D, to yield the total refined estimate ˆˆd = arg min d∈DKNF ˆd − d 2 . (4.34) of the data vector d.
- 56. 46 Chapter 4: Uplink transmission in the service area concept ˆd demod. FEC ˆˆd ˆu Figure 4.4. Data estimate refinement and decoding block of iterative JD with data estimate refinement by hard quantization 4.4.4 Data estimate refinement by soft quantization Data estimate refinement by soft quantization is an improvement of the data estimate refine- ment by hard quantization, in which the reliability of each estimated coded bit ˆd (k) m is taken into account. Fig. 4.5 shows the model for iterative JD with data estimate refinement by soft quantization. ˆd 2 ˆσd 2 σ2 d estimation sign(·) tanh(·/2) mod. demod. FEC ˆˆd ˆu Lˆd|d ˆd (k) m Figure 4.5. Data estimate refinement and decoding block of iterative JD with data estimate refinement by soft quantization Soft quantization is the data estimate refinement technique which minimizes the error [MH97, Lam00b, INF01, WOWB02, MW03] E ˆˆd(k) m − d(k) m 2 ˆd(k) m = ˆˆd(k) m − E d(k) m | ˆd(k) m 2 + var d(k) m | ˆd(k) m . (4.35) The error E ˆˆd (k) m − d (k) m 2 ˆd (k) m of (4.35) becomes minimal if the refined estimate ˆˆd(k) m = E d(k) m | ˆd(k) m (4.36)
- 57. 4.4 Iterative joint detection 47 is chosen. In the case of BPSK, the log-likelihood ratio [Hag97] Ld|ˆd ˆd(k) m = ln ⎛ ⎝ P d (k) m = +1| ˆd (k) m P d (k) m = −1| ˆd (k) m ⎞ ⎠ (4.37) of the a posteriori probabilities P d (k) m = ±1| ˆd (k) m of the coded bit d (k) m is used to complement the hard decision for d (k) m , expressed by the sign of Ld|ˆd ˆd (k) m with reliability information expressed by the magnitude of Ld|ˆd ˆd (k) m [Hag97]. The log-likelihood ratio Ld|ˆd ˆd (k) m of (4.37) can be expressed depending on the conditional probabilities P ˆd (k) m |d (k) m ± 1 of the estimated coded bit ˆd (k) m and on the a priori probabilities P d (k) m = ±1 of the coded bit d (k) m as Ld|ˆd ˆd(k) m = ln ⎛ ⎝ P ˆd (k) m |d (k) m = +1 P ˆd (k) m |d (k) m = −1 ⎞ ⎠ Lˆd|d ˆd(k) m + ln ⎛ ⎝ P d (k) m = +1 P d (k) m = −1 ⎞ ⎠ . (4.38) With (4.37), and assuming that all coded bits d (k) m , k = 1 . . . K, m = 1 . . . M, are equiprobable, i.e. ln ⎛ ⎝ P d (k) m = +1 P d (k) m = −1 ⎞ ⎠ = 0, k = 1 . . .K, m = 1 . . . M, (4.39) holds, P ˆd(k) m |d(k) m = +1 = exp Lˆd|d ˆd(k) m 2 exp Lˆd|d ˆd(k) m 2 + exp − Lˆd|d ˆd(k) m 2 (4.40) and P ˆd(k) m |d(k) m = −1 = exp − Lˆd|d ˆd(k) m 2 exp Lˆd|d ˆd(k) m 2 + exp − Lˆd|d ˆd(k) m 2 (4.41) follow and using (4.40) and (4.41), (4.36) becomes ˆˆd(k) m = tanh ⎛ ⎝ Lˆd|d ˆd (k) m 2 ⎞ ⎠. (4.42)
- 58. 48 Chapter 4: Uplink transmission in the service area concept To calculate the refined estimate ˆˆd (k) m as in (4.42), the log-likelihood ratio Lˆd|d ˆd (k) m , i.e., the probabilities P ˆd (k) m |d (k) m = ±1 , need to be calculated. To accomplish this task, it is assumed that zero-mean additive white Gaussian noise ˜nd with variance σ2 d disturbes the estimated coded bits ˆd(k) m = d(k) m + ˜nd. (4.43) Hence, with the probability density function pˆd ˆd(k) m |d(k) m = ±1 = 1 √ 2πσd exp − 1 2σ2 d ˆd(k) m ∓ 1 2 (4.44) of ˆd (k) m and the corresponding log-likelihood ratio Lˆd|d ˆd(k) m = 2 ˆd (k) m σ2 d , (4.45) the refined estimate ˆˆd(k) m = tanh ˆd (k) m σ2 d (4.46) of the coded bit d (k) m can be calculated from (4.42). Therefore by iterative JD with data estimate refinement by soft quantization, in each iteration intra-SA interference is reconstructed using the refined estimates ˆˆd (k) m , k = 1 . . .K, m = 1 . . .M, of (4.46) of the coded bits d (k) m , k = 1 . . .K, m = 1 . . . M and subsequently subtracted from the output r of the MF bank of (4.26). In the present Section it is shown that the data estimate refinement error E ˆˆd (k) m − d (k) m 2 ˆd (k) m of (4.35) is minimized if the continuous valued refined estimate ˆˆd (k) m of (4.46) is used for the discrete valued coded bit d (k) m ∈ {−1, +1}. 4.4.5 Optimum data estimate refinement — turbo multiuser data detec- tion The data estimate refinement techniques described in Sections 4.4.3 and 4.4.4 are based on quantization, i.e., on the exploitation of information regarding the modulation alphabet D. As by means of FEC coding, information concerning one bit u (k) l , is spread over more than one coded bit estimate ˆd (k) m , any approach not exploiting this knowledge is in its nature suboptimum. A data estimate refinement and decoding block in which the refined estimated vector ˆˆd is gained by means of optimum MAP evaluation of the FEC code is shown in Fig. 4.6.
- 59. 4.4 Iterative joint detection 49 ˆd 2 ˆσd 2 σ2 d estimation sign(·) tanh(·/2) mod. MAP demod. FEC ˆˆd ˆu Lˆd|d ˆd (k) m Ld|ˆd ˆd(k) Lu|ˆd ˆd(k) Figure 4.6. Data estimate refinement and decoding block of iterative JD with optimum data estimate refinement The criterion of optimum data estimate refinement is similar to the criterion of (4.35) of data estimate refinement with soft quantization. In particular, using the estimate ˆd(k) = ˆd (k) 1 . . . ˆd (k) M T , (4.47) of the coded bit vector d(k) of (4.3), the exploitation of the FEC code knowledge in the case of optimum data estimate refinement alters (4.35) to the criterion [WOWB02] E ˆˆd(k) m − d(k) m 2 ˆd(k) = ˆˆd(k) m − E d(k) m |ˆd(k) 2 + var d(k) m |ˆd(k) (4.48) of optimum data estimate refinement. By exploiting knowledge concerning FEC coding, not just a single estimated coded bit ˆd (k) m as in (4.35), but the whole coded estimated bit vector ˆd(k) of (4.47) is taken into account. The error E ˆˆd (k) m − d (k) m 2 ˆd(k) of (4.48) becomes minimum if the refined estimates ˆˆd(k) m = E d(k) m |ˆd(k) , k = 1 . . . K, m = 1 . . . M, (4.49) of the coded bits ˆˆd (k) m , k = 1 . . .K, m = 1 . . . M, are chosen by the refinement procedure. If BPSK is used, the log-likelihood ratio Ld|ˆd ˆd(k) = ln ⎛ ⎝ P d (k) m = +1|ˆd(k) P d (k) m = −1|ˆd(k) ⎞ ⎠ (4.50) of the a posteriori probabilities P d(k) m = ±1|ˆd(k) = d(k)|d(k)∈DK∧d (k) m =±1 P ˆd(k) |d(k) (4.51) can be used, from which with (4.50), the refined estimate ˆˆd(k) m = tanh ⎛ ⎝ Ld|ˆd ˆd(k) 2 ⎞ ⎠ (4.52)
- 60. 50 Chapter 4: Uplink transmission in the service area concept of each coded bit d (k) m can be calculated. An algorithm with the aid of which the log-likelihood ratios Ld|ˆd ˆd(k) , k = 1 . . . K, m = 1 . . .M, of (4.50) can be calculated is the Bahl Cocke Jelinek Raviv (BCJR) algorithm [BCJR74]. The BCJR algorithm is a soft-input-soft-output MAP symbol by symbol detector, which takes the log-likelihood ratios Lˆd|d ˆd (k) m , k = 1 . . .K, m = 1 . . .M, as inputs. At its output the BCJR algorithm provides the log-likelihood ratios Ld|ˆd ˆd(k) , k = 1 . . . K, m = 1 . . .M, of (4.50) from which the refined estimates ˆˆd (k) m , k = 1 . . . K, m = 1 . . . M, of the coded bits d (k) m , m = 1 . . . M, k = 1 . . .K, can be calculated according to (4.52), and Lu|ˆd ˆd(k) , k = 1 . . .K, from which the estimates ˆu (k) l = sign Lu|ˆd ˆd(k) , l = 1 . . .L, k = 1 . . . K, (4.53) of the bits u (k) l , l = 1 . . . L, k = 1 . . . K, can be calculated by means of hard quantization as Fig. 4.6 shows, i.e., the BCJR algorithm also performs FEC decoding [BCJR74]. With a closer look at Figs. 4.2 and 4.6, one can see that the iterative JD detector with optimum data estimate refinement by means of FEC coding evaluation is comprised of two parts. The part evaluating the FEC code, see Fig. 4.6, and the remaining part performing multiuser detection, see Fig. 4.2. In contrast to serial multiuser detection schemes, the two parts of the iterative JD detector of 4.2 and Fig. 4.6 exchange soft information. Hence, iterative JD with optimum data estimate refinement by means of FEC coding evaluation is a multiuser detector following the turbo principle [Hag97, Poo00]. It is therefore shown how turbo multiuser detection [Hag97, Poo00] can be used as an iterative JD algorithm in the CU in SA-based systems. From the said employment of iterative JD with optimum data estimate refinement, knowledge concerning the FEC code additionally to the knowledge of the spatial signatures of the MTs, contained in the total transfer matrix H, is exploited to combat intra-SA interference in an efficient way and to provide a high spectrum capacity ηc of (1.1) in SA-based systems.
- 61. 51 5 Downlink transmission in the service area con- cept 5.1 Transmission model After having dealt with the UL with JD in Chapter 4, the modelling of the DL with JT forms the topic of the present Chapter. In Fig. 5.1 a SA with a CU, KB APs and K MTs in DL transmission is illustrated. CU AP 1 AP 2 AP KB MT 1 MT 2 MT K d(1,nF) d(2,nF) d(K,nF) ˆd (1,nF) ˆd (2,nF) ˆd (K,nF) Figure 5.1. SA in DL transmission at subcarrier nF, consisting of a CU, K MTs and KB APs The transmission model for the DL can be derived in a subcarrierwise fashion, following the argumentation of Chapter 3. At a specific subcarrier nF, K data symbols d(k,nF) , k = 1 . . .K, have to be sent from the core network to the K MTs. From the K data symbols d(k,nF) , k = 1 . . . K, contained in the data vector d(nF) of (3.40), KB AP-specific transmit val- ues s(kB,nF) , kB = 1 . . . KB, contained in the transmit vector s(nF) of (3.31) are generated by the CU, and are fed into the MIMO channel of the SA with KI = KB (5.1)
- 62. 52 Chapter 5: Downlink transmission in the service area concept inputs and KO = K (5.2) outputs. If TDD is employed and the time elapsing between UL and DL transmission is sufficiently smaller than the coherence time of the wireless channel of the SA, reciprocity characterizes the channels of UL and DL. Therefore, as the KB × K transfer matrix H(nF) is used in the physical transmission model for the UL of (4.10), the K ×KB transfer matrix H(nF)T is used to model the physical transmission in the DL. Furthermore, it is assumed that all transfer factors h(k,kB,nF) , k = 1 . . .K, kB = 1 . . . KB, and hence the K × KB transfer matrix H(nF)T are exactly known to the CU. With the transmit vector s(nF) of (3.31) of dimension KB, the K × KB transfer matrix H(nF)T and the noise vector n(nF) of (3.33) of dimension K, the expression for the received vector e(nF) = H(nF)T s(nF) + n(nF) (5.3) of (3.32) of dimension K at subcarrier nF follows. Furthermore, using the total transmit vector s = s(1)T . . . s(NF)T T (5.4) of dimension KBNF, the KNF × KBNF total transfer matrix HT and the total noise vector n = n(1)T . . . n(NF)T T (5.5) of dimension KNF, (5.3) can be extended to include transmissions at all NF subcarriers yielding the total received vector e = HT s + n (5.6) of dimension KNF. Each MT k, k = 1 . . .K, contains a simple OFDM receiver employing no post-processing, taking the received value e(k,nF) as the estimated data symbol ˆd (k,nF) , i.e., the expression ˆd (nF) = e(nF) (5.7) describes the function of the K MTs as receivers. Under consideration of (5.7), the crux of JT consists in generating at each subcarrier nF the KB transmit values s(kB,nF) , kB = 1 . . .KB, jointly for all K MTs. As is the case in the UL transmission, it is assumed that KB ≥ K (5.8)
- 63. 5.2 Optimum joint transmission 53 holds, i.e., each of the NF systems of equations for determining the KB transmit values s(kB,nF) , kB = 1 . . .KB, from the K data symbols d(k,nF) , k = 1 . . . K, is underdetermined. By the employment of the JT algorithms presented in the following, the spatial transmit diversity in the DL transmission of SA-based systems is exploited and such transmit signals are generated by JT by the transmission of which interference between the active MTs is suppressed. 5.2 Optimum joint transmission 5.2.1 Introduction In the present Section, a novel nonlinear JT scheme is presented, which is optimum with re- spect to the average bit error probability P (nF) b at the MTs. In contrast to approaches to a minimum BER transmission for the DL of state-of-the-art CDMA mobile radio systems, see, e.g., [IRF03], a flexible and compact model characterizes the optimum nonlinear JT scheme for SA-based systems, due to the fact that optimum JT can be performed in a subcarrierwise fash- ion. In what follows, the term optimum JT is used to denote JT which is optimum in the sense of the average bit error probability P (nF) b at the MTs. For the sake of simplicity, investigations are carried out using real signals. The extension to complex valued signals is straightforward and can be performed by considering the real valued equivalent isomorphic form of the complex signals [ZF86]. With respect to the average bit error probability P (nF) b the transmission of data vectors d(nF) , d(nF) ∈ DK , where the data vector d(nF) is a rotated version of the data vector d(nF) , is equivalent, which means that the investigation of both data vectors d(nF) and d(nF) in terms of the average bit error probabilityP (nF) b is redundant. Equivalently, the set DK of the data vectors contains V effective data vectors d(nF) v , v = 1 . . .V , which contribute to the average bit error probability P (nF) b and DK − V data vectors which result from the V effective data vectors d(nF) v , v = 1 . . .V , by means of a rotation operation and do not contribute to the average bit error probability P (nF) b . Hence, for the purposes of investigation of the average bit error probability P (nF) b , it suffices to consider the set DK eff = d (nF) 1 , . . . , d (nF) V ⊂ DK (5.9) of effective data vectors d(nF) v , v = 1 . . . V , of cardinality V instead of the set DK of cardinality DK . For a given modulation scheme the choice of the effective data vectors d(nF) v ∈ DK eff is not unique, whereas the cardinality V of the set DK eff of (5.9) of effective data vectors is fixed. In this thesis, optimum JT with BPSK is investigated, i.e., D = {+1, −1} (5.10)
- 64. 54 Chapter 5: Downlink transmission in the service area concept holds, and the set DK eff of (5.9) of effective data vectors has the cardinality DK eff = V = 2K−1 . (5.11) The task of optimum JT is to determine for each subcarrier nF an effective transmit vector s (nF) v of dimension KB for each effective data vector d(nF) v of (5.9) of dimension K which, given a specific scenario, results in the minimum possible average bit error probability P (nF) b at the MTs. With the set S (nF) eff = s (nF) 1 , . . . , s (nF) V (5.12) of effective transmit vectors s (nF) v , v = 1 . . .V , of cardinality V and the set DK eff of (5.9) of effective data vectors, JT is described with a mapping function f(nF) : DK eff −→ S (nF) eff (5.13) with which the set DK eff of (5.9) of effective data vectors is mapped to the set S (nF) eff of (5.12) of effective transmit vectors. In the case of optimum JT, the mapping function f (nF) of (5.13) is nonlinear in contrast to linear JT schemes in the case of which f (nF) is linear. In order to investigate optimum JT, a novel parameterized representation of JT transmit signals for the case of BPSK is developed and presented in this Chapter. It is shown that in the con- sidered model, the average bit error probability P (nF) b is a function of the parameters describing the transmitted signal and that the parameter set corresponding to optimum JT results after nu- merical minimization. For the considerations concerning optimum JT, DL transmission without FEC coding is considered and therefore optimum JT is derived in a subcarrierwise fashion. 5.2.2 Transmit energy strategies Two different strategies concerning the transmit energy T (nF) tot,v = 1 2 s(nF) v ∗T s(nF) v (5.14) of each effective transmit vector s (nF) v can be followed, namely • fixed transmit energy T (nF) tot,v and • variable transmit energy T (nF) tot,v .
- 65. 5.2 Optimum joint transmission 55 With the V transmit energies T (nF) tot,v , v = 1 . . . V , of (5.14), the transmit energy T per data symbol and the number K of MTs, it is assumed that the average energy T (nF) tot,v = 1 V V v=1 T (nF) tot,v = KT (5.15) is fixed. According to the fixed transmit energy strategy, each effective transmit vector s (nF) v has a fixed given transmit energy T (nF) tot,v = KT. (5.16) On the other hand, in the case of the variable transmit energy strategy, the transmit energy T (nF) tot,v 1 2 3 4 0 1 2 3 4 5 6 T (nF) tot,v v Figure 5.2. Exemplary case for the energy T (nF) tot,v of each effective transmit vector s (nF) v , v = 1 . . .V , as a function of v, according to the variable transmit energy strategy (black bars) and fixed transmit energy strategy (white bars); Parameters: K = 3, T = 1 is fixed only at the average, i.e., the average value T (nF) tot,v of (5.15) is given. Fig. 5.2 illustrates the two strategies for T (nF) tot,v of (5.14) for the case of K = 3 and T = 1. With the vector s (nF) 0,v = s (1,nF) 0,v . . . s (KB,nF) 0,v T (5.17)
- 66. 56 Chapter 5: Downlink transmission in the service area concept of dimension KB, which is normalized as 1 2 s (nF) 0,v ∗T s (nF) 0,v = KT, (5.18) and with the energy factor t (nF) v , the effective transmit vector s (nF) v is expressed as s(nF) v = t(nF) v s (nF) 0,v . (5.19) Using (5.14) and (5.18), it can be seen from (5.19) that the energy T (nF) tot,v = t(nF) v 2 KT (5.20) of each effective transmit vector s (nF) v , v = 1 . . . V , is completely determined by the energy factor t (nF) v . For example, it can be deduced from (5.16) and (5.20) that the fixed transmit energy strategy can be realized by setting t(nF) v = 1, v = 1 . . .V. (5.21) 5.2.3 Parameterized representation of JT transmit signals The crux of the parameterized representation of JT signals consists in the expression of the vector s (nF) 0,v of (5.17) and the energy factor t (nF) v in a coordinate system, which is an extension of the spherical coordinate system in multidimensional spaces. The used coordinates are denoted as generalized spherical coordinates. With the KB − 1 angles ϕ (kB,nF) v ∈ [−π, π], kB = 1 . . .KB − 1, and with the dummy angle ϕ(KB,nF) v = 0, (5.22) the KB elements s (kB,nF) 0,v , kB = 1 . . .KB, of the vector s (nF) 0,v of (5.17) can be expressed with the aid of generalized spherical coordinates as s (kB,nF) 0,v = √ 2KT kB−1 kB=1 sin ϕ (kB,nF) v cos ϕ(kB,nF) v , kB = 1 . . . KB. (5.23) Moreover, with the V − 1 angles ϑ (nF) v ∈ [0, π/2], v = 1 . . . V − 1, and the dummy angle ϑ (nF) V = 0, (5.24) follows for the energy factor t(nF) v = √ V v−1 v =1 sin ϑ (nF) v cos ϑ(nF) v . (5.25)
- 67. 5.2 Optimum joint transmission 57 Using s (kB,nF) 0,v of (5.23) and t (nF) v of (5.25) follows from (5.19) that the set S (nF) eff of effective transmit vectors s (nF) v , v = 1 . . .V , and hence a given JT scheme, is fully described by the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . . KB − 1, v = 1 . . .V , and the V − 1 angles ϑ (nF) v , v = 1 . . .V − 1. For KB = 2 (5.26) and KB = 3 (5.27) the used generalized spherical coordinates are equivalent to polar and spherical coordinates, respectively. In the case of fixed transmit energy strategy, Figs. 5.3 and 5.4 and illustrate the constraint of (5.16) for the transmit energy T (nF) tot,v of the effective transmit signal vector s (nF) v in a geometric fashion. In particular, Fig. 5.3 shows that in the case of (5.26) s (nF) v lies on the periphery of the unity circle whereas according to Fig. 5.4, if (5.27) holds, s (nF) v lies on the surface of the unity sphere. 2 √ T sin ϕ (1,nF) v s (nF) v 2 √ T ϕ (1,nF) v s (1,nF) v s (2,nF) v 2 √ T cos ϕ (1,nF) v Figure 5.3. Representation of the energy constraint for the effective transmit vector s (nF) v ; Pa- rameters: KB = 2, K = 2, fixed transmit energy strategy Equivalently, the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . . KB − 1, v = 1 . . .V , and the V − 1 angles ϑ (nF) v , v = 1 . . . V −1, corresponding to a given JT scheme can be calculated from given
- 68. 58 Chapter 5: Downlink transmission in the service area concept effective transmit signal vectors s (nF) v . Introducing the four-quadrant arcus tangent function arctan2(x, y) = ⎧ ⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎩ arctan x y for y ≥ 0, arctan x y + π for y < 0, x > 0, arctan x y − π for y < 0, x < 0, , (5.28) using (5.19) and (5.23), the (KB − 1)V angles ϕ(kB,nF) v = arctan2 s(kB+1,nF) v , cos ϕ(kB+1,nF) v s(kB,nF) v , kB = KB − 1 . . .1, v = 1 . . .V, (5.29) and with T (nF) tot,v , v = 1 . . .V , of (5.20) the V − 1 angles ϑ(nF) v = arctan2 ⎛ ⎝ V v =v+1 T (nF) tot,v , T (nF) tot,v ⎞ ⎠, v = 1 . . . V − 1, (5.30) can be calculated from given effective transmit signal vectors s (nF) v , v = 1 . . .V . √ 6T sin ϕ (1,nF) v sin ϕ (2,nF) v √ 6T cos ϕ (1,nF) v s (nF) v ϕ (1,nF) v √ 6T sin ϕ (1,nF) v cos ϕ (2,nF) v s (2,nF) v s (1,nF) v s (3,nF) v ϕ (2,nF) v Figure 5.4. Representation of the energy constraint for the effective transmit vector s (nF) v ; Pa- rameters: KB = 3, K = 3, fixed transmit energy strategy
- 69. 5.2 Optimum joint transmission 59 5.2.4 Optimization The effective received vector e(nF) v = e(1,nF) v . . . e(K,nF) v T (5.31) of dimension K is introduced, which contains the K effective received values e (k,nF) v , k = 1 . . .K, received by each MT k, k = 1 . . . K. With the effective transmit vector s (nF) v of dimension KB, the K × KB channel transfer matrix H(nF)T , and the noise vector n(nF) of dimension K, e(nF) v = H(nF)T s(nF) v + n(nF) (5.32) follows for the effective received vector e (nF) v . In (5.32) it is assumed that the noise values n(k,nF) , k = 1 . . .K, are zero-mean Gaussian distributed random variables with variance σ2 . In the case of BPSK, the MTs contain only quantizers, and therefore with the cardinality V of DK eff of (5.9), the number K of MTs, and with the effective received value e (k,nF) v , the bit error probability P (k,nF) b,v = 1 2 erfc ± e (k,nF) v √ 2σ (5.33) can be calculated for MT k in the case that the effective data vector d (nF) v is transmitted. More- over, the bit error probability P (nF) b,v = 1 K K k=1 P (k,nF) b,v (5.34) results after averaging of P (k,nF) b,v of (5.33) over all K MTs, and the average bit error probability P (nF) b = 1 V V v=1 P (nF) b,v (5.35) results after averaging of P (nF) b,v of (5.35) over all V effective data vectors d (nF) v ∈ DK eff. The average bit error probability P (nF) b of (5.35) of JT is a real function of the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . . KB − 1, v = 1 . . . V , and the V − 1 angles ϑ (K) v , v = 1 . . .V − 1. Hence, for given DK eff, the mapping function f(nF) leading to the minimum average bit error probability P (nF) b can be determined by means of numerical minimization of P (nF) b of (5.35) with respect to the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . .KB − 1, v = 1 . . .V , and the V − 1 angles ϑ (nF) v , v = 1 . . . V − 1. The resulting s (nF) v,opt ∈ S (nF) eff,opt are the effective transmit vectors of optimum JT. The transmit vectors s (nF) opt comprising the total set S (nF) opt of transmit vectors s (nF) opt of optimum JT follow by corresponding rotation of the transmit vectors s (nF) v,opt ∈ S (nF) eff,opt.
- 70. 60 Chapter 5: Downlink transmission in the service area concept Various numerical minimization algorithms can be applied in order to yield the effective trans- mit vectors s (nF) v,opt of optimum JT. A first approach is the use of methods based on gradient approaches, such as Newton methods [Sto83]. Such minimization algorithms use information concerning the gradient of the objective function to be minimized, and in each iteration the direction of steepest descent is followed to locate the minimum of the objective function. The inverse of the Hessian matrix, needed for the location of the minimum of the objective function, is numerically calculated by Newton methods. In order to avoid the large number of computa- tions involved in the direct numerical calculation of the Hessian matrix, quasi-Newton methods [Bro70, Fle70, Gol70, Sha70] use the observed behavior of the objective function and of its gradient to make an approximation to the Hessian matrix using an appropriate updating tech- nique such as the formula of Broyden [Bro70], Fletcher [Fle70], Goldfarb [Gol70], and Shanno [Sha70] (BFGS). Instead of approximating the Hessian matrix and performing the inversion in a second step, the inverse of the Hessian matrix can be approximated using the formula from Davidon [Dav59], Fletcher and Powell [FP63] (DFP). 5.3 Transmit zero-forcing joint transmission In this Section, TxZF JT is dealt with. With regard to the considerations of Section 5.2, in the case of linear JT the mapping function f(nF) of (5.13) is linear and can be therefore described by a KB × K modulator matrix M(nF) . According to TxZF JT for SA-based systems, the transmit vector s(nF) of dimension KB is generated from the data vector d(nF) of dimension K under consideration of the structure of the K MTs given by (5.7), through a linear transformation [MBW+ 00, Fis02] s(nF) = M(nF) d(nF) . (5.36) In the present thesis, linear JT in the sense of TxZF JT [WMS+ 02, MBW+ 00, WSLW03] is considered. By TxZF JT, intra-SA interference in the DL of SA-based systems is completely eliminated, i.e., using (5.7), in the absence of noise the requirement of an interference free estimate reads ˆd (nF) = d(nF) (5.37) and with (5.6) follows H(nF)T s = d(nF) . (5.38) By posing the requirement of (5.38) on the transmit vector s(nF) of (5.36), given that KB ≥ K, an underdetermined system of K equations and KB unknowns results, which means that there exist infinitely many transmit vectors s(nF) which fulfill the requirement of (5.38), and that an additional requirement should be posed on the transmit vector s(nF) .
- 71. 5.4 Iterative joint transmission 61 With respect to the inter-SA interference in the DL, it is desirable to minimize the total transmit energy T (nF) tot = 1 2 s(nF)∗T s(nF) , (5.39) which is radiated from the investigated SA. Therefore, among all transmit vectors s(nF) which fulfill (5.38), the transmit vector [MBW+ 00, WMS+ 02] s(nF) = H(nF)∗ H(nF)T H(nF)∗ −1 M (nF) TxZF d(nF) (5.40) is used in TxZF JT, which has the least energy T (nF) tot of (5.39) and consequently causes the minimum possible inter-SA interference. As is the case with RxZF JD in the UL transmission, see Section 4.3.2, by TxZF JT intra-SA interference in the DL transmission of SA-based systems is eliminated using only the chan- nel signatures of the MTs in the transfer matrix H(nF)T of the DL transmission, as compared to TxZF JT in CDMA systems by which also the CDMA components are used to eliminate interference in each cell [MBW+ 00, WMS+ 02]. 5.4 Iterative joint transmission Drawing an analogy to iterative JD of Section 4.4, in this Section an iterative JT algorithm is presented. Unlike TxZF JT of Section 5.3, in iterative JT intra-SA interference is mitigated in an iterative fashion, rather than with a direct matrix inversion. Fig. 5.5 shows the model for iterative JT. As shown in Fig. 5.5, using the KNF × KNF forward path matrix F and the KNF × KNF reverse path matrix R, the data vector d of dimension KNF is pre-processed in an iterative way. With the initial value t(0) = 0, (5.41) in each iteration p, p = 1 . . . P, the transformed total data vector t(p) = F (d − R t(p − 1)) (5.42) of dimension KNF is produced, from which the total transmit vector s(p) = H∗ t(p) (5.43) of dimension KBNF is generated.
- 72. 62 Chapter 5: Downlink transmission in the service area concept H∗ d s(p)t(p) t(p − 1) F R Figure 5.5. Iterative JT model If iterative JT converges, then for the limiting value of the transformed data vector t(∞) = F (d − R t(∞)) = F−1 + R −1 d. (5.44) holds. Comparing the expression for the convergence value of the transformed data vector t(∞) of (5.44) to the expression (4.28) for the limiting value of the estimated data vector ˆd(∞) of iterative JD, it can be deduced that iterative JT and iterative JD with transparent data estimate refinement are described by the formally equivalent expressions (4.28) and (5.44). Hence, using the results of 4.4.2, with the the forward path matrix F and the reverse path matrix R, it follows that iterative JT converges if and only if for the spectral radius [Sch88b] λmax (F R) of the matrix product F R of dimension KNF × KNF λmax (F R) ≤ 1 (5.45) holds. In the case of convergence, with t(∞) of (5.44) and with the matrix M∞ = H∗ F−1 + R −1 (5.46) of dimension KBNF × KNF, the limiting value of the total transmit vector s(∞) = H∗ F−1 + R −1 d (5.47) is equal to the total transmit vector s = M∞ d (5.48) of a linear JT scheme characterized by the total modulator matrix M∞ of (5.46). For example, choosing F = diag HT H∗ −1 (5.49)
- 73. 5.4 Iterative joint transmission 63 and R = diag HT H∗ (5.50) M∞ of (5.46) becomes M∞ = H∗ HT H∗ −1 (5.51) and therefore the convergence of the transmit vector s(p) of iterative JT towards the transmit vector s of TxZF JT can be achieved.
- 74. 64 Chapter 6: Performance investigation of uplink transmission 6 Performance investigation of uplink transmission 6.1 Preliminary remarks In Chapter 4 the transmission and detection model for the UL in SA-based air interface archi- tectures employing OFDM is presented. The present Chapter deals with the assessment of the performance of the various JD algorithms which are described in Chapter 4. In particular, per- formance measures for JD are introduced and on the basis of these measures, the performance of the various JD algorithms is assessed in a number of different scenarios. In a first step, assumptions are introduced which significantly simplify the expressions that follow. Aspects concerning the performance comparison of SA-based systems employing dif- ferent modulation schemes are not dealt with in the present thesis. Therefore, without loss of generality it is assumed that QPSK modulation is employed. Furthermore, the data symbols d(k,nF) , k = 1 . . .K, transmitted at a specific subcarrier nF in the UL are assumed to be uncorre- lated. With the data vector d(nF) of (3.40) and the K×K identity matrix IK, the aforementioned assumption is expressed by the data correlation matrix R (nF) dd = E d(nF) d(nF)∗T = 2 IK (6.1) of dimension K × K. Finally, Gaussian distributed noise values n(kB,nF) , kB = 1 . . . KB, are assumed and with the variance σ2 of the real and imaginary part of each noise value n(kB,nF) and the KB × KB identity matrix IKB , the noise vector n(nF) of (3.33) is characterized by the noise correlation matrix R(nF) nn = E n(nF) n(nF)∗T = 2σ2 IKB (6.2) of dimension KB × KB. Target of JD in the UL of SA-based systems is the suppression of the interference between the received signals from the K MTs active in the SA. As far as the detection of the data symbol d(k,nF) is concerned, using (6.1), the transfer matrix H(nF) of (3.35), and introducing the operator [·]k,k which is used on a quadratic matrix returning the k-th element of its main diagonal, the price to be paid for the suppression of the intra-SA interference disturbing the partial received signal from MT k at subcarrier nF, is the suboptimum use of the receive energy R(k,nF) = 1 2 E |d(k,nF) |2 H(nF)∗T H(nF) k,k = H(nF)∗T H(nF) k,k , (6.3)
- 75. 6.1 Preliminary remarks 65 resulting from the transmission of data symbol d(k,nF) , when compared to an optimum single user reference system based on matched filtering, in which only the data symbol d(k,nF) is transmitted and hence no need for interference suppression is present. Common to all performance measures for JD introduced in this thesis is the assessment of the said suboptimum use of the receive energy R(k,nF) of (6.3). In particular, with the performance measures for JD introduced in the present Chapter, the use of the receive energy R(k,nF) of (6.3) by JD is assessed on the basis of the SNR of the estimate ˆd (k,nF) of the data symbol d(k,nF) and of the achieved bit error probability P (k,nF) b . Using the matrix operator [·]k which returns the k-th column of its argument as a column vector, in the reference system in which only the data symbol d(k,nF) is transmitted, transmission takes place over the mobile radio channel described by the transfer vector H(nF) k thus yielding the received vector e(nF) = H(nF) k d(k,nF) + n(nF) . (6.4) In terms of the use of the receive energy R(k,nF) of (6.3), in the reference system the optimum approach concerning data estimation is employed, being the use of a filter matched to the chan- nel H(nF) k by which the estimated data symbol ˆd (k,nF) = H(nF) k ∗T e(nF) (6.5) is obtained from the received vector e(nF) of (6.4). In this case, with the variance σ2 of real and imaginary parts of each noise value n(kB,nF) , the maximum possible SNR γ (k,nF) ref = E d(nF) 2 E ˆd (nF) − d(nF) 2 = 1 σ2 H(nF)∗T H(nF) k,k (6.6) and the minimum possible bit error probability P (k,nF) b,ref for given receive energy R(k,nF) of (6.3) is obtained, which in the case of QPSK reads P (k,nF) b,ref = 1 2 erfc 1 2σ2 H(nF)∗T H(nF) k,k . (6.7) Due to the fact that in the reference system a single data symbol d(k,nF) is considered, the performance of the reference system in terms of the bit error probability P (k,nF) b is also referred to as single user bound.
- 76. 66 Chapter 6: Performance investigation of uplink transmission 6.2 Bit error probability 6.2.1 The bit error probability as performance measure In this thesis, the main performance measure used to assess the efficiency with which the re- ceive energy R(k,nF) of (6.3) is used in JD is the bit error probability P (k,nF) b . In particular, using the receive energy R(k,nF) , the receive energy per bit E (k,nF) b corresponding to each of the information bits contained in the QPSK data symbol d(k,nF) is determined and, using the two- sided power spectral density N0/2 of the noise, the corresponding bit error probability P (k,nF) b is simulated for various values of E (k,nF) b /N0. In the case that the performance of JD averaged over a large number of realizations of the mobile radio channel is investigated, the average bit error probability P b is simulated for various values of Eb/N0. The suboptimum use of the receive energy R(k,nF) of (6.3) is expressed using simulations of the bit error probability P (k,nF) b versus E (k,nF) b /N0 through the fact that for a given E (k,nF) b /N0 JD produces a bit error probability P (k,nF) b larger than the bit error probability P (k,nF) b,ref of the reference system. Equivalently, in order to achieve a given bit error probability P (k,nF) b , JD needs a larger E (k,nF) b /N0 as compared to the single user reference system. In the simulation results for the bit error probability P (k,nF) b of JD presented in this Section, also the bit error probability P (k,nF) b resulting from single user estimation in the sense of MF [Ver98] is included for reasons of comparison. With MF, the estimated data symbols ˆd (nF) = diag H(nF)∗T H(nF) −1 H(nF)∗T e(nF) (6.8) are obtained from the received vector e(nF) of (4.5). In the case of single user estimation by MF, the estimated data symbols ˆd (nF) of (6.8) contain intra-SA interference. As intra-SA interfer- ence is a systematic estimation error present even at high E (k,nF) b /N0, the bit error probability P (k,nF) b of MF single user estimation of (6.8) converges, in the majority of cases, to an error floor. 6.2.2 Bit error probability of optimum versus linear joint detection As explained in Section 4.2, the fact that optimum JD can be performed in a subcarrierwise fashion in SA-based OFDM systems, makes the application of optimum JD feasible. Target of the present Section is to investigate the gains achievable with optimum JD as compared to linear JD in SA-based systems quantitatively, in terms of the average bit error probability Pb.
- 77. 6.2 Bit error probability 67 In Figs. 6.1 and 6.2 the average average bit error probability Pb is plotted versus Eb/N0 for the cases of ML JD, compared to RxZF JD and MMSE JD and single user detection in the sense of MF. Following parametrization characterizes the simulations of Figs. 6.1 and 6.2: • KB = 4 APs, • NF = 32 subcarriers, • the COST 207 RA channel model, • W = 14 paths, • a bandwidth of B = 20 MHz, • convolutional FEC code with rate R = 1/2, • FEC code generator matrix 1 0 0 1 1 1 1 1 0 1 , and • hard FEC decoding. The case of K = 2 MTs active in the SA is shown in Fig. 6.1. It can be seen from Fig. 6.1 that ZF JD and MMSE JD result in an average bit error probability Pb very close to the single user bound. In particular, ZF JD and MMSE JD need a 2 dB and 1.4 dB larger Eb/N0, respectively, in order to achieve an average bit error probability Pb = 10−2 as compared to the single user reference system. Moreover, when employing single user detection in the sense of MF a Eb/N0 increased by approximately 14.3 dB relative to the reference system is required to achieve a average average bit error probability Pb = 10−2 . Finally, by optimum JD in the sense of ML JD the increase in the Eb/N0 as compared to the reference system required to obtain an average bit error probability Pb = 10−2 is 0.9 dB. In the case of system load K/KB = 1, i.e., if K = 4 holds, the average bit error probability Pb obtained by optimum JD as compared to linear JD is shown in Fig. 6.2. It can be seen from Fig. 6.2 that by single user detection an error floor is quickly reached and RxZF JD requires a 12.7 dB larger Eb/N0 in order to obtain an average bit error probability Pb = 10−2 . On the other hand, MMSE JD achieves an average bit error probability Pb = 10−2 with a Eb/N0 which is by 6.6 dB larger than the Eb/N0 required by the single user reference system. Finally, in the case of ML JD the increase of the required Eb/N0 as compared to the reference system in order to obtain an average bit error probability Pb = 10−2 is limited to 2.7 dB.
- 78. 68 Chapter 6: Performance investigation of uplink transmission 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 Pb 10 log10 Eb/N0 / dB RxZF JD MF MMSE JD ML JD single user bound Figure 6.1. Average bit error probability P b of optimum JD in the sense of ML JD, MMSE JD and RxZF JD and single user detection by MF with the COST 207 RA channel model; Parameters: K = 2, KB = 4, R = 1/2, NF = 32, W = 14, B = 20 MHz 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 Pb 10 log10 Eb/N0 / dB RxZF JD MF MMSE JD ML JD single user bound Figure 6.2. Average bit error probability P b of optimum JD in the sense of ML JD, MMSE JD and RxZF JD and single user detection by MF with the COST 207 RA channel model; Parameters: K = 4, KB = 4, R = 1/2, NF = 32, W = 14, B = 20 MHz
- 79. 6.2 Bit error probability 69 Summarizing the simulation results concerning the bit error probability performance of opti- mum JD as compared to linear JD shown in Figs. 6.1 and 6.1, in SA-based systems optimum JD is feasible and significant performance gains of up to 10 dB in terms of the required Eb/N0 at a bit error probability P b = 10−2 can be achieved as compared to RxZF JD and MMSE JD in the case of the considered scenarios. Moreover, by comparing Fig. 6.1 to Fig. 6.2, it follows that the application of optimum JD is especially favorable in SA-based systems characterized by high system loads K/KB. For fixed KB, as K increases the number K −1 of partial received signals interfering with the useful signal of a desired MT also increases. In such a case the ex- ploitation of the knowledge concerning the data symbols d(k,nF) , k = 1 . . . K, to be detected by JD, proves to be especially beneficial in terms of the average bit error probability P b. Hence with the aid of ML JD, interference can be combated and a high spectrum capacity ηc of (1.1) can be offered in SA-based systems while a low price is paid in terms of the efficiency of the use of the receive energy R(k,nF) of (6.3), as compared to the case of linear JD in the sense of RxZF JD and MMSE JD. 6.2.3 Bit error probability of iterative joint detection Intra-SA interference can be also mitigated by iterative JD, as shown in Section 4.4, and the target of the present Section is the assessment of the performance of iterative JD as compared to the performance of linear JD in terms of the achievable bit error probability P (k,nF) b . In all simulations concerning the bit error probability P (k,nF) b of iterative JD in this Section, the forward path matrix F = diag H∗T H −1 (6.9) and the reverse path matrix R = diag H∗T H (6.10) are chosen. As shown in Section 4.4, with F of (6.9) and R of (6.10), if iterative JD with transparent data estimate refinement converges, then it converges towards RxZF JD. For this reason, iterative JD is compared to RxZF JD in the following. Finally, the bit error probability performance of single user detection in the sense of MF is provided for reference, because irrespective of the applied data estimate refinement technique, the estimated data vector ˆd(1) in the first iteration of iterative JD is the estimated data vector ˆd of (6.8) obtained with single user detection by MF. In a first step, Figs. 6.3 to 6.6 depict the simulation results of iterative JD in which the FEC code is not evaluated for the data estimate refinement procedure, i.e., iterative JD with trans- parent data estimate refinement, and iterative JD with data estimate refinement by hard and soft quantization is considered. In the simulations of Figs. 6.3-6.6 following parameters are used:
- 80. 70 Chapter 6: Performance investigation of uplink transmission • K = 4 MTs, • KB = 4 APs, • single subcarrier, • single snapshot of the MIMO parametric channel model, • no FEC coding, • P = 5 iterations, • forward path matrix F = diag H∗T H −1 , and • reverse path matrix R = diag H∗T H . Figs. 6.3 and 6.4 show the bit error probability P (1,1) b versus E (1,1) b /N0 of iterative JD with transparent data estimate refinement and of RxZF JD. With the parameter ρ of (2.6) of the MIMO parametric channel model, the cases of ρ = 0.1, (6.11) and ρ = 0.15, (6.12) are considered. If (6.11) holds, it can be seen from Fig. 6.3 that the bit error probability P (1,1) b obtained by iterative JD with transparent data estimate refinement converges to the bit error probability P (1,1) b obtained by RxZF JD. On the other hand, if (6.12) holds, Fig. 6.4 shows that P (1,1) b obtained by iterative JD with transparent data estimate refinement converges slower towards the bit error probability P (1,1) b obtained by RxZF JD as compared to the case of (6.11).
- 81. 6.2 Bit error probability 71 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 E (1,1) b /N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.3. Bit error probability P (1,1) b of iterative JD with transparent data estimate refinement and of RxZF JD and single user detection by MF; Parameters: K = 4, KB = 4, P = 5, no FEC coding, MIMO parametric channel model with ρ = 0.1 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 E (1,1) b /N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.4. Bit error probability P (1,1) b of iterative JD with transparent data estimate refinement and of RxZF JD and single user detection by MF; Parameters: K = 4, KB = 4, P = 5, no FEC coding, MIMO parametric channel model with ρ = 0.15
- 82. 72 Chapter 6: Performance investigation of uplink transmission Setting out from the results of Fig. 6.3, i.e., from the fact that RxZF JD requires only 0.4 dB larger E (1,1) b /N0 than the E (1,1) b /N0 required by the reference system in order to achieve a bit error probability P (1,1) b = 10−3 , it can be deduced that in the case of (6.11), shown in Fig. 6.3, less interference disturbs the useful received signal corresponding to data symbol d(k,nF) , as compared to the case of (6.12) shown in Fig. 6.4. The condition (4.33) for the convergence of iterative JD with transparent data estimate refine- ment can be analytically computed as a function of ρ in the case of the MIMO parametric channel model. Setting β = 2ρ + (K − 2)ρ2 1 + (K − 1)ρ2 , (6.13) from the characteristic polynom |F R − λI| = ((K − 1)β − λ)NF (−1)NF(K−1) (λ + β)NF(K−1) (6.14) follows the eigenvalue λ1 = (K − 1) 2ρ + (K − 2)ρ2 1 + (K − 1)ρ2 (6.15) with multiplicity NF and the eigenvalue λ2 = − 2ρ + (K − 2)ρ2 1 + (K − 1)ρ2 (6.16) with multiplicity NF(K − 1) of the KNF × KNF matrix product F R. From (6.15) and (6.16) the spectral radius λmax (F R) = (K − 1) 2ρ + (K − 2)ρ2 1 + (K − 1)ρ2 (6.17) of F R is obtained and using (4.33), it follows from (6.17) that iterative JD with transparent data estimate refinement in the case of the MIMO parametric channel model converges if ρ < 1 K − 3 2 K − 2 K − 1 − 1 (6.18) holds. In the specific case of K = 4 (6.19) (6.18) yields ρ < 0.155. (6.20)
- 83. 6.2 Bit error probability 73 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 E (1,1) b /N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.5. Bit error probability P (1,1) b of iterative JD with data estimate refinement by hard quantization and of RxZF JD and single user detection by MF; Parameters: K = 4, KB = 4, P = 5, no FEC coding, MIMO parametric channel model with ρ = 0.15 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 E (1,1) b /N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.6. Bit error probability P (1,1) b of iterative JD with data estimate refinement by soft quantization and of RxZF JD and single user detection by MF; Parameters: K = 4, KB = 4, P = 5, no FEC coding, MIMO parametric channel model with ρ = 0.15
- 84. 74 Chapter 6: Performance investigation of uplink transmission Figs. 6.5 and 6.6 show the performance of iterative JD with data estimate refinement by hard and soft quantization, respectively, in the case of the MIMO parametric channel model with ρ = 0.15 (6.21) in terms of the bit error probability P (1,1) b . As shown in Figs. 6.5 and 6.6, convergence is reached by both data estimate refinement techniques and data estimate refinement with hard quantization converges slower than data estimate refinement by soft quantization. Moreover, comparing Figs. 6.5 and 6.6 it can be seen that given a target bit error probability P (1,1) b = 10−3 , the E (1,1) b /N0 of iterative JD with data estimate refinement by soft quantization converges to a value of 0.7 dB larger than that required by the reference system, whereas in the case of hard quantization the required E (1,1) b /N0 in the limiting case is 2.7 dB larger than that of the reference system. The bit error probability performance of iterative JD with optimum data estimate refinement is illustrated in Figs. 6.7 and 6.8. As stated in Section 4.4.5, the crux of the optimum data estimate refinement consists in exploiting the knowledge of the employed FEC code for data estimate refinement. For this reason, the average bit error probability P b in a coded transmission is investigated. In the simulations of Figs. 6.7-6.8 following parameters are used: • KB = 4 APs, • NF = 32 subcarriers, • the COST 207 RA channel model, • W = 14 paths, • a bandwidth of B = 20 MHz, • convolutional FEC code with rate R = 1/2, • FEC code generator matrix 1 0 0 1 1 1 1 1 0 1 , • soft FEC decoding, and • P = 5 iterations. For the sake of simplicity iterative JD with optimum data estimate refinement is compared only to iterative JD with data estimate refinement by soft quantization and to RxZF JD.
- 85. 6.2 Bit error probability 75 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 Pb 10 log10 Eb/N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.7. Average bit error probability Pb of iterative JD with data estimate refinement by optimum data estimate refinement (solid lines), by soft quantization (dashed lines), of RxZF JD and of MF with the COST 207 RA channel model; Parameters: K = 2, KB = 4, P = 5, R = 1/2, NF = 32, W = 14, B = 20 MHz 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 Pb 10 log10 Eb/N0 / dB RxZF JD MF single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 6.8. Average bit error probability Pb of iterative JD with data estimate refinement by optimum data estimate refinement (solid lines), by soft quantization (dashed lines), of RxZF JD and of MF with the COST 207 RA channel model; Parameters: K = 4, KB = 4, P = 5, R = 1/2, NF = 32, W = 14, B = 20 MHz
- 86. 76 Chapter 6: Performance investigation of uplink transmission Fig. 6.7 presents the average bit error probability P b of iterative JD with optimum data estimate refinement and of iterative JD with data estimate refinement by soft quantization for K = 2. (6.22) From Fig. 6.7 it can be seen that with RxZF JD a 2.3 dB larger Eb/N0 relative to the reference system is needed for an average bit error probability P b = 10−2 whereas with iterative JD with data estimate refinement by soft quantization the corresponding required Eb/N0 is 1.1 dB larger than that of the reference system. By optimum data estimate refinement, an Eb/N0 larger than that in the reference system only by 0.2 dB is needed in iterative JD in order to achieve an average bit error probability P b = 10−2 . If K = 4 (6.23) holds, the average bit error probability P b of iterative JD with optimum data estimate refinement and of data estimate refinement by soft quantization and of RxZF JD is shown in Fig. 6.8. In the case of (6.23), Fig. 6.8 shows that both RxZF JD and iterative JD with data estimate refinement by soft quantization need a Eb/N0 larger by 14.3 dB than the Eb/N0 required by the reference system in order to achieve an average bit error probability P b = 10−2 . On the other hand, if optimum data estimate refinement is applied in iterative JD, an Eb/N0 larger by 2.7 dB is needed to achieve an average bit error probability Pb = 10−2 as compared to the single user reference system. Summarizing the results of Figs. 6.7 to 6.8, iterative JD with optimum data estimate refinement can bring substantial gains in terms of the bit error probability P b over iterative JD with data estimate refinement by soft quantization and over RxZF JD. In particular, given a bit error probability P b = 10−2 , it is shown in Fig. 6.7 that iterative JD with optimum data estimate refinement can reduce the required Eb/N0 by 0.9 dB as compared to iterative JD with data estimate refinement by soft quantization and by 2.1 dB as compared to RxZF JD. However, the gains in the required Eb/N0 by iterative JD with optimum data estimate refinement become higher in a fully loaded system as it is shown in Fig. 6.8. In this case, in contrast to RxZF JD and iterative JD with data estimate refinement by soft quantization which both need a Eb/N0 larger by 14.3 dB than the Eb/N0 required by the reference system in order to achieve an average bit error probability P b = 10−2 , by the employment of iterative JD with optimum data estimate refinement the bit error probability P b = 10−2 is obtained with a 2.7 dB higher Eb/N0.
- 87. 6.3 Asymptotic multiuser efficiency 77 6.3 Asymptotic multiuser efficiency 6.3.1 The asymptotic multiuser efficiency as performance measure The fact that JD needs a higher E (k,nF) b /N0 JD at its input than the E (k,nF) b /N0 ref required by the reference system in order to achieve a given target bit error probability P (k,nF) b is expressed by the multiuser efficiency [Ver98, LV89] η(k,nF) e (σ2 ) = E (k,nF) b /N0 ref E (k,nF) b /N0 JD P (k,nF) b,JD = P (k,nF) b,ref ∈ [0, 1] (6.24) of JD. The asymptotic value of the multiuser efficiency η (k,nF) e (σ2 ) of (6.24) for vanishing power σ2 of the noise is termed asymptotic multiuser efficiency [Ver98, LV89] η(k,nF) = lim σ2→0 η(k,nF) e (σ2 ). (6.25) The use of the asymptotic multiuser efficiency η(k,nF) of (6.25) instead of the multiuser effi- ciency η (k,nF) e (σ2 ) of (6.24) is advantageous when the description of the performance of JD by a single scalar value is desired. In the present thesis, the asymptotic multiuser efficiency η(k,nF) of (6.25) is used to assess linear JD in the sense of RxZF JD without FEC coding. Using (6.1), the variance σ2 of real and imaginary parts of each noise value n(kB,nF) and with the KB × K transfer matrix H(nF) , the SNR γ (k,nF) RxZF = E d(nF) d(nF)∗T k,k E ˆd (nF) − d(nF) ˆd (nF) − d(nF) ∗T k,k = 1 σ2 H(nF)∗T H(nF) −1 k,k (6.26) of the estimated data symbol ˆd (k,nF) of RxZF JD according to (4.21) is calculated. Due to the fact that the estimated data symbol ˆd (k,nF) of (4.21) is unbiased, the estimation error ˆd (nF) − d(nF) is Gaussian [XSR90, Ver98, LV89] and with the output SNR γ (k,nF) RxZF of (6.26), the bit error probability P (k,nF) b,RxZF = 1 2 erfc ⎛ ⎝ γ (k,nF) RxZF 2 ⎞ ⎠ (6.27)
- 88. 78 Chapter 6: Performance investigation of uplink transmission of each bit in the QPSK data symbol d(k,nF) results. Setting out from the fact that the bit error probability P (k,nF) b,RxZF of (6.27) is a bijective and strictly monotonically decreasing function of the output SNR γ (k,nF) RxZF of (6.26), η (k,nF) e (σ2 ) of (6.24) becomes η(k,nF) e (σ2 ) = E (k,nF) b /N0 ref E (k,nF) b /N0 JD γ (k,nF) RxZF = γ (k,nF) ref ∈ [0, 1]. (6.28) It can be shown with the receive energy R(k,nF) of (6.3) and with σ2 of (3.14) that in SA-based systems in the absence of FEC coding E (k,nF) b N0 = E (k,nF) b N0 ref = E (k,nF) b N0 JD = 1 2 R(k,nF) N0 = 1 2σ2 H(nF)∗T H(nF) k,k (6.29) holds. Further, using (6.26) and (6.29), the SNR γ (k,nF) RxZF = 2 H(nF)∗T H(nF) −1 k,k H(nF)∗T H(nF) k,k −1 E (k,nF) b N0 (6.30) of the estimate of the data symbol d(k,nF) by RxZF JD and with (6.6) and (6.29), the SNR γ (k,nF) ref = 2 E (k,nF) b N0 (6.31) of the estimate of the data symbol d(k,nF) by the reference system are calculated. As (6.30) and (6.31) show, both γ (k,nF) RxZF and γ (k,nF) ref are linear functions of E (k,nF) b /N0 of (6.29) and therefore the expression of the multiuser efficiency η (k,nF) e (σ2 ) of (6.28) is further simplified to η (k,nF) e,RxZF(σ2 ) = γ (k,nF) RxZF γ (k,nF) ref = H(nF)∗T H(nF) −1 k,k H(nF)∗T H(nF) k,k −1 (6.32) According to (6.32), the multiuser efficiency η (k,nF) e,RxZF(σ2 ) of RxZF JD in SA-based systems does not depend on E (k,nF) b /N0 and hence, with (6.25) a compact expression also for the asymptotic multiuser efficiency η (k,nF) RxZF = γ (k,nF) RxZF γ (k,nF) ref = H(nF)∗T H(nF) −1 k,k H(nF)∗T H(nF) k,k −1 (6.33) of RxZF JD without FEC coding is derived. For the case of QPSK using the asymptotic multiuser efficiency η (k,nF) RxZF of (6.33), for the bit error probability P (k,nF) b,RxZF of (6.27) P (k,nF) b,RxZF = 1 2 erfc ⎛ ⎝ η (k,nF) RxZF γ (k,nF) ref 2 ⎞ ⎠ (6.34)
- 89. 6.3 Asymptotic multiuser efficiency 79 follows. Closely related to the asymptotic multiuser efficiency η (k,nF) RxZF of (6.33) is the SNR degradation [Kle96, SWC+ 02] δ (k,nF) RxZF = γ (k,nF) ref γ (k,nF) RxZF = H(nF)∗T H(nF) −1 k,k H(nF)∗T H(nF) k,k (6.35) of RxZF JD. From the comparison of (6.35) and (6.33) follows that in the case of RxZF JD of the data symbol d(k,nF) the SNR degradation δ (k,nF) RxZF is the inverse of the asymptotic multiuser efficiency η (k,nF) RxZF and quantifies the decreased SNR γ (k,nF) RxZF of RxZF JD as compared to the SNR γ (k,nF) ref of the reference system. The said decrease of the SNR is the price to be paid for the elimination of intra-SA interference by RxZF JD. Moreover, in the case of RxZF JD, the SNR degradation δ (k,nF) RxZF of (6.35) and the asymptotic multiuser efficiency η (k,nF) RxZF of (6.33) both express the fact that only the component of the useful received signal of MT k is used which is orthogonal to the received signals corresponding to the other K − 1 MTs of the SA due to the need for elimination of the intra-SA interference. Hence, the SNR degradation δ (k,nF) RxZF of (6.35), and equivalently the inverse of the asymptotic multiuser efficiency η (k,nF) RxZF of (6.33) are a measure for the amount of intra-SA interference disturbing the estimation of data symbol d(k,nF) . 6.3.2 Statistics of the asymptotic multiuser efficiency of receive zero-forcing joint detection Following the argumentation of Section 6.3.1, according to which the asymptotic multiuser ef- ficiency η (k,nF) RxZF of (6.33) of RxZF JD is a measure for the intra-SA interference, in the present Section the asymptotic multiuser efficiency η (k,nF) RxZF is investigated by the aid of the indoor geo- metric channel model at a single subcarrier nF in order to provide insight into characteristics of the intra-SA interference. Using the indoor geometric channel model described in Section 2.3.2, with the distance r(k,kB) between MT k and AP kB and the wavelength λ, follows from (2.4) for the corresponding channel coefficient h(k,kB,nF) = 1 r(k,kB) exp −j 2π λ r(k,kB) . (6.36) In the considered scenario K = 2 (6.37)
- 90. 80 Chapter 6: Performance investigation of uplink transmission MTs and KB = 2 (6.38) APs are considered. If (6.38) holds, then the SA structure resulting from the geometric channel model of Section 2.3.2 is symmetrical. Due to the symmetry of the scenario, it suffices to con- sider only the space defined by x ∈ [0, xmax/2] and y ∈ [0, ymax/2]. Without loss of generality, MT 1 is placed at the origin, i.e., r(1,1) = r(1,2) = rB (6.39) holds. MT 2 is randomly positioned in the considered scenario and the variable α ∈ R is introduced to quantize the difference between r(2,1) and r(2,2) as r(2,2) = r(2,1) + α. (6.40) With the coefficients h(k,kB,nF) , k = 1 . . . K, kB = 1 . . .KB, of (6.36) and with the distances r(k,kB) , k = 1 . . . K, kB = 1 . . .KB, according to (6.39) and (6.40), the asymptotic multiuser efficiency η (nF) RxZF = 1 2 − (α + r(2,1) ) cos 2π λ α 2 r(2,1)2 + 2α r(2,1) + α2 (6.41) averaged over the K data symbols d(k,nF) , k = 1 . . .K, can be calculated from (6.33). As can be seen from (6.41), the average asymptotic multiuser efficiency η (nF) RxZF depends on r(2,1) and α, or equivalently, η (nF) RxZF of (6.41) is a scalar function of the coordinates x (2) MT, y (2) MT of MT 2. Hence, η (nF) RxZF of (6.41) at the considered scenario can be visualized with the aid of a three- dimensional plot of η (nF) RxZF of (6.41) with respect to the coordinates x (2) MT, y (2) MT of MT 2. Fig. 6.9 contains the aforementioned three-dimensional plot. As Fig. 6.9 shows, the spatial distribution of η (nF) RxZF is characterized by a periodical succession of maxima and minima. The expression of (6.41) for η (nF) RxZF can be rewritten as η (nF) RxZF = 1 2 − α r(2,1) + 1 cos 2π λ α 2 + 2 α r(2,1) + α r(2,1) 2 . (6.42) Given a fixed distance r(2,1) and if α/r(2,1) 1, which holds, e.g., if the distances r(2,kB) , kB = 1 . . .KB, of MT 2 to the APs of the SA are in the order of magnitude of tens of λ, the terms α/r(2,1) in (6.42) vanish and the variation of η (nF) RxZF of (6.42) is dominated by the variation of the term cos 2π λ α . Hence, it follows from (6.42) that η (nF) RxZF of (6.42) has • minima η (nF) RxZF = 0 at α = κλ, κ ∈ N, and
- 91. 6.3 Asymptotic multiuser efficiency 81 x (2) MT/λ η (nF) RxZF y (2) MT/λ Figure 6.9. Average asymptotic multiuser efficiency η (nF) RxZF of RxZF JD as a function of x (2) MT, y (2) MT ; Parameters: K = 2, KB = 2, geometric indoor channel model, xmax = 40λ, ymax = 40λ, rB = 5λ, λ = 0.15 m • maxima η (nF) RxZF = 1 at α = κ 2 λ, κ ∈ N. Moreover, due to the dependence of the minima and maxima of η (nF) RxZF on α, which according to (6.40) is the difference of the distances from MT2 to the APs of the SA, i.e., to two fixed points, the paths along which η (nF) RxZF presents maxima and minima have a hyperbolic form. In order to provide a physical explanation for the maxima and minima of the asymptotic mul- tiuser efficiency η (nF) RxZF of (6.42), the fact that the k-th column H(nF) k = h(k,1,nF) . . . h(k,KB,nF) T (6.43) of the KB × K channel matrix H(nF) describes the wireless channel between MT k and the KB APs of the SA at subcarrier nF is exploited. In the specific considered scenario, the wireless channel H(nF) 1 of MT 1 is a scaled all-ones vector, whereas if α/r(2,1) 1 holds, the wireless channel H(nF) 2 of MT 2 is determined by the value of α: • If α = κλ, κ ∈ N, using (6.36), (6.40) and (6.43), it follows that the wireless chan- nel H(nF) 2 of MT 2 is also a scaled all-ones vector. In this case, the wireless channels
- 92. 82 Chapter 6: Performance investigation of uplink transmission H(nF) k , k = 1 . . .K, are up to a scaling factor identical, i.e., the vectors H(nF) k , k = 1 . . . K, have the same direction, and because RxZF JD uses only the orthogonal parts of each of the partial received signals, a poor use of the receive energy R(k,nF) is made and a zero asymptotic multiuser efficiency η (nF) RxZF results. • If α = κ 2 λ, κ ∈ N, using (6.36), (6.40) and (6.43), it follows that the wireless channel H(nF) 2 of MT 2 consists of elements antipodal to each other. Equivalently, the vec- tors H(nF) k , k = 1 . . .K, are orthogonal which means that orthogonal partial signals comprise the received signal. Hence, RxZF JD makes optimum use of the receive energy R(k,nF) and a unity η (nF) RxZF results. Concluding, the dependence of the average asymptotic multiuser efficiency η (nF) RxZF of RxZF JD and equivalently, of the amount of intra-SA interference disturbing each of the partial received signals, on the correlation between the wireless channels H(nF) k , k = 1 . . . K, which is expected from theory, is visualized and analyzed with the aid of the geometrical indoor model. A further interesting aspect concerning the intra-SA interference is the investigation of the sta- tistical properties of the average asymptotic multiuser efficiency η (nF) RxZF of the data symbols d(k,nF) , k = 1 . . .K, of RxZF JD. For random positioning of the K MTs, Figs. 6.10 and 6.11 depict the complementary cumulative distribution function (CCDF) Prob η (nF) RxZF ≥ Γ of η (nF) RxZF. Following parameters are common to Figs. 6.10 and 6.11: • indoor geometric channel model, • single subcarrier, • rB = 5λ, • xmax = 40λ, and • ymax = 40λ. For K = 2 (6.44) Fig. 6.10 shows that by an equal number KB of installed APs an average asymptotic multiuser efficiency η (nF) RxZF of at least 0.6 is achieved with probability 0.3. Increasing the number of APs to 3,4,5, and 6 results in a corresponding increase of the probability Prob η (nF) RxZF ≥ 0.6 to 0.55, 0.65, 0.75, and 0.85, respectively.
- 93. 6.3 Asymptotic multiuser efficiency 83 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 −4 10 −3 10 −2 10 −1 10 0 Probη (nF) RxZF≥Γ Γ KB = 2 . . .6 Figure 6.10. CCDF of η (nF) RxZF; Parameters: K = 2, KB = 2 . . . 6, single subcarrier, geometric indoor channel model, rB = 5λ, xmax = 40λ, ymax = 40λ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 −4 10 −3 10 −2 10 −1 10 0 Probη (nF) RxZF≥Γ Γ KB = 3 . . .6 Figure 6.11. CCDF of η (nF) RxZF; Parameters: K = 3, KB = 3 . . . 6, single subcarrier, geometric indoor channel model, rB = 5λ, xmax = 40λ, ymax = 40λ
- 94. 84 Chapter 6: Performance investigation of uplink transmission In the case of K = 3 (6.45) it can be seen from Fig. 6.11 that by the use of a number KB = K of APs, an η (nF) RxZF of 0.6 is achieved with probability 0.06. On the other hand, if 4, 5, or 6 APs are used, an average asymptotic multiuser efficiency η (nF) RxZF of at least 0.6 is obtained with probabilities 0.15, 0.3, and 0.45, respectively. Comparing Figs. 6.10 and 6.11 the conclusion can be drawn that given a fixed number K of MTs in the SA, with an increasing number KB of the employed APs an also increasing value of the minimum average asymptotic multiuser efficiency η (nF) RxZF which can be achieved with a given probability results. Equivalently, if KB increases the degree by which the K wireless channels H(nF) k , k = 1 . . .K, are correlated decreases and intra-SA interference can be combated more efficiently. Moreover, Figs. 6.10 and 6.11 show that the cases of (6.44) and (6.45) are not equivalent in terms of the probability with which a given η (nF) RxZF can be obtained. In particular, if (6.45) holds, for a given ratio K/KB, a desired value of η (nF) RxZF is achieved with a lower probability as compared to the case of (6.44).
- 95. 85 7 Performance investigation of downlink transmis- sion 7.1 Preliminary remarks After having introduced the model for JT in the DL of SA-based systems in Chapter 5, the assessment of the performance of the various JT schemes forms the topic of the present Chapter. To this end, performance measures appropriate for the assessment of JT are introduced and with the aid of the said measures, the JT algorithms presented in Chapter 5 are assessed under different scenarios. As it is the case in Chapter 6, it is assumed that each data symbol d(k,nF) intended for MT k at subcarrier nF is the result of a QPSK modulation, if not explicitly stated otherwise. Moreover, data symbols intended for different MTs are assumed to be uncorrelated. Hence, with the K×K identity matrix IK, for the data correlation matrix R (nF) dd of dimension K × K at subcarrier nF R (nF) dd = E d(nF) d(nF)∗T = 2 IK (7.1) holds. It is also assumed that the noise value n(k,nF) present at the antenna of MT k at subcarrier nF is a complex zero-mean Gaussian variable with variance σ2 of real and imaginary parts. Moreover, due to the spatial separation of the MTs, noise values n(k,nF) and n(k ,nF) at different MTs k = k are uncorrelated. As a result, with the K × K identity matrix IK, for the noise correlation matrix R(nF) nn of dimension K × K at subcarrier nF holds R(nF) nn = E n(nF) n(nF)∗T = 2σ2 IK. (7.2) In JT, the transmit vector s(nF) is generated by the CU jointly from all data symbols d(k,nF) , k = 1 . . .K, as described in Chapter 5. Compared to a reference system, in which only the data symbol d(k,nF) is transmitted, in JT the additional task of suppressing the intra-SA interference exists. Therefore, with the partial transmit energy T (k,nF) associated with data symbol d(k,nF) , the price to be paid for the interference suppression in JT is the suboptimum use of the partial transmit energy T (k,nF) . All performance measures for JT introduced in the following assess the said suboptimum use of the partial transmit energy T (k,nF) . In particular, the suboptimum use of the partial transmit energy T(k,nF) is assessed in terms of the bit error probability measured at each MT, and by means of the efficiency with which JT converts the partial transmit energy T (k,nF) into receive energy R(k,nF) .
- 96. 86 Chapter 7: Performance investigation of downlink transmission The reference system is the system which optimally uses the transmit energy T (k,nF) . With the transfer matrix H(nF)T valid for the DL in a SA-based system, in the reference system a single data symbol d(k,nF) is transmitted from the core network over the mobile radio channel characterized by the row transfer vector H(nF) k T . To this end the TxMF transmit vector [JKG+ 02] s(nF) = H(nF) k ∗ d(k,nF) (7.3) is used, the choice of which is optimum in terms of use of the corresponding transmit energy T (k,nF) ref = 1 2 E s(nF)∗T s(nF) = 1 2 E |d(k,nF) |2 H(nF) k T H(nF) k ∗ = H(nF)T H(nF)∗ k,k . (7.4) Given the transmit energy T (k,nF) ref of (7.4), using (7.1), and with the transmit vector s(nF) of (7.3), the received value e(k,nF) = H(nF) k T s(nF) + n(k,nF) (7.5) with the maximum possible receive energy R (k,nF) ref = 1 2 E e(k,nF) 2 = 1 2 E H(nF) k T s(nF) ∗T H(nF) k T s(nF) = H(nF)T H(nF)∗ k,k 2 (7.6) is produced. Due to the fact that, given the transmit energy T (k,nF) ref of (7.4), the received energy R (k,nF) ref of (7.6) is maximum, the reference system achieves also the minimum possible bit error probability P (k,nF) b,ref [Pro95]. The resulting bit error probability P (k,nF) b,ref of the reference system can be computed for the case of QPSK using the received energy R (k,nF) ref of (7.6) and the variance σ2 or the real and imaginary parts of each noise value n(k,nF) , as P (k,nF) b,ref = 1 2 erfc 1 2σ2 H(nF)T H(nF)∗ k,k . (7.7) As only the transmission of d(k,nF) is considered, the optimum performance of the reference system in terms of the considered performance measures is also referred to as single user bound.
- 97. 7.2 Bit error probability 87 7.2 Bit error probability 7.2.1 The bit error probability as performance measure The bit error probability P (k,nF) b associated with each bit in the QPSK data symbol d(k,nF) de- pends on the receive energy R(k,nF) and on the variance σ2 of the real and imaginary parts of the noise value n(k,nF) at the antenna of the considered MT k. The MTs in a SA-based system employ no multiuser detection, and therefore the receive energy R(k,nF) is used in an optimum way by each MT k. In order to investigate the suboptimum conversion of the transmit energy T (k,nF) into receive energy R(k,nF) in terms of the bit error probability P (k,nF) b , with the variance σ2 or the real and imaginary parts of the noise value n(k,nF) the bit error probability P (k,nF) b of each bit in the QPSK data symbol d(k,nF) is simulated versus T (k,nF) /σ2 . Given a value of T(k,nF) /σ2 , the increased bit error probability P (k,nF) b of JT as compared to the bit error probability P (k,nF) b,ref of the reference system reflects the suboptimum use of the transmit energy T (k,nF) . 7.2.2 Bit error probability of transmit zero-forcing joint transmission In the present Section the performance of TxZF JT is assessed in terms of the bit error probabil- ity P (k,nF) b of the data symbol d(k,nF) . The target of the assessment is to quantify the effectiveness by which a given transmit energy T (k,nF) is used in TxZF JT relative to the reference system which achieves an optimum use of the transmit energy T (k,nF) . Due to the fact that TxZF JT in the DL transmission eliminates intra-SA interference just as RxZF JD eliminates intra-SA interference in the UL transmission, the bit error probability P (k,nF) b of TxZF JT is investigated in comparison to the bit error probability P (k,nF) b of RxZF JD. In order to perform the said comparison, in the case of RxZF JD each data symbol d(k,nF) is scaled with the factor H∗T H −1 k,k so that RxZF JD delivers the estimated data symbol ˆd (k,nF) with a fixed SNR γ (k,nF) RxZF = 1/σ2 , see (6.26), equal to the SNR of the estimated data symbol ˆd (k,nF) by TxZF JT. Fig. 7.1 shows the bit error probability P (1,1) b of the data symbol d(1,1) versus T(1,1) /σ2 obtained by TxZF JT for • KB = 4 APs,
- 98. 88 Chapter 7: Performance investigation of downlink transmission • a single subcarrier, • a frozen channel with a transfer matrix H(nF)T comprised of all KB columns and of the first K rows of the matrix ⎛ ⎜ ⎜ ⎝ 0.20 + 0.45j 0.20 − 0.32j 0.39 + 0.37j 0.20 − 0.22j −0.04 + 0.17j 0.08 + 0.12j −0.04 − 0.10j 0.10 + 0.34j 0.06 + 0.74j 0.06 − 0.12j −0.10 + 0.71j 0.31 + 0.02j 0.20 − 0.58j 0.20 − 0.59j 0.20 − 0.19j 0.20 − 0.72j ⎞ ⎟ ⎟ ⎠, and • no FEC coding. It is shown in Fig. 7.1 that the price to be paid for the elimination of intra-SA interference by TxZF JT with the considered parameters in the case of K = 2 MTs is that a 3.4 dB larger T(1,1) /σ2 is needed to achieve a bit error probability P (1,1) b = 10−2 as compared to the reference system. On the other hand, if K = 4 holds, i.e., under full system load K/KB = 1, the T(1,1) /σ2 needed by TxZF JT for a bit error probability P (1,1) b = 10−2 is 9 dB higher than in the case of the single user reference system. It can also be seen in Fig. 7.1 that the difference of T(1,1) /σ2 required by TxZF JT and by the single user reference system does not depend on the target bit error probability P (1,1) b . Moreover, in both cases of K = 2 and K = 4 MTs the same T (1,1) /σ2 is needed by TxZF JT and by RxZF JD to achieve a given bit error probability P (1,1) b . Fig. 7.2 depicts the bit error probability Pb of TxZF JT averaged over many channel snapshots for • KB = 6 APs, • a single subcarrier, and • random channel matrix H(nF)T with independent identically distributed complex ele- ments h(k,kB,nF) , Re h(k,kB,nF) and Im h(k,kB,nF) being zero-mean random variables with unit variance.
- 99. 7.2 Bit error probability 89 −5 0 5 10 15 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 T(1,1) /σ2 / dB K = 2 K = 4 single user bound TxZF JT RxZF JD Figure 7.1. Bit error probability P (1,1) b of TxZF JT as compared to RxZF JD in a frozen channel; Parameters: KB = 4, single subcarrier, no FEC coding −10 −8 −6 −4 −2 0 2 4 6 10 −4 10 −3 10 −2 10 −1 10 0 K = 2 K = 4 single user bound TxZF JT RxZF JD Pb 10 log10 T/σ2 / dB Figure 7.2. Bit error probability Pb of TxZF JT as compared to RxZF JD in a living channel; Parameters: KB = 6, single subcarrier, no FEC coding
- 100. 90 Chapter 7: Performance investigation of downlink transmission As it is shown in Fig. 7.2, if K = 2 holds, TxZF JT requires a T/σ2 which is 0.6 dB larger than the one required by the single user reference system, in order to obtain a bit error probability Pb = 10−2 . With K = 4 MTs the increase in the T/σ2 relative to the single user reference system, which is required to obtain a bit error probability Pb = 10−2 , is 2.4 dB. It is shown in Fig. 7.2 that the same T/σ2 is required by both TxZF JT in the DL transmission and RxZF JD in the UL transmission in order to obtain a given bit error probability Pb. An interesting duality between RxZF JD and TxZF JT is revealed by the results of Figs. 7.1 and 7.2. In particular, it can be deduced from the said comparison that the same price has to be paid by both RxZF JD in the UL and TxZF JT in the DL for the elimination of the intra- SA interference. Moreover, the said duality between RxZF JD and TxZF JT holds in the case of a frozen channel, as Fig. 7.1 shows, as well as in the case of a living channel, shown in Fig. 7.2. The aforementioned duality between UL and DL in the case of intra-SA interference elimination by JD and JT is further investigated in Chapter 8. 7.2.3 Bit error probability of optimum versus transmit zero-forcing joint transmission In Section 5.2 a novel JT scheme is introduced which is optimum with respect to the average bit error probability at the MTs. In particular, it is shown that for each effective BPSK data vector d (nF) v , an effective transmit vector s (nF) v is determined by the transmission of which the minimum possible average bit error probability P (nF) b,v results at the MTs. Target of the present Section is to assess the performance of optimum JT in comparison to the performance of linear JT in the sense of TxZF in terms of the average bit error probability P (nF) b,v at the MTs. Moreover, the angles corresponding to the transmit signals of TxZF JT are taken as the initial values for the numerical minimization procedure for optimum JT. It is shown in Section 5.2.4 that the average bit error probability P (nF) b of JT is a function of the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . .KB − 1, v = 1 . . .V , and the V − 1 angles ϑ (nF) v , v = 1 . . . V − 1. For this reason, in a first step the dependence of P (nF) b on the KB − 1 angles ϕ (kB,nF) v , kB = 1 . . .KB − 1 for a fixed given v and for the case of fixed transmit energy strategy is investigated and the solutions corresponding to optimum JT and to TxZF JT are visualized in Figs. 7.3 and 7.4. Following parameters are common to Figs. 7.3 and 7.4: • full system load K/KB = 1, • single subcarrier,
- 101. 7.2 Bit error probability 91 • extended MIMO parametric model, • BPSK modulation, • fixed transmit energy strategy, • v = 1, with d (nF) v = [1 . . . 1]T , and • T/σ2 = 1. In Fig. 7.3 the bit error probabilities P (k,nF) b,v , k = 1 . . .K, and the average bit error probability P (nF) b,v for the case of K = 2 (7.8) as a function of ϕ (1,nF) v are depicted. As can be seen from Fig. 7.3, there are intervals in which −3 −2 −1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 P (1,nF) b,v P (2,nF) b,v P (nF) b,v ϕ (1,nF) v,TxZF ϕ (1,nF) v,opt ϕ (1,nF) v Pb Figure 7.3. Bit error probabilities P (k,nF) b,v , k = 1 . . . K, and average bit error probability P (nF) b,v , as a function of ϕ (1,nF) v ; Parameters: K = 2, KB = 2, T/σ2 = 1, v = 1, d (nF) v = [1 1]T , extended MIMO parametric channel model, ρ12 = 0.81, ρ21 = 0.01. the bit error probabilities P (k,nF) b,v , k = 1 . . .K, are greater than 0.5. This happens due to the fact that in the said intervals the corresponding transmit signals are not suited for the transmission of the data vector d (nF) v = [1 1]T . As an example, for the considered d(nF) v = [1 1]T , (7.9)
- 102. 92 Chapter 7: Performance investigation of downlink transmission the received value e(1,nF) v = cos ϕ(1,nF) v + ρ12 sin ϕ(1,nF) v (7.10) at the absence of noise results in a correct decision after quantization only if − arctan 1 ρ12 ≤ ϕ (1,nF) v ≤ π − arctan 1 ρ12 ⇒ −0.89 ≤ ϕ (1,nF) v ≤ 2.25 (7.11) holds. Moreover, in Fig. 7.3, the angle ϕ (1,nF) v,TxZF = 1.38 (7.12) resulting in an average bit error probability P (nF) b,v,TxZF = 0.025 (7.13) corresponding to TxZF JT, as well as the angle ϕ (1,nF) v,opt = 1.22 (7.14) yielding the minimum average bit error probability P (nF) b,v,opt = 0.022 (7.15) corresponding to optimum JT are marked. From (7.12) and (7.14) it is deduced that the TxZF JT solution does not yield the minimum possible P (nF) b,v , hence, (7.12) and (7.14) suggest that there are gains over TxZF JT in terms of average bit error probability P (nF) b,v which can be achieved by optimum JT. On the other hand, from (7.12) to (7.15) it turns out that for the considered channel the TxZF JT solution, although not optimum in terms of P (nF) b,v , is close to the optimum solution corresponding to optimum JT. If K = 3, (7.16) holds, the average bit error probability P (nF) b,v is a function of two angles ϕ (kB,nF) v,opt , kB = 1 . . .KB− 1, and is illustrated in Fig. 7.4. In the case of (7.16), the search for the tuple ϕ (1,nF) v,opt , ϕ (2,nF) v,opt corresponding to optimum JT is a two-dimensional minimization task. As Fig. 7.4 shows, the tuple ϕ (1,nF) v,TxZF, ϕ (2,nF) v,TxZF = (2.12, 0.73) (7.17) corresponds to TxZF JT and leads to a bit error probability P (nF) b,v,TxZF = 0.189, (7.18)
- 103. 7.2 Bit error probability 93 −2 0 2 −3 −2 −1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 ϕ (1,nF) v ϕ (2,nF) v P (nF) b,v ϕ (1,nF) v,TxZF, ϕ (2,nF) v,TxZF ϕ (1,nF) v,opt , ϕ (2,nF) v,opt Figure 7.4. Average bit error probability P (nF) b,v , as a function of ϕ (kB,nF) v , kB = 1 . . .KB − 1; Parameters: K = 3, KB = 3, v = 1, d (nF) v = [1 1 1]T , T/σ2 = 1, extended MIMO parametric channel model, ρ12 = 0.15, ρ13 = 0.70, ρ21 = 0.38, ρ23 = 0.86, ρ31 = 0.85, ρ32 = 0.59. whereas the solution for optimum JT ϕ (1,nF) v,opt , ϕ (2,nF) v,opt = (0.86, 0.57) (7.19) yields the minimum possible bit error probability P (nF) b,v,opt = 0.001. (7.20) Comparing (7.17) and (7.19) to (7.12) and (7.14), it can be seen that the TxZF JT solution of (7.17) and the optimum JT solution of (7.19) have a larger Euclidean distance than the TxZF JT solution of (7.12) and the optimum JT solution of (7.15). Moreover, from the comparison of (7.18) and (7.20) to (7.13) and (7.15) follows that larger gains in terms of P (nF) b,v are achievable in the case of higher K in the considered channel snapshots. In particular, optimum JT achieves
- 104. 94 Chapter 7: Performance investigation of downlink transmission a reduction of 12% of P (nF) b,v in the case of (7.8) and a reduction of 95% of P (nF) b,v in the case of (7.16). In Figs. 7.5-7.6, optimum JT is assessed in terms of the bit error probability P (nF) b averaged over all data vectors d(nF) . Following parameters are common to Figs. 7.5-7.6: • single subcarrier, • BPSK modulation, • KB = 8 APs, • K = 2 . . .6 MTs, and • transfer matrix H(nF)T comprised of all KB columns and of the first K rows of the matrix ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 0.50 0.43 0.49 0.07 0.23 0.44 0.16 0.20 0.14 0.27 0.55 0.12 0.56 0.01 0.11 0.52 0.39 0.40 0.26 0.13 0.30 0.44 0.12 0.55 0.27 0.45 0.50 0.34 0.24 0.21 0.38 0.33 0.48 0.50 0.03 0.15 0.45 0.45 0.16 0.27 0.45 0.43 0.21 0.12 0.31 0.29 0.32 0.53 0.31 0.12 0.56 0.01 0.14 0.48 0.10 0.56 0.01 0.27 0.01 0.50 0.45 0.29 0.46 0.43 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . Fig. 7.5 shows the performance of optimum JT and TxZF JT in terms of the bit error probability P (nF) b versus T/σ2 for the case of fixed transmit energy strategy. It can be seen from Fig. 7.5 that no noticeable difference between optimum JT and TxZF JT exists in the case of 2 MTs. This fact is to be expected as follows from the discussions concerning Fig. 7.3. By a stepwise increase of the number of MTs from 2 to 6, the T/σ2 gains of optimum JT as compared to TxZF JT increase to 0.3 dB, 0.4 dB, 0.5 dB and 0.9 dB, respectively, at a bit error probability P (nF) b = 10−1 . The bit error probability P (nF) b of optimum JT and TxZF JT in the case of variable transmit energy strategy is shown in Fig. 7.6. As Fig. 7.6 shows, by employing the variable transmit energy strategy, for K = 2 . . . 6 optimum JT yields T/σ2 gains of 0.8 dB, 0.8 dB, 0.8 dB and 1.2 dB over TxZF JT, respectively, at a bit error probability P (nF) b = 10−1 .
- 105. 7.2 Bit error probability 95 −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20 10 −3 10 −2 10 −1 10 0 K = 2 K = 3 K = 4 K = 5 K = 6 10 log10 (T/σ2 ) /dB Pb (nF) singe user bound Figure 7.5. Average bit error probability Pb (nF) for optimum JT (solid lines), and TxZF JT (dashed lines); Parameters: KB = 8, K = 2 . . . 6, fixed transmit energy −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20 10 −3 10 −2 10 −1 10 0 K = 2 K = 3 K = 4 K = 5 K = 6 10 log10 (T/σ2 ) /dB Pb (nF) singe user bound Figure 7.6. Average bit error probability Pb (nF) for optimum JT (solid lines), and TxZF JT (dashed lines); Parameters: KB = 8, K = 2 . . . 6, variable transmit energy
- 106. 96 Chapter 7: Performance investigation of downlink transmission Summarizing the findings of the simulations of Figs. 7.5 and 7.6, up to 1.2 dB of T/σ2 at a bit error probability P (nF) b = 10−1 can be gained by employing optimum JT as compared to TxZF JT. Moreover, higher gains in terms of bit error probability P (nF) b are possible by optimum JT over TxZF JT in the case of the variable transmit energy strategy than in the case of fixed transmit energy strategy. The minimization of P (nF) b not only with respect to the (KB − 1)V angles ϕ (kB,nF) v , kB = 1 . . .KB − 1, v = 1 . . . V , but also with respect to the V − 1 angles ϑ (nF) v , v = 1 . . . V −1, in the case of optimum JT with variable transmit energy brings additional degrees of freedom, a fact which translates into higher gains in P (nF) b as compared to the case of fixed transmit energy strategy. In both cases of Figs. 7.5 and 7.6 the gains of optimum JT over TxZF JT decrease as the target bit error probability P (nF) b decreases. Hence, TxZF JT is the optimum approach in terms of bit error probability P (nF) b in the case of high T/σ2 . −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20 10 −3 10 −2 10 −1 10 0 K = 2 K = 3 K = 4 K = 5 K = 6 singe user bound 10 log10 (T/σ2 ) /dB Pb (nF) Figure 7.7. Average bit error probability Pb (nF) for optimum JT, with variable transmit energy (solid lines) and fixed transmit energy (dashed lines); Parameters: KB = 8, K = 2 . . . 6 The investigation of the influence of the two transmit energy strategies on the performance of optimum JT is the target of the simulations of Fig. 7.7. From Fig. 7.7 it can be seen that approximately 2 dB of T/σ2 at a bit error probability Pb (nF) = 10−2 are gained by the use of optimum JT with the variable energy strategy as compared to when optimum JT with the fixed energy strategy is used. However, by increasing the number K of MTs and by constant number KB of APs, the gain in terms of T/σ2 slowly vanishes. Moreover, if the system load K/KB
- 107. 7.2 Bit error probability 97 remains constant, Fig. 7.7 shows that for low T/σ2 only small differences in the achieved bit error probability Pb (nF) for given T/σ2 exist between the two transmit energy strategies. 7.2.4 Bit error probability of iterative joint transmission In Section 5.4 an iterative JT scheme is introduced, as an alternative to TxZF JT of Section 5.3. It is shown that in the DL transmission of SA-based systems intra-SA interference is mitigated in an iterative manner by iterative JT and that iterative JT of Section 5.3 in the DL is dual to iterative JD with transparent data estimate refinement of Section 4.4.2 in the UL. In the present Section, the performance of iterative JT in terms of the bit error probability P (k,nF) b is assessed. Figs. 7.8 and 7.9 depict the bit error probability P (1,1) b of iterative JT for the following parametriza- tion • K = 4 MTs, • KB = 4 APs, • single subcarrier, • single snapshot of the MIMO parametric channel model, • no FEC coding, • P = 5 iterations, • forward path matrix F = diag H∗ HT −1 , and • reverse path matrix R = diag H∗ HT . If ρ = 0.1 (7.21) holds, Fig. 7.8 shows that iterative JT converges towards TxZF JT, which needs a 0.4 dB higher T/σ2 than the reference system in order to achieve a bit error probability P (1,1) b = 10−3 . In the case of ρ = 0.15, (7.22) shown in Fig. 7.9, iterative JT converges towards TxZF JT, which needs a 1 dB higher T (1,1) /σ2 than the reference system in order to achieve a bit error probability P (1,1) b = 10−3 . As compared to Fig. 7.8, convergence of iterative JT towards TxZF JT in Fig. 7.9 takes place at a lower speed.
- 108. 98 Chapter 7: Performance investigation of downlink transmission Taking advantage of the duality between iterative JT and iterative JD with transparent data estimate refinement outlined in Section 5.4, the results concerning convergence of iterative JD can be directly applied to iterative JT. In particular, it can be shown that the matrix product F R of dimension KNF × KNF has the spectral radius λmax (F R) = (K − 1) 2ρ + (K − 2)ρ2 1 + (K − 1)ρ2 , (7.23) with which it can be shown that iterative JT in the case of the MIMO parametric channel model converges if ρ < 1 K − 3 2 K − 2 K − 1 − 1 (7.24) holds. In the specific case of K = 4 (7.25) (7.24) yields ρ < 0.155. (7.26) 7.3 Transmission efficiency 7.3.1 The transmission efficiency as performance measure With the aid of the transmission efficiency, the efficiency by which JT in the DL of SA-based systems converts the available transmit energy T (k,nF) into receive energy R(k,nF) is assessed. The assessment of the said efficiency is based on a comparison of R(k,nF) /T(k,nF) JT with the maximum possible ratio R(k,nF) /T(k,nF) ref corresponding to the reference system, i.e., the transmission efficiency of JT is defined as [TWMB01] t(k,nF) = R(k,nF) T(k,nF) JT (R(k,nF) /T(k,nF) )ref . (7.27) Due to the suboptimum conversion of the transmit energy T (k,nF) into receive energy R(k,nF) , the transmission efficiency t(k,nF) of (7.27) takes the values t(k,nF) ∈ [0, 1].
- 109. 7.3 Transmission efficiency 99 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 T(1,1) /σ2 / dB TxZF JT single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 7.8. Bit error probability P (1,1) b of iterative JT and of TxZF JT; Parameters: K = 4, KB = 4, no FEC coding, MIMO parametric channel model with ρ = 0.1 −10 −5 0 5 10 15 20 10 −4 10 −3 10 −2 10 −1 10 0 P (1,1) b 10 log10 T(1,1) /σ2 / dB TxZF JT single user bound p = 1 p = 2 p = 3 p = 4 p = 5 Figure 7.9. Bit error probability P (1,1) b of iterative JT and of TxZF JT; Parameters: K = 4, KB = 4, no FEC coding, MIMO parametric channel model with ρ = 0.15
- 110. 100 Chapter 7: Performance investigation of downlink transmission In the case of TxZF JT as described in (5.40), with the transfer matrix H(nF)T and using (7.1) and with the modulator matrix M (nF) TxZF of (5.40), R(k,nF) T(k,nF) JT = 1 2 E |d(k,nF) |2 1 2 E |d(k,nF) |2 M (nF) TxZF ∗T M (nF) TxZF k,k = 1 H(nF)T H(nF)∗ −1 k,k (7.28) follows for the ratio R(k,nF) /T(k,nF) JT . As far as the reference system is concerned, with the transmit energy T (k,nF) of (7.4) and the receive energy R(k,nF) of (7.6), follows R(k,nF) T(k,nF) ref = H(nF)T H(nF)∗ k,k . (7.29) Hence, with R(k,nF) /T(k,nF) JT of (7.28) and R(k,nF) /T(k,nF) ref of (7.29), the transmission efficiency t(k,nF) of (7.27) becomes t (k,nF) TxZF = H(nF)T H(nF)∗ −1 k,k H(nF)T H(nF)∗ k,k −1 . (7.30) The transmission efficiency t (k,nF) TxZF of (7.30) expresses the fact that, given a receive energy R(k,nF) , a higher transmit energy T (k,nF) is required by TxZF JT as compared to the reference system in order to render the partial received signal corresponding to MT k orthogonal to the useful received signals of the other MTs of the SA. 7.3.2 Statistics of the transmission efficiency of transmit zero-forcing joint transmission In this Section TxZF JT is assessed on the basis of the transmission efficiency t (k,nF) TxZF of (7.30). In Section 7.3.1 it is shown that the transmission efficiency t(k,nF) of (7.27) assesses the effi- ciency of the conversion of the transmit energy T (k,nF) into receive energy R(k,nF) by JT, when compared to a reference system. According to an alternative interpretation of (7.27), the trans- mission efficiency t(k,nF) measures the increase in the transmit energy T (k,nF) required by JT relative to the reference system in order to achieve a given bit error probability P (k,nF) b . More- over, in the case of TxZF JT the transmission efficiency t (k,nF) TxZF of (7.30) does not depend on the power σ2 of the noise at the MTs. Hence, a duality is revealed between the transmission efficiency t (k,nF) TxZF of (7.30) of TxZF JT in the DL and the asymptotic multiuser efficiency η (k,nF) RxZF of (6.33) of RxZF JD in the UL, i.e., both t (k,nF) TxZF and η (k,nF) RxZF express the price to be paid for the intra-SA interference elimination.
- 111. 7.3 Transmission efficiency 101 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 −4 10 −3 10 −2 10 −1 10 0Probt (nF) TxZF≥Γ Γ KB = 2 . . . 6 Figure 7.10. CCDF of t (nF) TxZF; Parameters: K = 2, KB = 2 . . . 6, single subcarrier, geometric indoor channel model, rB = 5λ, xmax = 40λ, ymax = 40λ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 −4 10 −3 10 −2 10 −1 10 0 Probt (nF) TxZF≥Γ Γ KB = 2 . . . 6 Figure 7.11. CCDF of t (nF) TxZF; Parameters: K = 3, KB = 3 . . . 6, single subcarrier, geometric indoor channel model, rB = 5λ, xmax = 40λ, ymax = 40λ
- 112. 102 Chapter 7: Performance investigation of downlink transmission The said duality is further confirmed by the simulation results of the bit error probability P (k,nF) b of TxZF JT of Section 7.2.2. It is shown that relative to the corresponding reference systems, the increase in the transmit energy T (k,nF) required by TxZF JT in order to achieve a given bit error probability P (k,nF) b relative to the reference system is equal to the increase in the receive energy R(k,nF) required by RxZF JD in order to achieve the same bit error probability P (k,nF) b relative to the corresponding reference system of Section 6.1. In order to further confirm that the results and conclusions regarding the average asymptotic multiuser efficiency η (k,nF) RxZF of RxZF JD in the UL are directly applicable to the case of TxZF JT in the DL, Figs. 7.10 and 7.11 depict the CCDF of t (nF) TxZF of TxZF JT for K = 2 (7.31) and K = 3 (7.32) MTs respectively, for the following parameters: • Indoor geometric channel model, • single subcarrier, • rB = 5λ, • xmax = 40λ, and • ymax = 40λ. For the case of (7.31), Fig. 7.10 shows that a transmission efficiency t (nF) TxZF of at least 0.6 is achieved with probability of 0.3 with 2 APs. With 3, 4, 5, or 6 APs the corresponding probability Prob t (nF) TxZF ≥ 0.6 becomes 0.55, 0.65, 0.75, and 0.85, respectively. If (7.32) holds, according to Fig. 7.10 a minimum average transmission efficiency t (nF) TxZF of 0.6 is obtained with a probability of 0.06 in the case of full system load K/KB = 1. An increase of the number KB of APs to 4, 5, or 6 results in an increase of the probability Prob t (nF) TxZF ≥ 0.6 to 0.15, 0.3, and 0.45, respectively. By comparing of Figs. 7.10 and 7.11 to Figs. 6.10 and 6.11 the conclusion is drawn that the transmission efficiency t (nF) TxZF of TxZF JT in the DL is characterized by the same CCDF as the asymptotic multiuser efficiency η (k,nF) ZF of RxZF JD in the UL. Hence, all results and conclusions regarding the asymptotic multiuser efficiency η (k,nF) RxZF of RxZF JD in Chapter 6 hold also for the transmission efficiency t (nF) TxZF of TxZF JT.
- 113. 103 8 Performance assessment of service area based systems 8.1 Introduction The main advantageous characteristic of SA-based systems in comparison to state-of-the-art cellular systems is that the intercell interference which disturbs the transmissions in cellular systems can be combated by interference mitigation techniques in SA-based systems offering the potential of an increased spectrum capacity ηc of (1.1). As it is shown in Chapters 4 and 5, there exists freedom of choice with respect to the employment of techniques for the mitigation of intra-SA interference in the UL and in the DL transmission. Among the various techniques described in Chapters 4 and 5, RxZF JD and TxZF JT are of special interest due to the fact that by their use unbiased data transmission is achieved in the SA. RxZF JD and TxZF JT are subcases of the general class of linear unbiased data transmission techniques. Target of the present Chapter is to derive a unified data transmission model for UL and DL as well as the corresponding performance measures for linear unbiased data transmission techniques for SA-based systems. Moreover, system layer aspects of SA-based systems employing unbiased linear data transmission are investigated. In order to provide insight into the motivation of the investigations of the present Chapter, first a brief overview of the dominant characteristics of RxZF JD and TxZF JT is performed. In the UL of SA-based systems, the received signals available to the CU are comprised of K partial received signals, each corresponding to one of the K MTs of the SA. As the K partial received signals are in general not orthogonal to each other, the estimation of the data symbol d(k,nF) sent by MT k by RxZF JD consists in using only the part of the useful received signal corresponding to MT k, which is orthogonal to the partial received signals of the other K − 1 MTs of the SA. Due to the fact that only a part of the useful received signal of each MT is used, RxZF JD is suboptimum with respect to the use of the corresponding receive energy R(k,nF) in comparison to a reference system which uses the whole useful received signal of MT k. The aforementioned suboptimum use of the receive energy R(k,nF) by RxZF JD is quantified by the asymptotic multiuser efficiency η (k,nF) ZF of (6.33) of RxZF JD. Likewise in the DL of SA-based systems, the received signal at each MT k is in general a superposition of K partial received signals and the partial received signal intended for MT k is the useful received signal of MT k. Equivalently, a partial received signal corresponding to MT k is received by all K MTs of the SA. In order to eliminate intra-SA interference in the DL transmission, TxZF JT uses for data symbol d(k,nF) an increased transmit energy T (k,nF) as compared to a single user reference system in order to render the partial received signals
- 114. 104 Chapter 8: Performance assessment of service area based systems corresponding to data symbol d(k,nF) orthogonal to the useful received signal of every other MT in the SA, resulting into a lower receive energy R(k,nF) at MT k as compared to the single user reference system. The aforementioned suboptimum transformation of the transmit energy T(k,nF) into receive energy R(k,nF) with respect to the reference system is quantified by the transmission efficiency t (k,nF) TxZF of (7.30) of TxZF JT. Using the more general terms transmitter and receiver instead of CU and MTs to characterize a SA-based system independently of whether UL or DL transmission is considered, it can be deduced that the price to be paid for the elimination of intra-SA interference by JD and JT is that in a SA suboptimum use is made of a given transmit energy T (k,nF) as compared to the single user reference system. The latter conclusion is further verified by the simulation results of Chapter 7, which reveal that the same energy loss compared to the single user reference system has to be paid for the intra-SA interference elimination by RxZF JD and TxZF JT. This commonality between RxZF JD and TxZF JT is treated with in detail in the present Chapter. Moreover, a unified performance assessment method of linear unbiased data transmission for UL and DL is presented. 8.2 Dualities between uplink and downlink 8.2.1 Model of general unbiased linear data transmission In this Section, a generalized transmission model for unbiased linear data transmission is pre- sented. With respect to the nomenclature of Chapter 3 regarding OFDM-based MIMO sys- tems, a SA-based system in which intra-SA interference is eliminated in the UL transmission is a MIMO system in which the transmitters employ no pre-processing whereas linear post- processing is performed by the receiver. On the other hand, in the DL transmission the transmit- ter employs linear pre-processing and no post-processing is performed by the receivers. Hence, the UL and DL transmission in a SA-based system employing linear pre- and post-processing are subcases of a generalized unbiased data transmission with linear pre- and post-processing stages, i.e., of an unbiased data transmission in which the transmit vector s(nF) is a linear func- tion of the data vector d(nF) and the estimated data vector ˆd (nF) is a linear function of the received vector e(nF) , as shown in Fig. 8.1. As linear processing can be performed in a subcar- rierwise fashion, the model depicted in Fig. 8.1 models transmission and estimation at a single subcarrier nF of the SA-based system. Nevertheless, the presented transmission model is also more generally valid for flat fading MIMO channels. It is assumed that each MT and each AP is equipped with a single antenna and that no spreading is employed.
- 115. 8.2 Dualities between uplink and downlink 105 n(nF) d(nF) s(nF) e(nF) ˆd (nF) D(nF) H(nF) M(nF) Figure 8.1. Model of general subcarrierwise linear data transmission At the considered system of Fig. 8.1 pre-processing is linear, i.e., a modulator matrix M(nF) of dimension KI × K can be used to describe the generation of the transmit vector s(nF) = M(nF) d(nF) (8.1) of dimension KI from the data vector d(nF) of dimension K. In the case of the UL in the considered SA-based system, M(nF) of (8.1) is a diagonal matrix, due to the fact that the K MTs are spatially separated. With the transmit vector s(nF) , and using the KO ×KI transfer matrix H(nF) and the noise vector n(nF) of dimension KO, the received vector e(nF) = H(nF) s(nF) + n(nF) (8.2) of dimension KO is obtained. Regarding n(nF) of (8.2), it is assumed that it contains uncorre- lated complex elements with Gaussian distributed real and imaginary parts of variance σ2 . At the receiver side linear post-processing is performed, which means that estimation can be described by a demodulator matrix D(nF) of dimension K × KO with the aid of which the estimated data vector ˆd (nF) = D(nF) e(nF) (8.3) of dimension K is obtained from the received vector e(nF) of dimension KO of (8.2). Due to the spatial separation of the MTs, in the DL D(nF) of (8.3) is a diagonal matrix. (8.1), (8.2), and (8.3) model a generalized linear data transmission scheme. The said data transmission is unbiased, if the restriction D(nF) H(nF) M(nF) = IK (8.4) holds for the modulator matrix M(nF) and the demodulator matrix D(nF) .
- 116. 106 Chapter 8: Performance assessment of service area based systems 8.2.2 Energy efficiency As shown by the simulation results of Chapters 6 and 7, RxZF JD and TxZF JT are characterized by the same energy loss with respect to the corresponding reference system. In this Section, a performance measure is derived, quantifying the common energy loss in UL and DL by RxZF JD and TxZF JT, respectively. In a first step, the reference system is defined, in which only a single data symbol d(k,nF) is transmitted. However, unlike the reference systems used for the investigations in Chapters 6 and 7, the chosen reference system for the generalized unbiased linear data transmission utilizes all KI inputs and all KO outputs due to the need for application on both UL and DL. The reference system is optimum with respect to the use of the transmit energy T(k,nF) = 1 2 s(nF)∗T s(nF) (8.5) per data symbol. In order to achieve the said optimum use, the transmit vector s(nF) in the reference system is the eigenvector corresponding to the eigenvalue of H(nF)∗T H(nF) with the largest magnitude. With the spectral radius λmax H(nF)∗T H(nF) of H(nF)∗T H(nF) [Sch88b], the maximum possible receive energy E (k,nF) b,opt = 1 2 T(k,nF) λmax H(nF)∗T H(nF) (8.6) and the minimum possible bit error probability P (k,nF) b,opt = 1 2 erfc 1 2σ2 T(k,nF)λmax H(nF)∗T H(nF) (8.7) for each bit in the QPSK data symbol d(k,nF) are obtained [Pro95] given the transmit energy T(k,nF) of (8.5). SA-based systems with linear pre- and post-processing are suboptimum with respect to the use of the transmit energy T (k,nF) , due to the following two reasons: • Due to the spatial separation of the MTs, the eigenvector corresponding to the eigenvalue of H(nF)∗T H(nF) with the largest magnitude cannot be used as the transmit vector, which means that the transmit energy T (k,nF) cannot be converted in receive energy R(k,nF) as efficiently as in the reference system and • only a part of the receive energy R(k,nF) is used, in contrast to the reference system.
- 117. 8.2 Dualities between uplink and downlink 107 The above mentioned reasons hold due to the multiuser nature of the SA-based system. In contrast to the reference system, more than one data symbols have to be transmitted and the eigenvector corresponding to the maximum eigenvalue of H(nF)∗T H(nF) cannot be used for all the data symbols d(k,nF) , k = 1 . . . K. The corresponding suboptimum conversion of T (k,nF) into R(k,nF) is quantified by the transmission efficiency [WSLW03, TWMB01] t(k,nF) = M(nF)∗T H(nF)∗T H(nF) M(nF) k,k λmax H(nF)∗T H(nF) M(nF)∗T M(nF) k,k (8.8) of generalized unbiased linear data transmission. At the receiver side, in contrast to the reference system, in which the whole E (k,nF) b is used, only a part of the receive energy R(k,nF) and thus of the receive energy E (k,nF) b per bit in the QPSK data symbol d(k,nF) is used, due to the need for the elimination of intra-SA interference. The said suboptimum use of E (k,nF) b is measured by the asymptotic multiuser efficiency [WSLW03, Ver98] η(k,nF) = 1 M(nF)∗T H(nF)∗T H(nF) M(nF) k,k D(nF) D(nF)∗T k,k (8.9) of generalized unbiased linear data transmission. Both the transmission efficiency t(k,nF) of (8.8) and the asymptotic multiuser efficiency η(k,nF) of (8.9) are heavily influenced by the spatial separation of the MTs in the SA which is expressed in a diagonal form of the modulator matrix M(nF) or the demodulator matrix D(nF) in the UL or the DL transmission, respectively. Moreover, as t(k,nF) of (8.8) measures the suboptimum conversion of the transmit energy T (k,nF) to receive energy R(k,nF) and η(k,nF) of (8.9) the sub- optimum use of the available receive energy R(k,nF) , the energy efficiency ε(k,nF) = t(k,nF) η(k,nF) = 1 λmax H(nF)∗T H(nF) M(nF)∗T M(nF) k,k D(nF) D(nF)∗T k,k (8.10) collectively expresses the suboptimum use of the transmit energy T (k,nF) by both transmitter and receiver sides together. With ε(k,nF) of (8.10), and using (8.8) and (8.9), and with E (k,nF) b,opt of (8.6), the bit error probability P (k,nF) b = 1 2 erfc ⎛ ⎝ E (k,nF) b,opt ε(k,nF) σ2 ⎞ ⎠ = 1 2 erfc ⎛ ⎜ ⎝ T(k,nF) 2σ2 M(nF)∗T M(nF) k,k D(nF) D(nF)∗T k,k ⎞ ⎟ ⎠ (8.11)
- 118. 108 Chapter 8: Performance assessment of service area based systems of each bit in the QPSK data symbol d(k,nF) is calculated [Pro95]. As (8.11) shows, P (k,nF) b depends on the matrices M(nF) and D(nF) , i.e., on the linear processing in the transmitter and receiver side, and implicitly also on the transfer matrix H(nF) due to the requirement for unbi- ased linear data transmission of (8.4). Hence, in the case of unbiased linear data transmission in SA-based systems, independently of whether UL or DL is considered, the energy efficiency ε(k,nF) of (8.10) expresses the subopti- mum use of the transmit energy T (k,nF) by the transmitter and receiver sides in the generalized unbiased linear data transmission, as compared to the reference system. In particular, if a certain transmit energy is required by the reference system in order to achieve a given a target bit error probability P (k,nF) b , a SA-based system employing unbiased linear data transmission requires an transmit energy T (k,nF) increased by the factor 1 ε(k,nF) to obtain the same bit error probability P (k,nF) b as compared to the reference system, and this increase of the required transmit energy T(k,nF) is the price to be paid for the elimination of the intra-SA interference in the generalized unbiased linear transmission. In what follows, ε(k,nF) of (8.10) is determined for UL and DL of SA-based systems. In the UL transmission of SA-based systems, the spatial separation of the MTs results in the modulator matrix M (nF) UL = IK. (8.12) Due to the said spatial separation of the MTs, the K inputs to the KB ×K MIMO channel of the SA are not jointly available as it is the case in the reference system. With the modulator matrix M (nF) UL according to (8.12) and the transfer matrix H (nF) UL valid for the UL, the aforementioned fact results in a decreased transmission efficiency t (k,nF) UL = H (nF) UL H (nF) UL ∗T k,k λmax H (nF) UL ∗T H (nF) UL . (8.13) Linear post-processing is performed by the CU at the receiver side. With the use of the demod- ulator matrix D (nF) UL = H (nF) UL ∗T H (nF) UL −1 H (nF) UL ∗T (8.14) according to the RxZF principle [Kle96, SWC+ 02, WMS+ 02], all intra-SA interference is can- celled. Due to the need for intra-SA interference elimination, only the orthogonal parts of the partial received signals are used. With (8.9) and using the demodulator matrix D (nF) UL of (8.14) and the transfer matrix H (nF) UL , the said suboptimum use of the available receive energy R(k,nF) in the UL is quantified by the asymptotic multiuser efficiency η (k,nF) UL = 1 H (nF) UL ∗T H (nF) UL −1 k,k H (nF) UL ∗T H (nF) UL k,k . (8.15)
- 119. 8.2 Dualities between uplink and downlink 109 With t (k,nF) UL of (8.13) and η (k,nF) UL of (8.15) follows from (8.10) the energy efficiency ε (k,nF) UL = 1 λmax H (nF) UL ∗T H (nF) UL H (nF) UL ∗T H (nF) UL −1 k,k (8.16) of the UL transmission. In the DL transmission of SA-based systems, he spatial separation of the MTs in the DL is expressed by the diagonal demodulator matrix D (nF) DL = IK. (8.17) Because each MT uses the whole available received energy R(k,nF) , an asymptotic multiuser efficiency η (k,nF) DL = 1 (8.18) follows from (8.9) for the DL transmission. At the transmitter side, the modulator matrix M (nF) DL = H (nF) DL ∗T H (nF) DL H (nF) DL ∗T −1 (8.19) is used according to the TxZF principle [MBW+ 00, WMS+ 02]. Because a part of the avail- able transmit energy T (k,nF) is devoted to eliminate intra-SA interference, from (8.8) and using M (nF) DL of (8.19) and the transfer matrix H (nF) UL , the suboptimum use of T (k,nF) in the DL trans- mission is is quantified by the transmission efficiency t (k,nF) DL = 1 λmax H (nF) DL H (nF) DL ∗T H (nF) DL H (nF) DL ∗T −1 k,k . (8.20) With t (k,nF) DL of (8.20) and η (k,nF) DL of (8.18), follows from (8.10) for the DL transmission the energy efficiency ε (k,nF) DL = 1 λmax H (nF) DL H (nF) DL ∗T H (nF) DL H (nF) DL ∗T −1 k,k . (8.21) Given that TDD is employed and that the channels of UL and DL are reciprocal, H (nF) DL = H (nF) UL T (8.22)
- 120. 110 Chapter 8: Performance assessment of service area based systems holds for the transfer matrices of UL and DL. Moreover, for a square matrix X λmax XT = λmax (X) (8.23) holds [ZF86]. Using (8.22) and (8.23), the comparison of ε (k,nF) UL of (8.16) and ε (k,nF) DL of (8.21) yields ε (k,nF) UL = ε (k,nF) DL (8.24) and for the corresponding bit error probabilities P (k,nF) b,UL = P (k,nF) b,DL (8.25) holds. (8.24) expresses an important characteristic of SA-based systems. According to (8.24), with the transfer matrix H(nF) valid for the UL transmission, UL and DL are characterized by the same energy efficiency ε(k,nF) = 1 λmax H(nF)∗T H(nF) H(nF)∗T H(nF) −1 k,k . (8.26) In other words, the price to be paid for intra-SA interference elimination is the same for RxZF JD and TxZF JT. Consequently, investigations regarding the energy efficiency ε(k,nF) in the case of unbiased linear data transmission in SA-based systems can be carried out jointly for UL and DL. 8.3 System layer aspects The energy efficiency ε(k,nF) as defined in (8.24) is an energy related measure. As such, it is useful also in investigations concerning the system layer of SA-based systems with unbiased linear data transmission, in which not the structure of the signals, but the transmit and receive energies play a role. For this reason, the energy efficiency ε(k,nF) as defined in (8.24) is used in this Section to provide an insight in issues regarding the system layer of SA-based systems, i.e., in issues related to inter-SA interference. The energy efficiency ε(k,nF) as defined in (8.24) quantifies the efficiency of the use of the transmit energy T (k,nF) . An energy efficiency ε(k,nF) smaller than unity means that a higher transmit energy T (k,nF) is required by the SA-based system than by the reference system in
- 121. 8.3 System layer aspects 111 order to achieve a given bit error probability P (k,nF) b , and that higher energy is radiated towards the neighboring SAs causing inter-SA interference. Equivalently, for given transmit energy T(k,nF) lower receive energy R(k,nF) is achieved relative to the reference system, which means that the sensitivity of the receivers in a SA to noise, i.e., to inter-SA interference is increased. Hence, the energy efficiency ε(k,nF) of (8.24) is a measure for the inter-SA interference caused from the transmitters of a SA to neighboring SAs or equivalently, for the sensitivity of the receivers in a SA to inter-SA interference stemming from neighboring SAs. An important aspect of interest to system level considerations is the dependence of the energy efficiency ε(k,nF) of (8.24) on the number K of MTs and the number KB of APs. Fig. 8.2 depicts the average energy efficiency ε(nF) of unbiased linear data transmission in a SA for fixed system load K/KB. The transfer matrix H(nF) used consists of independent and identically distributed complex random variables, each having a magnitude following the Rayleigh distribution. As 1 3 5 7 9 11 13 15 0 0.2 0.4 0.6 0.8 1 K ε(nF) K/KB = 1 K/KB = 0.5 K/KB = 0.33 K/KB = 0.25 Figure 8.2. Average energy efficiency ε(nF) of a SA employing unbiased linear data transmission for Rayleigh fading can be seen from Fig. 8.2, the energy efficiencies ε(nF) are unity for K = 1 MT, for all sys- tem loads K/KB, as expected from theory. The energy efficiency ε(nF) initially decreases for increasing number of MTs K, and for large K converges to a constant value. The said limiting value of ε(nF) could be computed analytically with the aid of random matrix theory [Meh91]. Ultimately, Fig. 8.2 shows that for a large number K of MTs, the energy efficiency ε(nF) is a function only of the system load K/KB and is independent of the number K of MTs.
- 122. 112 Chapter 8: Performance assessment of service area based systems The transmit energy used by the reference system in which a single data symbol is transmitted is antiproportional to the number KB of employed APs, i.e., of the number of antennas jointly available in the SA [God97a, God97b]. Therefore, due to the fact that the average energy efficiency ε(nF) is a function of the system load K/KB only, the transmit energy used in a SA for a single data symbol d(k,nF) is also antiproportional to the number KB of APs for given system load K/KB. From the latter observation follows directly that the total transmit power in a SA is a function of the system load K/KB only and independent of the number K of MTs. Hence, the inter-SA interference induced from a SA to its neighboring SAs in a SA-based system for a given system load K/KB does not depend on the number K of MTs. Equivalently, if the system load K/KB is kept constant, the number K of MTs in a SA of a SA-based system employing unbiased linear data transmission can be increased without any increase in the inter- SA interference. With respect to the spectrum capacity ηc of (1.1), it follows that a decisive increase in the spectrum capacity ηc is achievable in SA-based systems as compared to state-of-the-art mobile radio systems based on the cellular air interface architecture. For this reason, the choice of the SA air interface architecture is especially attractive for application on beyond 3G mobile radio systems, on which the demand for high spectrum capacity ηc is posed.
- 123. 113 9 Summary 9.1 Summary in English The present thesis deals with a novel air interface concept for beyond 3G mobile radio systems. Signals received at a certain reference cell in a cellular system which originate in neighboring cells of the same cellular system are undesired and constitute the intercell interference. Due to intercell interference, the spectrum capacity of cellular systems is limited and therefore the reduction of intercell interference is an important goal in the design of future mobile radio systems. In the present thesis, a novel service area based air interface concept is investigated in which interference is combated by joint detection and joint transmission, providing an increased spectrum capacity as compared to state-of-the-art cellular systems. Various algorithms are studied, with the aid of which intra service area interference can be combated. In the uplink transmission, by optimum joint detection the probability of erroneous decision is minimized. Alternatively, suboptimum joint detection algorithms can be applied offering reduced complexity. By linear receive zero-forcing joint detection interference in a service area is eliminated, while by linear minimum mean square error joint detection a trade- off is performed between interference elimination and noise enhancement. Moreover, iterative joint detection is investigated and it is shown that convergence of the data estimates of itera- tive joint detection without data estimate refinement towards the data estimates of linear joint detection can be achieved. Iterative joint detection can be further enhanced by the refinement of the data estimates in each iteration. For the downlink transmission, the reciprocity of uplink and downlink channels is used by joint transmission eliminating the need for channel estima- tion and therefore allowing for simple mobile terminals. A novel algorithm for optimum joint transmission is presented and it is shown how transmit signals can be designed which result in the minimum possible average bit error probability at the mobile terminals. By linear transmit zero-forcing joint transmission interference in the downlink transmission is eliminated, whereas by iterative joint transmission transmit signals are constructed in an iterative manner. In a next step, the performance of joint detection and joint transmission in service area based systems is investigated. It is shown that the price to be paid for the interference suppression in service area based systems is the suboptimum use of the receive energy in the uplink trans- mission and of the transmit energy in the downlink transmission, with respect to the single user reference system. In the case of receive zero-forcing joint detection in the uplink and transmit zero-forcing joint transmission in the downlink, i.e., in the case of linear unbiased data trans- mission, it is shown that the same price, quantified by the energy efficiency, has to be paid for interference elimination in both uplink and downlink. Finally it is shown that if the system load is fixed, the number of active mobile terminals in a SA and hence the spectrum capacity can be increased without any significant reduction in the average energy efficiency of the data transmission.
- 124. 114 Chapter 9: Summary 9.2 Summary in German Die vorliegende Dissertation befaßt sich mit einem neuartigen Konzept f¨ur die Luftschnittstelle von Mobilfunksystemen jenseits der dritten Generation. In einer Referenzzelle eines zellu- laren Mobilfunksystems empfangene Signale, die in Nachbarzellen des selben Mobilfunksys- tems abgestrahlt wurden, sind unerw¨unscht und bilden die Interzellinterferenz. Wegen der Interzellinterferenz ist die spektrale Kapazit¨at zellularer Systeme begrenzt und daher ist die Reduktion der Interzellinterferenz ein wichtiges Ziel beim Entwurf zuk¨unftiger Mobilfunksys- teme. In der vorliegenden Dissertation wird ein neuartiges Luftschnittstellenkonzept auf der Basis von Service Gebieten, in dem Interferenz mittels Joint Detection und Joint Transmission bek¨ampft wird und dadurch eine h¨ohere spektrale Kapazit¨at als in zellularen Mobilfunksyste- men gem¨aß dem Stand der Technik erzielt werden kann, untersucht. Eine Vielfalt von Algorithmen, mit deren Hilfe die Intraserviceareainterferenz unterdr¨uckt wer- den kann, werden untersucht. In der Aufw¨artsstrecke wird die Wahrscheinlichkeit der Fehlentschei- dung mittels optimalem Joint Detection minimiert. Alternativ kann durch geringere Kom- plexit¨at gekennzeichnetes suboptimales Joint Detection eingesetzt werden. Mit linearem Zero- Forcing Joint Detection wird die Interferenz innerhalb eines Service Gebietes eliminiert und lineares Minimum Mean Square Error Joint Detection bildet einen Kompromiss zwischen In- terferenzelimination und Rauschenverst¨arkung. Zus¨atzlich wird Iteratives Joint Detection un- tersucht und es wird gezeigt, daß Konvergenz der Datensch¨atzungen von Iterativem Joint De- tection ohne Sch¨atzwertverbesserung und linearem Joint Detection erreicht werden kann. Iter- atives Joint Detection kann man verbessern, indem man die Datensch¨atzungen in jeder Itera- tion verbessert. F¨ur die Abw¨artsstrecke wird die Reziprozit¨at zwischen den Kan¨alen der Auf- und Abw¨artsstrecke von Joint Transmission ausgenutzt. Somit wird die Notwendigkeit einer Kanalsch¨atzung in der Abw¨artsstrecke eliminiert und die Komplexit¨at der Mobile Terminals gering gehalten. Ein neuartiges Verfahren f¨ur optimales Joint Transmission wird eingef¨uhrt und der Entwurf von Sendesignalen, die zu minimaler Bitfehlerwahrscheinlichkeit an den Mo- bile Terminals f¨uhren, beschrieben. Mit Hilfe von linearem Joint Transmission kann Inter- ferenz in der Abw¨artsstrecke eliminiert werden und mit Iterativem Joint Transmission werden die Sendesignale iterativ konstruiert. In einem n¨achsten Schritt wird die Performanz von Joint Detection und Joint Transmission in auf Service Gebieten basierenden Systemen untersucht. Es wird gezeigt, daß das sub- optimale Nutzen der Empfangsenergie in der Aufw¨artsstrecke und der Sendeenergie in der Abw¨artsstrecke im Vergleich zum Referenzsystem der f¨ur die Unterdr¨uckung der Interferenz zu zahlende Preis ist. Es folgt, daß im Fall von linearem Zero-Forcing Joint Detection und lin- earem Transmit Zero-Forcing Joint Transmission der selbe Preis f¨ur die Interferenzunterdr¨uck- ung zu zahlen ist, der sich mit der Energieeffizienz quantitativ beschreiben l¨aßt. Schließlich wird gezeigt, daß bei konstanter Systemlast in einem Service Gebiet die Anzahl der Mobile Terminals beliebig erh¨oht werden kann, ohne daß die Energieffizienz der Daten¨ubertragung merklich abnimmt.
- 125. 115 Appendix A Frequently used abbreviations and symbols A.1 Abbreviations AP access point BPSK binary phase shift keying BS base station BU bad urban CCDF complemetary cumulative distribution function CDMA code division multiple access COST european cooperation in the field of science and technology CU central unit dB decibel DL downlink FEC forward error correcting HT hilly terrain JD joint detection JT joint transmission LOS line of sight MAP minimum a posteriori MF matched filter ML maximum likelihood MIMO multiple input multiple output MMSE minimum mean square error MT mobile terminal OFDM orthogonal frequecy division multiplexing QPSK quadrature phase shift keying RA rural area RxZF receive zero - forcing SA service area SNR signal to noise ratio TDD time division duplexing TU typical urban TxMF transmit matched filter TxZF transmit zero - forcing UL uplink ZF zero - forcing
- 126. 116 Appendix A: Frequently used abbreviations and symbols A.2 Symbols A area covered by the mobile radio system b(kI,kO) nF,nS (t) combined time continuous impulse response between input kI and output kO of the MIMO mobile radio channel, (3.12) B system bandwidth c0 speed of propagation of electromagnetic waves in the vacuum cr(t) basic receive signature in the analysis filter bank, (3.17) cr,nF,nS (t) impulse response of each filter in the analysis filter bank at subcarrier nF and symbol slot nS, (3.18) ct(t) basic transmit signature, (3.9) ct,nF,nS (t) transmit signature at subcarrier nF and symbol slot nS, (3.10) d(k,nF) data symbol of MT k sent at subcarrier nF , (3.38) ˆd (k,nF) estimated data symbol of MT k at subcarrier nF d (k) m m-th coded bit of MT k ˆd (k) m m-th estimated coded bit of MT k d total data vector, (3.41) ˆd total estimated data vector, (3.43) ˆd(p) total estimated data vector by iterative JD at iteration p ˆˆd(p) total refined estimated data vector by iterative JD at iteration p d(k) coded bit vector of MT k, (4.3) ˆd(k) estimated coded bit vector of MT k, (4.47) d(nF) data vector at subcarrier nF, (3.40) ˆd (nF) estimated data vector at subcarrier nF, (3.42) dv effective data vector d (nF) v effective data vector at subcarrier nF D cardinality of the data symbol alphabet D D data symbol alphabet DK set of data vectors d DK eff set of effective data vectors dv, (5.9) D(nF) demodulator matrix of linear JD at subcarrier nF D (nF) DL demodulator matrix in the DL of the generalized linear data transmission, (8.17) D (nF) MMSE demodulator matrix of MMSE JD at subcarrier nF, (4.25) D (nF) ZF demodulator matrix of RxZF JD at subcarrier nF, (4.21) D (nF) UL demodulator matrix in the DL of the generalized linear data transmission, (8.14) e(k,nF) receive value at MT k at subcarrier nF at the downlink e(kB,nF) receive value at AP kB at subcarrier nF at the uplink e(kO) (t) time-continuous received signal at output kO of the MIMO mobile radio chan- nel, (3.11)
- 127. A.2 Symbols 117 e(kO,nF,nS) receive value at output kI, subcarrier nF and symbol slot nS, (3.21) e (k,nF) v effective received value by MT k at subcarrier nF e total received vector e(kO) receive vector at output kI, (3.3) e(nF) receive vector at subcarrier nF e(nF,nS) receive vector at subcarrier nF and symbol slot nS, (3.32) e (nF) v effective received vector, (5.31) Eb average received energy per bit E (k,nF) b received energy per bit in the data symbol d(k,nF) E (k,nF) b,opt received energy per bit in the data symbol d(k,nF) in the single user reference system, (8.6) fD,w doppler shift exhibited by path w of the mobile radio channel F subcarrier spacing in a multicarrier system F forward path matrix of iterative JD (4.30) and iterative JT (5.49) h(k,kB,nF) transfer factor of the wireless channel between MT k, AP kB at subcarrier nF h(kI,kO) (t) time continuous channel impulse response between input kI and output kO of the MIMO mobile radio channel h(kI,kO,nF) discrete transfer coefficient between input kI and output kO at subcarrier nF, (3.26) H(f) time invariant complex transfer function of the point to point mobile radio channel H(f, t) time variant complex transfer function of the point to point mobile radio chan- nel H(k,kB) (f) time invariant complex transfer function of the point to point mobile radio channel between MT k and AP kB H total transfer function matrix of the uplink transmission, (4.7) H(nF) transfer function matrix at subcarrier nF of the uplink transmission H(nS,nF) transfer function matrix at subcarrier nF and symbol slot nS, (3.35) k index of MTs in the SA kB index of APs in the SA kI index of inputs of the MIMO channel kO index of outputs of the MIMO channel K number of MTs in the SA KB number of APs in the SA KI number of inputs to the MIMO channel KO number of outputs of the MIMO channel L number of bits corresponding to each MT k M number of outputs of a MIMO channel MB number of receivers in an excerpt of a MIMO system M total modulator matrix for TxZF JT M(nF) modulator matrix of linear JT at subcarrier nF M (nF) DL modulator matrix in the DL of the generalized linear data transmission, (8.19)
- 128. 118 Appendix A: Frequently used abbreviations and symbols M (nF) TxZF modulator matrix for TxZF JT at subcarrier nF, (5.40) M (nF) UL modulator matrix in the UL of the generalized linear data transmission, (8.12) M∞ linear modulator matrix, to which iterative JT converges (5.46) n(kO) (t) noise at output kO n(kO,nF,nS) noise value at output kO, subcarrier nF and symbol slot nS, (3.22) ˜nd noise value disturbing the coded bit d (k) m nF subcarrier index nS symbol slot index n total noise vector n(nF) noise vector at subcarrier nF n(nF,nS) noise vector at subcarrier nF and symbol slot nS, (3.33) N number of inputs of a MIMO channel N0 one-sided power spectral density of the noise n(kO) (t) NB number of transmitters in an excerpt of a MIMO system NF number of subcarriers NS number of symbol slots p index of iterations of iterative JD and iterative JT P number of iterations of iterative JD and iterative JT P (k,nF) b bit error probability of data symbol d(k,nF) P (nF) b bit error probability averaged over the V effective data vectors d(nF) v , v = 1 . . .V , (5.35) P (nF) b,v average bit error probability of the effective data vector d(nF) v , (5.34) P (k,nF) b,ref bit error probability of data symbol d(k,nF) in the single user reference system P (k,nF) b,RxZF bit error probability of data symbol d(k,nF) in RxZF JD, (6.27) P (k,nF) b,v bit error probability of data symbol d(k,nF) in the effective data vector d(nF) v P (k,nF) b,v,opt bit error probability of data symbol d(k,nF) in the effective data vector d(nF) v in optimum JT P (k,nF) b,v,TxZF bit error probability of data symbol d(k,nF) in the effective data vector d(nF) v in TxZF JT r(k,kB) distance between MT k and AP kB in the indoor geometric channel model, (2.3) rB radius of the circular periphery on which the APs are positioned in the SA according to the geometric channel model r output vector of matched filter bank in iterative JD, (4.26) R rate of the FEC code R(k,nF) receive energy corresponding to data symbol d(k,nF) R (k,nF) ref receive energy corresponding to data symbol d(k,nF) in the single user refer- ence system, (7.6) R reverse path matrix by iterative JD (4.31) and iterative JT (5.50) Rn noise correlation matrix, (3.34) R (nF) dd data correlation matrix at subcarrier nF, (4.24)
- 129. A.2 Symbols 119 s(kB,nF) transmit value from AP kB at subcarrier nF at the downlink s(kI,nF,nS) transmit value at input kI, subcarrier nF and symbol slot nS s (kI) nF,nS(t) partial time continuous transmit signal corresponding to transmit value s(kI,nF,nS) , (3.5) s(kI) (t) time continuous transmit signal fed to the input kI of the time continuous MIMO mobile radio channel, (3.6) s total transmit vector s(p) total transmit vector at iteration p of iterative JT, (5.43) s(kI) transmit vector at input kI, (3.2) s(nF,nS) transmit vector at subcarrier nF and symbol slot nS, (3.31) s(nF) transmit vector at subcarrier nF s (nF) opt transmit vector of optimum JT s (nF) v effective transmit vector corresponding to the effective data vector d (nF) v , (3.31) s (nF) v,opt effective transmit vector corresponding to the effective data vector d (nF) v of optimum JT s (nF) 0,v normalized effective transmit vector corresponding to the effective transmit vector s (nF) v , (5.17) S (τ, fD) scattering function of the mobile radio channel Sc (0, fD) Doppler power spectrum of the mobile radio channel S (nF) eff set of effective transmit vectors s (nF) v , (5.12) S (nF) opt set of transmit vectors s (nF) opt of optimum JT S (nF) eff,opt set of effective transmit vectors s (nF) v of optimum JT t(p) transformed total data vector at iteration p of iterative JT, (5.42) t(k,nF) transmission efficiency of data symbol d(k,nF) , (7.27) t (k,nF) DL transmission efficiency of data symbol d(k,nF) in the DL of the generalized unbiased linear data transmission, (8.20) t (k,nF) TxZF transmission efficiency of data symbol d(k,nF) in TxZF JT, (7.30) t (nF) TxZF transmission efficiency averaged over the K data symbols d(k,nF) , k = 1 . . .K, in TxZF JT t (k,nF) UL transmission efficiency of data symbol d(k,nF) in the UL of the generalized unbiased linear data transmission, (8.13) t (nF) v energy factor of effective transmit vector s (nF) v T transmit energy corresponding to a single data symbol T(k,nF) transmit energy corresponding to data symbol d(k,nF) Th time duration of the time continuous channel impulse response h(kI,kO) (t) Ts time duration of an OFDM symbol slot T (k,nF) ref transmit energy corresponding to data symbol d(k,nF) in the single user refer- ence system, (7.4) T (nF) tot total transmit energy of JT at subcarrier nF, (5.39) T (nF) tot,v energy of effective transmit vector s (nF) v , (5.14)
- 130. 120 Appendix A: Frequently used abbreviations and symbols T (nF) tot,v transmit energy averaged over all V effective transmit vector s (nF) v , (5.15) u(k) bit vector corresponding to MT k, (3.1) ˆu(k) estimated bit vector corresponding to MT k, (3.4) u (k) l l-th bit corresponding to MT k ˆu (k) l l-th estimated bit corresponding to MT k v index of effective data vectors V cardinality of the set DK eff of effective data vectors dv, (5.11) W number of paths of the mobile radio channel xmax horizontal dimension of the SA in the indoor geometric channel model x (kB) AP horizontal coordinate of AP kB in the indoor geometric channel model x (k) MT horizontal coordinate of MT k in the indoor geometric channel model ymax vertical dimension of the SA in the indoor geometric channel model y (kB) AP vertical coordinate of AP kB in the indoor geometric channel model y (k) MT vertical coordinate of MT k in the indoor geometric channel model γ (k,nF) ref SNR corresponding to data symbol d(k,nF) of the single user reference system in the UL (6.6) γ (k,nF) RxZF SNR corresponding to data symbol d(k,nF) in RxZF JD (6.26) δ (k,nF) RxZF SNR degradation of data symbol d(k,nF) in RxZF JD (6.35) ε(k,nF) average energy efficiency in the generalized unbiased linear data transmission ε(k,nF) energy efficiency of data symbol d(k,nF) in the generalized unbiased linear data transmission (8.26) ε (k,nF) DL energy efficiency of data symbol d(k,nF) in the DL of the generalized unbiased linear data transmission (8.21) ε (k,nF) UL energy efficiency of data symbol d(k,nF) in the UL of the generalized unbiased linear data transmission (8.16) θw null phase angle of path w of the mobile radio channel θ (nF) v angles for the representation of the energy factors t (nF) v , v = 1 . . . V , in the generalized coordinate system, (5.30) η(k,nF) asymptotic multiuser efficiency of data symbol d(k,nF) , (6.25) η (k,nF) DL asymptotic multiuser efficiency of data symbol d(k,nF) in the DL of the gen- eralized unbiased linear data transmission, (8.18) η (k,nF) UL asymptotic multiuser efficiency of data symbol d(k,nF) in the UL of the gen- eralized unbiased linear data transmission, (8.15) ηc spectrum capacity, (1.1) η (k,nF) e (σ2 ) multiuser efficiency of data symbol d(k,nF) , (6.24) η (k,nF) RxZF asymptotic multiuser efficiency of data symbol d(k,nF) in RxZF JD, (6.33) η (nF) RxZF asymptotic multiuser efficiency averaged over the K data symbols d(k,nF) , k = 1 . . .K, in RxZF JD λ system wavelength λmax(X) spectral radius of matrix X, (4.32) λq eigenvalue q, q = 1 . . . Q, of a complex matrix ρ parameter of the MIMO parametric channel model, (2.6)
- 131. A.2 Symbols 121 ρkkB parameter of the extended MIMO parametric channel model, describing the transfer factor between MT k and AP kB, (2.7) ρT(τ, 0) delay power spectrum of the mobile radio channel σ2 variance of real and imaginary parts of the noise n(kO) (t) σ2 d variance of the noise value ˜nd disturbing the coded bit d (k) m ˆσ2 d estimated variance of the noise value ˜nd disturbing the coded bit d (k) m τw delay of path w of the mobile radio channel ϕ (kB,nF) v angles for the representation of the normalized effective transmit vector s (nF) 0,v in the generalized coordinate system, (5.29) ϕ (kB,nF) v,opt angles corresponding to optimum JT in the generalized coordinate system ϕ (kB,nF) v,TxZF angles corresponding to TxZF JT in the generalized coordinate system
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- 145. Tabellarischer Lebenslauf 135 Tabellarischer Lebenslauf Name: Alexandros Sklavos Adresse: Hermann–Hesse–Straße 30 67663 Kaiserslautern Geburtsdatum: 15. Juli 1977 Familienstand: ledig Staatsangeh¨origkeit: griechisch Schulausbildung: September 1983 – Juni 1989 Grundschule in Athen September 1989 – Juni 1992 Gymnasium in Athen September 1992 – Juni 1995 Lyzeum in Athen Schulabschluß: Abitur Hochschulaufnahmenpr¨ufung: Juni 1995 Studium: Oktober 1995 – Juli 2000 Studium der Elektrotechnik an der Technischen Universit¨at Athen Studienabschluß: Diplom Berufst¨atigkeit: September 2000 – Dezember 2000 wissenschaftliche Hilfskraft am Lehrstuhl f¨ur hochfrequente Signal¨ubertragung und –verarbeitung der Universit¨at Kaiserslautern seit Januar 2001 wissenschaftlicher Mitarbeiter am Lehrstuhl f¨ur hochfrequente Signal¨ubertragung und –verarbeitung der Universit¨at Kaiserslautern