Receive Antenna Diversity and Subset Selection in MIMO Communication Systems

ACEEE Int. J. on Communication, Vol. 02, No. 03, Nov 2011

Receive Antenna Diversity and Subset Selection in
MIMO Communication Systems
Prof. Shreedhar A. Joshi 1, Dr. Rukmini T S 2, and Dr. Mahesh H M 3
1
Assistant Professor, Electronics& Communication Department, SDMCET, Dharwad, India
2
Professor in Telecommunication Department and Fellow IEEE member, RVCE, Bangalore, India.
3
Associate Professor & Chairman Applied Electronics Department, Bangalore University, Bangalore, India.
Shreedhar.j@rediffmail.com

Abstract— The performance of Multiple-input Multiple-output capacity of wireless communications systems is investigated
(MIMO) systems can be improved by employing a larger in [10]When the MIMO channel is time-varying, the optimal
number of antennas than actually used or selected subset of antenna subset is no longer fixed. To cope with this situation
antennas. Most of the existing antenna selection algorithms one has to track the time-varying optimal antenna subset.
assume perfect channel knowledge and optimize criteria such
Early work on antenna selection focused on selection in
as Shannon’s capacity on bit error rates. The proposed work
examines Antenna diversity and optimal/ sub optimal receive MISO/SIMO systems. This included the hybrid selection/
strategy in antenna selection. The numerical results for BER, maximal ratio combining approach in [11]. Recently, there has
Information capacity with SNR are obtained using mat lab been increasing interest [12]–[16] in applying antenna subset
selection techniques to MIMO links. In [12], the authors
Index Terms— SISO, SIMO, MRC, SNR, BER, SC. present a criterion for selecting antenna subsets that maximize
the channel capacity. As shown in [13], antenna selection
I. INTRODUCTION techniques applied to low-rank channels can increase
Although MIMO technology improves reliability and capacity. A fast selection algorithm based on “water-pouring”
transmission rates achievable in wireless systems [1–6], the type ideas is presented in [14]. In [15], Heath et al., discuss
improvement comes at the expense of higher hardware cost. antenna subset selection for spatial multiplexing systems with
Indeed, every extra transmit/receive antenna requires its own practical receivers. Antenna selection algorithms/analysis for
hardware chain (power amplifier, low noise amplifier (LNA), space–time codes based on exact and statistical channel
analog to digital (A/D) convertors, etc.). Therefore, cost- knowledge may be found in [16]. An Efficient Transmit
effective implementation of MIMO technology remains a antenna subset selection with OFDM technique is considered
major challenge. Antenna subset selection, where in [17]. In [18] optimal antenna subset selection problem for
transmission/reception is performed through a subset of the maximizing the mutual information in a point-to-point MIMO
available antenna elements, helps in reducing the system is considered. The remainder of this paper is
implementation cost while retaining most of the benefits of organized as follows. In Section 2, the MIMO system model
MIMO technology. We begin by reviewing some well-known with antenna selection is presented. We also formulate the
results on maximum ratio combining and receive antenna Receive antenna diversity problem. In Section 3, optimal and
selection for single-input-multiple-output (SIMO) antenna sub-optimal selection techniques are analyzed theoretically.
systems. In this way, only the best set of antennas is used, In Section 4, several antenna selection criteria are presented,
while the remaining antennas are not employed, thus reducing including maximum capacity, minimum bound on error rate
the number of required RF chains. The proposed technique and minimum error rate with respect to SNR. In Section 5,
only selects the subset of transmit or receive antennas based Numerical results are addressed. Section 6 contains the
on the Shannon capacity criterion. Antenna selection conclusions.
algorithms that minimize the bit error rate (BER) of linear
receivers in spatial multiplexing systems are presented in [7]. II. SIGNAL AND CHANNEL MODELS

In [8], antenna selection algorithms are proposed to minimize The proposed signal model uses channel matrix approach
the symbol error rate when orthogonal space-time block between the NT transmit and NR receive antennas and is
coding is used in MIMO systems. In [9] a framework is assumed to be non-selective, that is, flat fading and linear
presented to analyze the performance of multiuser diversity time invariant. The signal model follows the equation
(MUD) in multiuser point-to-multipoint (PMP) MIMO
systems with antenna selection and average symbol error Where x[k] = [x1[k]. . . xNR [k]]T is the NR × 1 vector corre-
rate are derived for the multiuser transmit antenna selection sponding to the signal received at the NR receivers and
with maximal-ratio combining (TAS/MRC) system. The sampled at the symbol rate, s[k] = [s1[k], . . sNT [k]]T Corre-
influence of radiation efficiency on diversity gain and MIMO sponds to the NT × 1 symbol vector transmitted by the NT
This is the part of Research work for Prof. Shreedhar A Joshi with RV transmit antennas, ρ is the average signal energy per receive
Center for Cognitive Technologies (RVCCT) Bangalore, and Dept of antenna and per channel use. n[k] = [n1[k], . . ., nNR [k]]T. is the
Research in Electronics, KU, India. additive white Gaussian noise (AWGN) with variance 1/2
© 2011 ACEEE 21
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per real dimension and H =[H:,1, . . . ,H:,NT ] is the NR ×NT In other words, the weight factor of each branch in the above
channel matrix, H:,q = [H1,q, . . . ,HNR,q ]T , 1 d” q d” NT , where equation must be matched to the corresponding channel for
Hp,q is a scalar channel between the pth receive and the qth maximal ratio combining (MRC). Equal gain combining (EGC)
transmit antenna. Figure 1 shows different antenna configu- is a special case of MRC in the sense that all signals from
rations and SIMO, MISO and MISO signal models leads to multiple branches are combined with equal weights. In fact,
antenna diversity gains h i,j which represents different gains MRC achieves the best performance, maximizing the post-
resulted from various links. combining SNR. The simulation result shown in section 4
indicates that the performance improves with the number of
receiving antennas.
B. MRC versus antenna selection: performance Comparison
The analytical characterization of MRC and antenna
selection depends on the receive SNR and antenna selection.
With one optimally selected antenna, as a function of the
number of receive antennas, the increasing number of receive
antenna elements and its performance “gap” between MRC
and antenna selection becomes quite substantial. This is
hardly surprising since using fewer antennas ought to lead
Figure 1. Different Antenna configurations results Receive to a loss in average received energy. The real gain of antenna
Diversity selection in a fading environment is the improved diversity
A. Maximum ratio combining with receive diversity benefit. The inequality states that the SNR through selection
is bounded above by the squared channel Frobenius norm
Consider a receive diversity system with NR receiver (upper bound through MRC) and below by the average power
antennas. Assuming a single transmit antenna as in the single over all antennas. Since both quantities are gamma distributed
input multiple output (SIMO) channel of Figure 1, the channel with parameter NR the post selection SNR is bounded above
is expressed as and below by two quantities with the same diversity. This
h= [ h1,h 2, ….. h NR ] T (2) implies that receive selection delivers the same diversity as
for NR independent Rayleigh fading channels. Let x denote MRC [19, 20].
the transmitted signal with the unit variance in the SIMO
channel. III. ANTENNA SELECTION IN MIMO SYSTEMS
Assume the presence of MT transmit antenna elements
and MR receive antenna elements, shown in Figure.2. For a
Where Z is zero mean signal Gaussian noise with respect to given channel instantiation, NT out of MT transmit antenna
NR. The received signals in the different antennas can be elements and NR out of MR receive antenna elements are
combined by various techniques. These combining selected and used for transmission and reception,
techniques include selection combining (SC), maximal ratio respectively. In general, RF modules include low noise
combining (MRC), and equal gain combing (EGC). amplifier (LNA), frequency down-converter, and analog-to-
In MRC, all N R branches are combined by the following digital converter (ADC). In an effort to reduce the cost
weighted sum: associated with the multiple RF modules, antenna selection
YMRC = [ w1(MRC) w2(MRC) ….. wNR (MRC)] y techniques can be used to employ a smaller number of RF
modules than the number of transmit antennas. Figure
illustrates the end-to-end configuration of the antenna
Where y is the received signal in equation (4) and w MRC is selection in which only few RF chains are used to support
the weight vector. Equation (3), the combined signal can be NT transmit antennas and even Note that few RF modules are
decomposed into signal and noise parts selectively mapped to NT transmit antennas.

The average SNR for the MRC is given as

ρ MRC = Ps / Pz = E X / N0

Where term contains upper bounds of rescued SNR for all
signals with equal weights. Note that the SNR is maximized at
Figure 2. Antenna selections with RF chains and N T transmit
W MRC = h*, which yields
a ntenna s

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A. Optimum Antenna Selection Technique IV. WORKING ALGORITHMS
A set of Q transmit antennas must be selected out of NT Based on the theoretical assumptions, we have
transmit antennas so as to maximize the channel capacity. constructed the following algorithms (later converted as m-
When the total transmitted power is limited by P, the channel files). The first algorithm depicts receive diversity technique
capacity of the system using Q selected transmit antennas is with MRC under Rayleigh fading channel. The working
given by procedure for the same is as follows:
1. Start.
2. Assume No of frames, No of Packets, set Digital
Modulation method as QPSK and SNR limit in db.
Where Rxx is Q is covariance matrix. If equal power is allocated 3. For first iteration, assume No of Transmit and Receive
to all selected transmit antennas, which yields the channel antennas as NT= NR=1.
capacity for the given as 4. For further iterations, let the Numbers of Tx/Rx
antennas are either NT=1, NR=2 or NT=1, NR=4 and
obtaining a parameter sq_NT = sqrt (NT).
5. From SNR in dB, each packet, L, No of frames, obtain
Sigma as sigma=sqrt (0.5/(10^(SNR_dB/10)
The optimal selection of P antennas corresponds to
6. Channel matrix H can be constructed from frame
computing Equation (7) for all possible antenna combinations.
length, NR
In order to maximize the system capacity, one must choose
7. For i=1:NR then autocorrelation factor R is calculated
the antenna with the highest capacity, that is,
with respect to number of iterations (i) as
{p1opt, p2opt ….. pQopt } = arg max C { p1, p2,….. pQ } (9)
R (i) = sum (H(i))/sq_NT + sigma*(randn (L_frame,1)
{p 1, p 2,….. pQ}ª A Q
8. The noise vector Z is calculated as
Where A Q represents a set of all possible antenna Z = Z + R(i).*conj(H(i))
combinations with Q selected antennas. 9. Plot SNR Vs BER.
B. Sub-optimal Antenna Selection 10. Stop.
As mentioned in the previous subsection, optimal antenna Similarly the working procedure for optimal antenna
selection may involve too much complexity depending on selection in MIMO system is as follows;
the total number of available transmit antennas. In order to 1. Start.
reduce its complexity, we may need to resort to the sub-optimal 2. Select transmit/ Receive antennas as NT= NR=4; 3.
method. For example, additional antenna can be selected in 3. Calculate I=eye (NR, NR)
ascending order of increasing the channel capacity. More 4. Assume SNR range SNR dBs.
specifically, one antenna with the highest capacity is first 5. Assume Q as antenna selection factor (sel_ant) from
selected as 1to 4 and determine the length of SNR_dBs.
p1subopt = arg max pi C{ pi} (10) 6. For Individual antenna selection SNR is assumed as
= arg max pi log2 det (I N + EX/QNO H{ p } HH { p } )
R 1 1,
SNR_sel_ant = 10 ^ (SNR_dB /10) / Q.
7. Obtain H as
Given the first selected antenna, the second antenna is H = (randn (NR,NT) + j*randn (NR,NT))/sqrt (2)
selected such that the channel capacity is maximized, that is, 8. If Q > NT | Q < 1 then
p1subopt = arg max subopt
C{ p1subopt,p2} Display as ‘sel_ant must be between 1 and NT !’
= arg max p2‘“ p1 subopt
log2 det (I N + EX/QNO 9. Determine capacity from H (n) factor and
R

H{ p ,p } HH { p ,p } )
subopt
(11) subopt
Select capacity for maximum iterations.
1 2 1 2,
10.Plot (SNR_dBs, sel_capacity)
After the nth iteration which provides { p1subopt, p 2subopt,…. The sub-optimal selection working procedure is as follows;
Pn subopt} the capacity with an additional antenna l, assumed 1. Start.
as ( n+1) th antenna that maximizes the channel capacity in 2. Determine Number of antennas to select as sel_ant=2.
Equation (10), that is, This process continues until all Q 3. Assume 0/1 for increasingly/decreasingly ordered
antennas are selected ( till n +1 = Q) with only one matrix Selection
inversion. 4. Assume Number of Tx / Rx antennas as NT=NR=4.
p1subopt = arg max l{pi} Cl (12) 5. Obtain, I=eye (NR, NR).
= arg max l p … p } H{l} ((QNO/ EX) I N
1
subopt
n
subopt
R 6. From SNR range (SNR_dBs)
+ H{ p … p } HH { p … p } )-1
1
subopt
n
subopt
1
subopt
n
subopt SNR with selection antenna is given by
SNR_dBs = 10 ^ (SNR_dB/10) / sel_ant;
7. Determine selection_antenna_indices upto [1:NT]
8. Calculate Channel matrix (H) as
H = (randn (NR,NT)+j*randn(NR,NT))/sqrt(2);
© 2011 ACEEE 23
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9. If sel_method==0 then, assume increasingly ordered In order to reduce the complexity of optimal selection process
Selection method. the sub-optimal antenna selection method, with additional
10. For current_sel_ant_number =1:sel_ant antenna can be selected in ascending order that increases
obtain H(n) as the channel capacity. The performance is evident from
log_SH(n) = log2(real(det (I+SNR_sel_ant*Hn*Hn’))) Figure.5.
11. The maximum capacity is depicted as
Maximum capacity = max (log_SH);
12. With the help of selected antenna index and
Current_del_ant_number determine increasing order
Maximum capacity with n+1=Q antennas else repeat
the same procedure for decreasingly ordered selection
method with n-1=Q and determine maximum capacity
13. Plot SNR_dB Vs capacity.

V. RESULTS AND DISCUSSIONS
The effect of symbol errors with SNR in MRC technique
is shown in Figure.3. Here SISO (Single Input Single Output) Figure 5. Sub- Optimal antenna selection for different Q
scheme is compared with SIMO (Single Input Multiple
Output) scheme. The results clearly indicating improvement CONCLUSIONS
in Error propagation.
In this paper, we have considered Antenna Diversity
method and MIMO antenna selection. MRC scheme
improves the information capacity with auto correlation factor.
One of the main theoretical conclusions is that selecting a
subset of antennas at the transmitter and/or receiver delivers
the diversity gain of a “full” system that makes use of all
available transmit/receive antennas. This fundamental result
extends the well-known observation that selecting a single
receive antenna delivers the full diversity gain in a system
with a single transmit antenna. Additionally, we extended the
Figure 3. Receive antenna diversity with MRC framework of diversity versus multiplexing trade-off of MIMO
systems to systems with antenna selection. The optimal and
We consider the performance of Algorithm II (optimal
Sub-optimal antenna selection techniques provide a
selection method) which selects the antenna subset
possibility of substantial gain increase through increasing
maximizing the channel capacity. Here, the transmitter and
and decreasing order by ascending/ descending selection
Receiver antennas are assumed as Tx=Rx= 4 . Even
strategies with respect to antennas.
considering all possible antenna combinations according to
equations mentioned in section III, involving with the
ACKNOWLEDGMENT
enormous complexity, especially when NT is very large.
Figure. 4 shows the channel capacity with antenna selection The authors wish to thank The Director, RVCCT
for NT = 4 and NR = 4 as the number of the selected antennas Bangalore and Principal / Director SDMCET Dharwad India
varies by antenna selection factor (Q) assumed as Q = 1; 2; 3; for extending co-operation and support.
4. It is clear that the channel capacity increases in proportion
to the number of the selected antennas. When the SNR is REFERENCES
less than 10dB, the selection of three antennas is enough to
[1] J. Winters, “On the capacity of radio communication systems
warrant the channel capacity as much as the use of all four with diversity in a Rayleigh fading environment,” IEEE J. Sel. Areas
antennas. Commun., vol. 5, no. 5, pp. 871–878, Jun. 1987.
[2] A. Paulraj and T. Kailath, “Increasing capacity in wireless
broadcast systems using distributed Transmission directional
reception,” U. S. Patent, no. 5,345,599, 1994.
[3] I. Telatar, “Capacity of multi-antenna Gaussian channels,”
AT & T Bell Laboratories, Tech. Rep. #BL0112170-950615-07TM,
1995.
[4] G. Foschini, “Layered space-time architecture for wireless
communication in a fading environment when using multi-element
antennas,” Bell Labs Tech. J., vol. 1, no. 2, pp. 41–59, 1996.
[5] I. Telatar, “Capacity of multi-antenna Gaussian channels,”Eur.
Trans. Telecomm., vol. 10, no. 6, pp. 585–595, Nov. /Dec. 1999.
Figure 4. Optimal antenna selection for different Q
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[6] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space- [18] Rahul Vaze, Harish Ganapathy,” Sub-modularity and
time Wireless Communications. Cambridge University Press, May Antenna Selection in MIMO systems” Cornell University
2003. Library [ August 2011] ,In press.
[7] I. A. Gore and A.I. Paulraj. “MIMO antenna subset [19] A. Gorokhov, D. Gore, and A. Paulraj, “Receive antenna
selection with space time coding,” IEEE Pane Sig. Prc... selection for MIMO flat-fading channels,”IEEE Trans. Inf.
50(10):2580-2588. Oct. 2002. Theory, vol. 49, pp. 2687–2696, Oct. 2003.
[8] R. Heath and A. Paulraj, “‘Antenna selection for spatial [20] A. Gorokhov, D. Gore, and A. Paulraj, “Receive antenna
Multiplexing systems based on minimum error rate,’’ In Prc. /IEEE selection for spatial multiplexing: theory and algorithms,” IEEE
Int. Conf on Communication.(ICC). Helsinki, Finland, IUD. 2001. Trans. Signal Proc., vol. 51, pp. 2796–2807, Nov. 2003.
[9] Xing Zhang Zhaobiao Lv Wenbo Wang,”Performance analysis
of Multiuser Diversity in MIMO Systems with Antenna Selection”, Mr. Shreedhar A Joshi received B.E degree in
Key Lab of Universal Wireless Commun., Beijing, IEEE Wireless Electronics and Communication from Karnataka
Transactions, [Issue 1,pp 15-21,Jan 2008] University Dharwad 1994. He has obtained his
[10] Juan F. Valenzuela-Valdés, Miguel A. García-Fernández, M. Tech degree in Digital Electronics from VTU
Antonio M. Martínez-González, and David A. Sánchez-Hernández, Belgaum in 2001. He served as a senior faculty
Senior Member, IEEE,” The Influence of Efficiency on Receive member in various Engineering colleges.
Diversity and MIMO Capacity for Rayleigh-Fading Channels”, Presently he is working as a Assistant Professor in
IEEE transactions on antennas and propagation, [vol. 56,pp. 5, Department of Electronics and communication, SDM College of
may 2008]. Engineering Dharwad India. He is persuing PhD in Kuvempu Uni-
[11] M. Win and J. Winters, “Virtual branch analysis of symbol versity Shimoga and doing research in MIMO wireless communi-
Error probability for hybrid selection/maximal-ratio combining in cation field. He has published many international journal papers,
Rayleigh fading,”IEEE Trans. Commun., vol.49, pp. 1926–1934, IEEE papers Recently He has presented and published a springer
Nov. 2001. LNCIST paper at Kuala Lmpur Malaysia.
[12] R. Nabar ,D. Gore, and A. Paulraj, “Optimal selection and use Dr.T. S. Rukmini, Professor, Dept of
of transmit antennas in wireless systems,” in Proc. Int. Conf. Telecommunication Egineering & P G obtained her
Telecommunications (ICT’2000), Acapulco, Mexico,2000. Doctoral degree in Microwave Engineering and
[13] D. A. Gore, R. U. Nabar, and A. Paulraj, “Selecting an optimal Antenna Design Microwave Engineering from
set of transmit antennas for a low rank matrix channel,” in Proc. IISc, Bangalore, Master Degree in P.C.M
IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol. 5, (P.M.majors) from Bangalore University and
Istanbul, Turkey, May 2000, pp. 2785–2788.
Bachelors degree in P.C.M. From Mysore University. Her research
[14] S. Sandhu, R. Nabar, D. Gore, and A. Paulraj, “Near-optimal
interests are Microwave, Antenna and Radars. She is investigating
selection of transmit antennas for a MIMO channel based on
two funded research projects from ISRO & DRDO. She has
Shannon capacity,” in Proc. Asilomar Conf. Signals, Systems and
presented and published papers at national and International
Computers, vol. 1, Pacific Grove, CA, Nov. 2000, pp. 567–571.
conference and Journals. She is also IEEE fellow member.
[15] R. Heath and A. Paulraj, “Antenna selection for spatial
Dr. Mahesh H. M. received B Sc degree in 1988, M.
multiplexing systems based on minimum error rate,” in Proc. IEEE
Sc. degree in 1992 from University of Mysore
Int. Conf. Communications, vol. 7, Helsinki, Finland, June 2001,
respectively. He has obtained his Ph.D from
pp. 2276–2280.
University of Mangalore in 2002. From 2002 onwards,
[16] A. Gorokhov, “Antenna selection algorithms for MEA
worked a post doctoral research Fellow in Queen’s
Transmission systems,” in Proc. IEEE Int. Conf. Acoustics,
University, Belfast, Ireland. From 2004 onwards, he
Speech, and Signal Processing, vol. 3, Orlando, FL, May2002, pp. has worked as a lecturer and coordinator, Department of studies &
2857–2860. research in Electronics, Kuvempu University, shimoga. He is
[17] Madan Lal,”An Efficient Technique for Optimal Selection of presently working as Associate Professor & chairman in the
Transmit Antenna Subset in MIMO-OFDM Systems using GA Department of Applied Electronics Science, Bangalore University,
with Adaptive Mutation” ,European Journal of Scientific Bangalore. His research interests are thin film electronics, molecular
Research,[Vol.38 No.3 (2009), p.396- 410] electronics, radiation physics,, Wireless Communication etc.

© 2011 ACEEE 25
DOI: 01.IJCOM.02.03. 514

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