PERFORMANCE ANALYSIS OF THE LINK-ADAPTIVE COOPERATIVE AMPLIFY-AND-FORWARD RELAY NETWORKS WITH OPPORTUNISTIC RELAYING STRATEGY

International Journal of Computer Networks & Communications (IJCNC) Vol.8, No.3, May 2016
DOI: 10.5121/ijcnc.2016.8301 1
PERFORMANCE ANALYSIS OF THE LINK-ADAPTIVE
COOPERATIVE AMPLIFY-AND-FORWARD RELAY
NETWORKS WITH OPPORTUNISTIC RELAYING
STRATEGY
Bhuvan Modi, O. Olabiyi and A.Annamalai
Center of Excellence for Communication Systems Technology Research
Department of Electrical and Computer Engineering,
Prairie View A & M University, TX 77446 United States of America
ABSTRACT
This paper analyzes the performance of cooperative amplify-and-forward (CAF) relay networks that
employ adaptive M-ary quadrature amplitude modulation (M-QAM)/M-ary phase shift keying (M-PSK)
digital modulation techniques in Nakagami-m fading channel. In particular, we present and compared the
analysis of CAF relay networks with different cooperative diversity and opportunistic routing strategies
such as regular Maximal Ratio Combining (MRC), Selection Diversity Combining (SDC), Opportunistic
Relay Selection with Maximal Ratio Combining (ORS-MRC) and Opportunistic Relay Selection with
Selection Diversity Combining (ORS-SDC). We advocate a simple yet unified numerical approach based on
the marginal moment generating function (MGF) of the total received SNR to compute the average symbol
error rate (ASER), mean achievable spectral efficiency, and outage probability performance metrics.
KEYWORDS
Cooperative communications, adaptive M-QAM/MPSK modulation, Opportunistic relay selection
1. INTRODUCTION
The current and the future network design is highly challenged in every front due to increasing
connectivity and data rate requirements. The global internet traffic has experienced exponential
growth in the past 10 years and this plummeting growth is expected to continue in the future.
Cisco has predicted that annual global internet traffic is expected to reach zettabyte threshold by
2015 from current 15 billion network connections (including machine-to-machine connections)
[1]. This means, an average of more than two devices are expected to be in use per person on
earth. This surge in connectivity is attributed to the proliferation of the communication devices
such as tablets, mobile phones, connected appliances, and other smart machines. Since most of
these devices are mobile in nature, the increased connectivity requirement will be placing a huge
demand on already limited wireless network access resources. Also, as most of the predicted
internet traffic is expected to be dominated by video contents, there is a need to find more cost
effective ways of delivering these high data rate services to the end users within the limited
wireless channel bandwidth. Therefore, the development of very high-speed wireless access
system is imperative. Most of the ongoing communication research and industrial standard efforts
are dedicated to solving this problem. In fact the evolution of mobile networks from 2/2.5G
(GSM, GPRS, EDGE, IS95/IS98) to 3G (WCDMA/HSPA/CDMA2000) and to 4G (LTE/
HSPA+/ WIMAX) has been in response to address this issue [2]. While the current 4G access

2
network holds the promise of delivering up to 1GBps data rate to end users (mostly available at
the macrocell base station), the proliferation of mobile devices has lead to very small-size "hot
spot" and therefore require extensive dimensioning of network resources in terms of coverage.
These hot spots could be homes, trains, airports and possibly buses with high data rate wireless
access requirements. The range extension (with high speed connectivity) has been a major point
of interest in LTE advance standard, and femtocells (very small base stations installable by the
end users) have been identified as the most promising potential solution. Since femtocells will act
as relays between the end user and the macrocells (regular base station) with multiple femtocells
expected to cooperate, the 4G network can greatly benefit from the ongoing research on the new
communication paradigm of cooperative relay system. The deployment of a large number of
femtocells can then be used to improve coverage, capacity (area and system spectral efficiency),
and energy efficiency of the wireless network access system.
The cooperative relay communication system takes advantage of the broadcast nature of the
wireless channel to improve the communication between the source node and a destination node
with the aid of one or more relay nodes. The system harnesses the new form of spatial diversity
and combat multipath fading, thereby improving the spectral efficiency, and reducing the
transmission error, system outages, and transmission power. The reduced transmission power (of
wireless device, femtocell and macrocell) effectively lowers the inter and intra macrocell
interference, thereby improving both the system and the area spectral efficiency. In another
development, the “cooperative diversity system” concept has gained research impetus owing to its
inherent ability to overcome the practical implementation issue of packing a large number of
antenna elements (to exploit the benefits of multiple-input-multiple-output (MIMO) space-time
processing techniques) in small form-factor devices. In general, there are three cooperative
relaying protocols: amplify-and-forward, decode-and-forward, and compress-and-forward [3-7].
The other variations include incremental, opportunistic, blind and semi-blind relays. In this
article, we advocate the implementation of the amplify-and-forward protocol on femtocell. The
advantages of this include its simplicity, lower implementation cost (i.e., relay nodes (femtocells)
do not have to decode and then re-encode the information received prior transmission) and
possibly the better privacy. The main drawback of the regular cooperative amplify-and-forward
(CAF) diversity system which employs the maximum ratio combining (MRC) or selection
diversity combining (SDC) at the destination's receiver is that each relay has to transmit on the
orthogonal channels (TDMA/CDMA). Therefore, the spectral efficiency is scaled by 1/(N+1),
where N is the number of relays, which reduces the capacity with increasing number of relays. In
order to improve this, Bletsas et al. and Zhao et al. [8-11], proposed relay selection method
otherwise known as the opportunistic relaying system (ORS). Here, the best relay is selected prior
to relay-to-destination transmission to limit the number of orthogonal transmissions to two. The
destination would then employ either MRC (subsequently referred to as ORS-MRC) or SDC
(subsequently referred to as ORS-SDC) diversity scheme on the two final diversity paths. In
addition to reducing the number of independent transmissions, the ORS protocols have been
shown to achieve full diversity just like regular relay system [27].
Adaptive transmission is yet another powerful wireless communication strategy for improving the
spectral utilization efficiency, wherein the signal constellation size, power level and/or the coding
rate are “matched” to the prevailing channel conditions based on the acquired channel-side-
information (CSI) on the feedback channel. Several articles have investigated the combination of
the link adaptation and the regular cooperative diversity system, both from theoretical limit
(ergodic capacity) and practical implementation (using digital modulation schemes) perspectives.

3
For instance, the ergodic capacity of cooperative amplify-and-forward (CAF) relay networks with
the limited CSI were derived in [12-19] for different source-adaptive transmission policies in a
myriad of stochastic fading environments. The performance of practical adaptive digital
modulation scheme with regular relay system was considered in [20 -23]. The performance of
CAF relay with constant power M-QAM adaptive rate transmission, when average bit error rate
(ABER) in Rayleigh fading is constrained to be below a specified target bit error rate (BER) is
examined in [21] and [22] for fixed and optimum mode switching thresholds, respectively. In
[23], the performance of discrete-rate adaptive M-QAM for a single incremental relay in
Nakagami-m environment was examined, while [22] investigates the performance of a
cooperative decode-and-forward relay network with five-modes adaptive M-QAM transmission
in an i.i.d Nakagami-m wireless fading environment. All these articles and related references
indicate the advantage of the adaptive cooperative diversity system over the non-adaptive and/or
the non-cooperative system especially at low and medium signal-to-noise ratio (SNR). However,
the half-duplex nature of regular relay system makes the performance worse at high SNRs.
With the introduction of ORS in [8-11], several articles have been published on its performance,
but mostly focusing on non-adaptive system (i.e. fixed modulation). Average symbol or bit error
rate (ASER/ABER) performance for ORS-MRC scheme over Rayleigh, independent and
identically distributed (i.i.d) Nakagami-m, and independent and non-identically distributed (i.n.d)
Nakagami-m fading channels was investigated in [26-27], [28], and [29] respectively, while [30]
investigated ASER of both ORS-MRC and ORS-SDC scheme over i.i.d Nakagami-m fading
channel. Outage capacity for ORS-MRC and ORS-SDC has been considered in [31]. It is
important to note that until now; only a few articles have considered the link adaptive ORS
system. For instance, ergodic capacity with the source adaptation techniques have been
considered in [32-35] for the ORS-MRC scheme over Rayleigh fading channel, while the variable
rate constant power adaptive M-QAM modulation with ORS-MRC and ORS-SDC schemes over
Rayleigh fading have been considered in [35-36] and [37] respectively. Also, [38] analyzed the
performance of link adaptive incremental opportunistic relaying over i.n.d Rayleigh fading
channels. However [39] studied the performance analysis of cooperative communication with
only ORS-SDC scheme. Careful study of the adaptive ORS schemes [32-39] indicates that, the
analyses of both the ergodic capacity and the practically achievable spectral efficiency have been
obtained using the probability density function method, which can be very tedious and may not
always yield compact solutions.
In contrast, in this article we develop a new analytical framework based on the marginal MGF
method for evaluating the ASER, mean spectral utilization efficiency and outage probability
performance metrics (i.e., since the MGF of total received SNR may be easier to compute or
readily available for CAF relay networks).The developed analytical framework is thenused to
analyze and compare the performance of regular MRC, SDC, opportunistic MRC and SDC CAF
relay schemes that employ constant power adaptive discrete rate M-QAM/M-PSK transmission.
The proposed analytical framework is general, and can be applied to any arbitrary fade
distribution as long as the MGF of the end-to-end SNR is available unlike channel specific
derivations in [32-38]. For completeness purpose, the ergodic capacity with optimal rate
adaptation was also presented. Numerical analysis indicates that ORS-MRC leads the pack
considering the ergodic capacity and achievable spectral efficiency, while the regular MRC is the
best in terms of the outage probability and ASER. In the overall, the ORS-MRC is the best due to
the additional power saving as it consumes only 2/(N+1), of the total power consumed by regular
MRC. Therefore, not only does it perform well as a communication paradigm, it also supports
green technology due to its low transmit power requirement. Careful literature search indicates
that, this is perhaps the first time such comprehensive analysis of regular and opportunistic CAF
relay network with the link adaptation is being reported.

4
The remainder of this article is organized as follows. In Section 2, the system model is discussed.
Section 3 derives the performance metrics for the CAF relay networks with adaptive M-QAM/M-
PSK modulation. Selected numerical results are presented in Section 4. Our conclusions are given
in Section 5.
Figure 1. Link-adaptive cooperative relay networks
2. SYSTEM MODEL
2.1 TOTAL MGF OF CAF RELAY NETWORKS
In this section, we will present the moment generating function (MGF) of the relayed path of
different cooperative diversity and opportunistic routing protocols that will be utilized in
evaluating the end-to-end ASER, mean spectral efficiency and the outage probability
performance metrics of the proposed network over a myriad of fading channels with the adaptive
M-QAM/M-PSK modulation schemes.
2.1.1 REGULAR COOPERATION: CAF RELAYING WITH MAXIMUM RATIO COMBINING
(MRC) AT THE DESTINATION
In this protocol, as shown in Fig 1, source node S which communicates with a destination node D
via a direct-link and through N amplify-and-forward relays, Ri, ,{1,2,...., }i N∈ in two transmission
phases. During the initial Phase I, S transmits signal x to D as well as to the relays Ri, where the
channel fading coefficients between S and D, S and the i-th relay node Ri, and Ri and D are
denoted by ,s dα , ,s iα and ,i dα , respectively. During the second phase of cooperation, each of the N
relay nodes transmits the received signal after amplification via orthogonal transmissions (e.g.,
TDMA in a round-robin fashion and/or FDMA). Hence, the channel usage per source
transmission, ( ) 1.U N N= +
Now, consider that the maximum ratio combiner (MRC) is employed at a D to coherently
combine all the signals received during Phase I and Phase II, the total received SNR at output of
the MRC detector can be shown to be (e.g., [19,20, 25])
, , ( )
, , ,
, ,1 1 11
N N N
s i i d H MM R C
i iT s d s d s d
s i i di i i
γ γ
γ γ γ γ γ γ
γ γ= = =
≤= + = + +
+ +∑ ∑ ∑
(1)

5
where ( )
, ,, , ,HM
i s i s ii d i dγ γ γ γ γ= + is the harmonic mean SNR,
2
, , sa b a b oE Nγ α=
corresponds to the
instantaneous SNRs of link a-b, sE denotes the average symbol energy and 0N corresponds to the
noise variance.
The approximation of (1) is obtained by recognizing that the instantaneous SNR of a two hops
path can be accurately estimated to be the harmonic mean of the individual link SNRs, especially
at moderate/high SNR regimes [43]. Hence, it is straight-forward to show that the MGF of end-to-
end SNRis given by
, 1
( ) ( ) ( )MRC
s d iT
N
i
s s sγ γγ
φ φ φ=
= ∏ (2)
where ,
( )s d
sγφ and ( )i
sγφ are the MGFs of the SNR for the S-D link and the relayed paths,
respectively. The MGF of SNR for single channel reception is readily available in the literature. It
has been shown in the literature that the evaluation of the MGF, PDF and CDF of i
γ is a daunting
task with existing results limited to Rayleigh fading [41] and Nakagami-m [42] fading channels
with integer m and even in such cases the expressions are too complicated, and mostly useless for
the system level analysis. However, it has been shown in [43] that, ( )HM
i
γ in (1) can effectively
approximate i
γ especially at medium and high SNRs. Also, in this case the MGF expressions are
still difficult to obtain with the existing results limited to Raleigh fading [44] and i.i.d. Nakagami-
m [43] channels. Due to this limitation, the bounds have been developed for iγ and it is given by
( )
, ,
min( , ).UB
i s i i d
γ γ γ=
For instance, the closed-form formula for the MGF of ( )UB
i
γ in a Nakagami channel with i.n.d
fading statistics is given by [51]
( )
2 1
{( , ),( , )}
( ) ( )
( ) 1 , ; 1 ;
( ) ( )i
k
UB
m
k j j k k k j
j k k
k s i i d k k j j k j k k j j k j k k j
j k
m m m s m
s F m m m
m m m s m m s m m
γφ
∈
≠
   Γ + Ω Ω + Ω
= − +   
   Γ Γ Ω Ω +Ω +Ω Ω Ω +Ω +Ω   
∑
(3)
where [ ]q q
E γΩ = corresponds to the mean SNR of link q, (.)Γ is the Gamma function and mqis the
Nakagami-m fading index.
2.1.2 REGULAR COOPERATION: CAF RELAYING WITH SELECTION DIVERSITY COMBINING
(SDC) AT THE DESTINATION
In this kind of protocol implementation, the best route is selected at the destination node based on
the end-to-end relay SNR. Here in the case of SDC, the channel usage per source transmission is
similar to the MRC case (i.e., ( ) 1U N N= + ).
For this protocol, the effective SNR at the output of the SDC detector (i.e., all the signals received
during Phase I and Phase II) is given by
( ), 1 2 , ,1 1, ,2 2, , ,max( , , ,... ) max ,min( ),min( ),...min( )SDC
T s d N s d s d s d s N N dγ γ γ γ γ γ γ γ γ γ γ γ= ≈ (4)
For instance, the MGF of SDC
Tγ for a special case of independent and identically distributed (i.i.d)
Nakagami-m fading statistics can be obtained from Appendix A as [45]

6
( )
( ) ( )
1 2 2
21
2 11
1 , ,... 1
( 1)
( ) 1 ( 1) 1, 1; 1;
! (1 2 )( 1) (1 2 )
j
SDC
T
p
i m
m mpN m mm ps
m m mmp i i i j j
s mN
s F m m
p i s pm s p
λγ
λ
φ λ
−− Ω Ω ΩΩ
+ +
= = ΩΩ
  
    
     
Γ + +
≈ + + − × + + +
+ +Γ + + +
∑ ∑ ∏
(5)
where 2 1(.,.;.;.)F is the Gauss hypergeometric function.
2.1.1 CAF RELAYING WITH OPPORTUNISTIC ROUTE SELECTION AND SDC (ORS-SDC) AT
THE SOURCE
The (ORS-SDC) relaying protocol focuses on limiting the number of cooperating relay to one.
Additionally, the choice of the appropriate route is selected by the source (assuming that the relay
with the best transmission parameter is already determined during the route discovery process) or
can be accomplished in a distributed fashion among the relays as proposed in [8]. Compared to
the regular cooperative diversity protocol discussed above, the best route is selected at the source
based on the end-to-end relay SNR. Therefore, the statistics of the best route selection is the same
as the selection diversity combining at the destination as the best among N+1 links is being
selected. However, the channel usage per source transmission in the case is ( ) 2U N = (i.e., source
will broadcast the signal to all the relays and destination in first time slot; and in the second time
slot, one of the best relay amplify and forward the signal to the destination). Therefore, the
spectral efficiency here does not reduce with the increasing number of relays as in the case of
regular cooperative diversity protocols discussed above (i.e., MRC and SDC only). Also, the
amount of channel side information and the implementation complexity is highly reduced.
2.1.2 CAF RELAYING WITH OPPORTUNISTIC RELAY SELECTION AND MRC (ORS-MRC) AT
THE DESTINATION
This protocol implementation takes advantage of the half duplex nature of the relay transmission
to achieve better performance than the ORS-SDC protocol. Here, since the source transmits in the
first transmission phase, and due to the broadcast nature of the wireless channel, the destination
can be close enough to receive this signal before receiving the signal from the relay. This is
particularly true in the distributed ORS protocol implementation proposed in [8]. Therefore, if the
channel side information of both the links is available, the received signal can be combined with
the MRC scheme at the destination. Note that the transmission channel usage ( ) 2U N = each
source transmission, but the statistics is slightly different from the pure ORS-SDC protocol. The
effective end-to-end SNR of the ORS-MRC protocol can be expressed as
( ),1 2 ,1 ,2, , 1, 2, ,max( , ,... ) max min( ),min( ),...min( )ORS MRC
T N s Ns ss d s d d d N dγ γ γ γ γ γ γ γ γ γ γ γ−
= + ≈ + (6)
The MGF of ORS MRC
Tγ −
for a special case of independent and identically distributed (i.i.d)
Nakagami-m fading statistics can be obtained from Appendix B as [45]
( )
( )
( )1 2 2
21
( 1)
1 , ,... 1
( 1)
( ) 1 1 ( 1)
! 2
j
ORS MRC
T
p
impN m
m ps
m
m
p i i i j j
N s
s
p i s p
λγ
λ
φ −
−
− ΩΩ
+
= = Ω
Γ +
≈ + + −
+
  
  
   
∑ ∑ ∏ (7)
Hence, by utilizing the above mentioned closed-form MGFs of the four protocol schemes, we can
easily analyse and compare the performance of CAF relay networks in terms of mean achievable
spectral efficiency, outage probability and average symbol error rate.

7
2.2CUMULATIVE DISTRIBUTION FUNCTION (CDF) OF THE TOTAL END-TO-END SNR
To evaluate the various performance measures, the knowledge of the CDF of total effective SNR
T
γ of the CAF relay networks is required. Since the analytical CDF expression for the CAF relay
networks is difficult to obtain, the alternative is to compute the CDF from the MGF expression in
(2).
One of the most efficient frequency inversion method is the Abate’s Fixed-Talbot method (i.e.,
multi-precision Laplace transform inversion) [16], viz.,
( )
1
( )
1
11
2
( )
( ) ( ) Re{ ( ) }
( )
Z
xsrx k k
X X X k
k
k
r
Z Z
j
F x r e e s
s
θσ θ
φ φ θ
θ
−
=
+
≅ + ∑ (8)
where 2 / (5 ),r Z x= / , ( ) ( cot( )),k k k kk Z s r jθ π θ θ θ= = + ( ) ( cot( ) 1)cot( ),k k k k kσ θ θ θ θ θ= + − and positive
integer Z can be chosen to get the desired accuracy. Utilizing (8), we can easily compute the CDF
expressions from its respective total MGF expression for the CAF relay networks.
3. ADAPTIVE MODULATION
In this section, we develop a new analytical framework based on the marginal MGF for
evaluating the ASER, mean spectral utilization efficiency and outage probability performance
metrics.It will shown that the mean achievable spectral efficiency of ADR M-QAM/M-PSK and
ASER of CAF relay networks with adaptive source transmission can be expressed in terms of
difference of two “CDF” terms.The ADR M-QAM/M-PSK schemes are first explained, followed
by the outage probability, the mean spectral efficiency, and the average SER analysis.
3.1 ADR M-QAM/M-PSK SCHEMES
In the adaptive modulation techniques, the destination node needs only to compute the total
received SNR, select the appropriate transmission rate, and feedback this information to the
transmitter. In context of CAF relay system, the destination node only needs to compute and
convey the information on the total (effective) received SNR to the source node for it to select an
appropriate transmission rate. This results into a higher mean achievable spectral efficiency
without having to sacrifice the error rate performance. For this reason and more specifically due
to several other practical advantages of the adaptive rate modulation, we consider both the
adaptive M-QAM and the M-PSK digital modulation schemes in this paper to improve the
performance of the CAF relay networks.
In order to simplify the analysis of the adaptive modulation, there is a need to express
instantaneous error rate in desirable exponential form, similar to the one in the existing literatures
[21-25]. Here, we employ the exponential-type representations of the instantaneous (SER) for the
M-PSK and the M-QAM schemes and are respectively given by [40, Table II]
1 1
2 2sin 2 sin1 1
S
b M b Ms s
P a e c e
γ π γ π   
      
   
− −
≈ + (9)
( )( ) ( )
1 1 1 13 63 9
2 2 22 1 1 1 2 1
1 1 1 1 1 12 2
s s s s
S
b b b b
M M M MP ka e kc ka e kc e k a c e
γ γ γ γ
− − − −
− − − −≈ + − − − (10)

8
where ( ) ,1M Mk = − M is the constellation size and parameters 1 1
0.2938; 1.0483;a b= =
1
0.5070c = are obtained from [40, Table I]. The above exponential forms particularly facilitate
the averaging of the SER over the fade distribution. The resulting average symbol error rate
(ASER) expression (taking advantage of Laplace transform property), which can be evaluated as
the weighted sum of the MGF of end-to-end SNR of fading channel, can be expressed as
( ) ( )1 1 1 1
2 2sin 2 sinM PSKP a b M c b Mγ γφ π φ π−
   
   
   
= + (11)
( )2 2 21 1 1 1
1 1 1 1 1 1
3 3 6 9
2 2 ( ) ( )
2( 1) 1 1 2( 1)
M QAM
b b b b
P ka kc ka kc k a c
M M M M
φ φ φ φ−
      
         
      
= + − − −
− − − −
(12)
where (.)γφ is the MGF of SNR for single channel.
In the ADR M-QAM/M-PSK system, the range of the effective received SNR is divided into T+1
fading regions. When the fading causes the total received SNR to fall into the n-th region (n = 0,
1,T), the constellation size 2n
n
M = is employed for the transmission. Also, the SNR thresholds
for partitioning of the total received SNR depends on the target SER level, Ps. The region
boundary n
γ is chosen for the corresponding transmission mode n to be the minimum SNR
required to achieve Ps, which can be easily obtained by inverting (9) and (10) for M-PSK and M-
QAM modulation schemes respectively
( )
2
1 1 1
2
11
41
ln
sin 2
S
n
n
a a c P
b M c
γ
π
 − + +
 ≈ −
 
 
(13)
( )( )2
1 1 1 1
11
4 1 1
2( 1)
ln
3 2
Mn
SMnn
n
a a c P
M
b c
γ
−
 
 
 
 
 
 
− + + − −
−
≈ −
(14)
where , 1,2,3...,n T= and 1 .Tγ + = +∞
It is worth to mention here that, the two exponential terms are more accurate than the existing
invertible expressions in the literature [46-48]. Representative example has been shown in Fig. 2,
where a comparison has been made between the proposed approximation and the single and two
exponential term approximation in [47] and [48] respectively. This figure highlights that our
proposed exponential approximation (11-12), yields a very good estimate of the actual ASER
performance over a wide range of average link SNRs, different fading severity indices and for
different constellation sizes. It is evident from the figure that, the proposed approximation
performs better than [47] and [48] for the M-QAM and better than [48] for the M-PSK.
Therefore, for the rest of the analysis in this article, the proposed two exponential term
approximation will be utilized.

9
Figure 2 ASER of M-PSK and M-QAM over Nakagami fading channels (m = 1 and 3) without diversity
3.2 OUTAGE PROBABILITY
When the total received SNR falls below the region boundary threshold 1
γ ( 1
γ can be obtained by
setting, n = 1 in (13) or (14)), we cease the transmission, because the prescribed target SER
cannot be satisfied even with the smallest constellation size. The probability of such an outage
event is given by 1
( )out FP γ γ= , where the CDF term can be evaluated efficiently using (8).
3.3 MEAN SPECTRAL EFFICIENCY
The normalized average achievable spectral efficiency for ADR M-QAM/PSK is given by the
weighted sum of the data rates in each of the partitioned regions [21, 25] viz.,
1
1
( )
T
adr
n
n
R
np
B U N =
= ∑ (15)
where n
p denotes the transmission mode selection probability (i.e., probability that the total
received SNR falls in the n-th partition region):
1
1
( ) ( ) ( )
n
n n n
n
p f d F F
γ
γ γ γ
γ
γ γ γ γ
+
+
= = −∫ (16)
Hence, using the appropriate MGF expressions derived in [43-44, 49] in (8), we can readily
compute the mean spectral efficiency of the ADR M-QAM/PSK in a myriad of wireless fading
environments.
0 5 10 15 20 25 30
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Mean SNR Per Symbol (dB)
AvearageSymbolErrorRate
[47, Eq.(17)]
Exact
Proposed Method
[48, Eq.(10)]
32PSK, m = 1
16QAM, m = 3
4QAM, m = 1
8PSK, m = 3

10
3.4 ASER OF ADAPTIVE M-QAM/PSK
The ASER of ADR M-QAM/PSK can be calculated as the ratio of the average number of error
bits per transmission divided by the average number of bits per transmission [47], viz.,
1
1
1
,
( ) ( )
T
n
n
adr T
n n
n
n SER
ASER
n F Fγ γγ γ
=
+
=
=
 − 
∑
∑
(17)
where n
SER is the average SER in a specific SNR region of 1[ , ]n nγ γ+ and can be represented as
1
( )
n
n M
n
PSER f d
γ
γ
γ
γ γ
+
= ∫ (18)
where PM is the CEP of the modulation scheme in AWGN channel. For the special case of M-
PSK scheme, we can derive the n
SER by substituting (9) in to (18) viz.,
( )( ) ( )( )}{
( ) ( ) ( ) ( )
1
2 2
1 1 1 1
2 2 2 2
1 1 1 1 1 11 1
exp sin exp 2 sin ( )
sin sin sin sin( , ) ( , ) (2 , ) (2 , )
n
n
n
n nn n
SER a b M c b M f d
a M M c M Mb b b b
γ
γ
γ
γ γ γ γ
γ π γ π γ γ
π π π πφ γ φ γ φ γ φ γ
+
+ +
   
   
= − + −
= +− −
∫ (19)
and the term ( )( , ) e f dβγ
γ
α
γ γ γφ β α
∞
−
= ∫ in (19) denotes the marginal MGF of the total received SNR.
Note that although this quantity is available in closed-form for non-cooperative system (e.g. [48]),
similar expressions do not appear to be readily available or generalized for the CAF relay
networks, particularly in a generalized wireless fading environment. Utilizing [51, Appendix C],
we can compute the desired marginal MGF as a difference between two “CDF” terms of an
auxiliary function, viz.,
1 1 1 1ˆ ˆ ˆ ˆ
( ) ( ) ( ) ( )n n nn na a b b
SER a F F c F Fγ γ γ γ
γ γ γ γ+ +
  
    
= − + − (20)
where ˆ ( )a
F xγ
and ˆ
( )b
F xγ
in (20) can be evaluated efficiently via (8), but using the “MGF” formulas
of the auxiliary functions (i.e., ( )( )2
1
sin( )a
Ms s bγ γ πφ φ= + and ( )( )2
1
sin( ) 2b
Ms s bγ γ πφ φ= + ). Similarly treatment
can also be applied to the M-QAM modulation scheme by substituting (10) into (18).
Eq. (20) allows us to generalize the evaluation of adr
ASER over arbitrary multipath/shadowing
fading as long as the MGF of SNR of fading channel is available. This is in sharp contrast with
channel specific PDF methods in [32-34] which limited their analysis to Rayleigh fading channel.
4. NUMERICAL RESULTS
In this section, selected numerical results are provided for the normalized mean achievable
spectral efficiency, outage probability and ASER performance metrics of CAF relay networks
with both the adaptive discrete rate M-QAM and M-PSK digital modulation schemes. In
particular, we are comparing the performance of four distinct cooperative diversity and

11
opportunistic routing protocols: (i) ORS-MRC (ii) ORS-SDC (iii) MRC and (iv) SDC, over the
i.i.d Nakagami fading environment (including special case of Rayleigh fading). Moreover, the
ergodic capacity analysis with the optimal rate adaptation policy is also presented for the
theoretical performance limit of the above protocol schemes. To generate plots, the mean link
SNRs are chosen arbitrarily as: ,1s
Ω = ,2s
Ω = ,3s
Ω = 1,d
Ω = 2,d
Ω = 3,d
Ω = ,s d
Ω = Es/N0 and the fading indexes
on the each links is chosen as m = 3 (unless states otherwise). For the ADR system, the target
SER of 10-3
is arbitrarily chosen.
Fig. 3 illustrates the ergodic capacities of the ORA policy using four different protocols (i.e.,
ORS-MRC, ORS-SDC, SDC and MRC). To generate the plots, we have used the following
generalized expressions in terms of the MGF of end-to-end SNR of CAF relay networks [11]
02
1 1
1 ( )
( ) ln
y
O RAC e
y dy
B U N y γφ
−∞
 
 −= ∫ (21)
Expression (21) indicates that the ORA capacity evaluation requires only the knowledge of the
MGF of SNR of the fading channel. By substituting the total MGF of the above mentioned
protocols into (21), we can easily generate the curves as shown in the figure. From the figure, we
can observe that the performance of the opportunistic relay scheme (i.e., ORS-MRC and ORS-
SDC) is better than the regular cooperation (i.e., MRC and SDC) respectively. This improvement
in the performance of the ORS scheme is due to the utilization of the two orthogonal slots for the
total transmissions compared to the three slots in the regular cooperation. Moreover, it is
interesting to note that, the authors in [28], compares the ergodic capacities of the CAF relay
network using best relay selection and the regular MRC scheme. However, their framework does
not lend itself to the analysis of the ORS-SDC or the SDC case, whereas our framework
encapsulates the performance of all the four protocols.
Figure 3 Ergodic channel capacities of the optimal rate adaptation (ORA) policy with two cooperative
relays (N =2)
0 5 10 15 20
0
0.5
1
1.5
2
2.5
3
3.5
4
Es
/N0
(dB)
NormalizedChannelCapacityC/B(bits/sec/Hz)
ORS-MRC
ORS-SDC
SDC
MRC

12
Fig. 4 shows the comparison in terms of spectral efficiency of the different cooperative diversity
and the opportunistic routing protocols, with the adaptive M-PSK modulation. It is worth to
mention that for a single relay case, the ORS-MRC gives the same performance as the MRC
scheme, while the ORS-SDC scheme also gives the same performance as the SDC scheme.
However, as the number of relay increases, ORS-MRC performs better than the regular MRC
protocol at medium and high SNRs, while the ORS-SDC protocol performs better than the regular
SDC protocol throughout the SNR range. This is because irrespective of the number of relays in
the participation, the total channel usage for the ORS-MRC and the ORS-SDC is kept constant at
two time slots per source transmission; whereas the channel usage for MRC and SDC schemes
increases with increasing number of relays. Moreover, to further improve the spectral efficiency,
we incorporate the adaptive M-PSK modulation scheme (compared to fixed modulation schemes
in the previous literatures) to adapt the transmission rate with the varying channel conditions. It is
evident from Fig. 4 that by increasing the maximum constellation size (transmission modes) in
the ADR M-PSK directly translates into improved spectral efficiency. However, this
improvement is achieved at the expense of the increased ASER (see Fig. 5). In summary, the link
adaptive ORS-MRC scheme gives the best overall performance. Hence, it can be concluded that
the ORS-MRC protocols are recommended for the cooperating nodes at the tactical edge or at the
cell boundary, where the received signal strength is weak.
Figure 4 Comparison of different cooperative diversity and opportunistic routing protocols with adaptive
M-PSK modulation (T = 3 and 4)
Fig. 5 illustrates the average symbol error rate (ASER) of a CAF relay network with the adaptive
M-PSK modulation (using T = 3 and 4). We observe that the ASER of the MRC scheme is the
lowest, whereas, the ORS-SDC scheme is the highest. This is due to the availability of the total
N+1 diversity paths in the MRC scheme. However, this is achieved at the expense of the power
efficiency as the ORS-SDC and the ORS-MRC requires only 1/(N+1) and 2/(N+1) of the total
power of the regular MRC scheme respectively.
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
SNR Es
/No
(dB)
NormalizedAverageSpectralEfficiency(bits/sec/Hz)
ORS-MRC
ORS-SDC
MRC
SDC
N = 3
N = 1
T = 4
T = 4
T = 3
T = 3

13
Figure 5 Average symbol error rate of a CAF system with different cooperative diversity and opportunistic
routing protocols using adaptive M-PSK modulation (T =3 and 4)
Figure 6 Comparison of different cooperative diversity and opportunistic routing protocols with adaptive
M-MQAM modulation (T = 5) consisting of two relays
Fig. 6 shows the spectral efficiency performance comparison of the four cooperative diversity and
the opportunistic routing protocols with the ADR M-QAM modulation scheme with T = 5. This
figure highlights the influence of the channel fading severity on the performance of the link
adaptive cooperative system. While the performance trend among the protocols is similar to the
one obtained in Fig. 4, Fig. 6 in particularly shows that, as the channel condition improves, the
0 5 10 15 20 25 30
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
SNR Es
/No
(dB)
AverageSymbolErrorRate
N = 1
N = 3
ORS MRC
ORS SDC
MRC
T = 3
T = 4
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
SNR Es
/No
(dB)
NormalizedAverageSpectralEfficiency(bits/sec/Hz)
m = 4
m = 1
ORS-MRC
ORS-SDC
MRC
SDC

14
achievable spectra efficiency improves. To the best of our knowledge, this effect has never been
reported in the earlier literature, and it also demonstrates the versatility of our mathematical
framework.
Figure 7 Probability of outage of a CAF system with different cooperative diversity and
opportunistic routing protocols using adaptive M-PSK modulation (T = 3) (Note that for N=1, the
ORS-MRC and MRC, whereas for any values of N, ORS-SDC and SDC schemes are the same)
Figure 7 depicts the outage probability as a function of SNR at the target SER of 10-3
and it
highlights the benefit of the cooperative diversity to maximize the performance of the wireless
communication system. From figure 7, we conclude the following important observations. First,
we notice that the case with cooperative diversity (i.e., N = 3) evidently outperforms the case with
N = 1. Second, the outage probability with the MRC protocol has a better performance than all the
other protocols (similar to the case in fig. 5 for the ASER analysis with the MRC protocol). This
performance gain is due to the additional diversity path offered by all the relays and direct path in
the system, but still at the expense of the power efficiency.
5. CONCLUSIONS
This paper analyzes the performance of cooperative amplify-and-forward (CAF) relay networks
that employ the adaptive M-ary quadrature amplitude modulation (M-QAM)/M-ary phase shift
keying (M-PSK) digital modulation techniques in the Nakagami-m fading channel model. In
particular, we present and compared the analysis of the CAF relay networks with different
cooperative diversity and opportunistic routing protocols such as Maximal Ratio Combining
(MRC), Selection Diversity Combining (SDC), Opportunistic Relay Selection with Maximal
Ratio Combining (ORS-MRC) and Opportunistic Relay Selection with Selection Diversity
Combining (ORS-SDC).We advocate a simple yet unified numerical approach based on the
marginal moment generating function (MGF) of the total received SNR to compute the average
symbol error rate (ASER), mean achievable spectral efficiency, and the outage probability
performance metrics. These analytical frameworks and results will facilitate the choice of
cooperation protocol and configurations that can be employed in the design and deployment of
femtocells.
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR Es
/No
(dB)
OutageProbability
MRC
ORS-MRC
ORS-SDC
N = 1
N = 3

15
APPENDIX A
This section provides the derivation for the MGF of end-to-end SNR of CAF relay system with
SDC protocol at the destination. This is also applicable to the ORS scheme with SDC at the
destination.
The CDF of the end-to-end SNR given in (4) can be expressed as
( ), , , ,1 1
( ) ( ) ( ) ( ) 1 [1 ( )][1 ( )]SDC
s d r s d s r r dT
N N
r r
F F F F F Fγ γ γ γ γγ
γ γ γ γ γ γ= =
= ≈ − − −∏ ∏ (A.1)
where ,
( )s d
Fγ γ , ,
( )s r
Fγ γ and ,
( )r d
Fγ γ are the CDFs of the source-to-destination, source-to-relay and
relay-to-destination links, respectively.
The effective MGF can then be evaluate using the differentiation property of the Laplace
transform via a single integral expression
( )
,
, , ,
10
10
( ) ( ) ( )
( ) 1 [1 ( )][1 ( )]
SDC
s d rT
s d s r r d
Ns
r
Ns
r
s s e F F d
s e F F F d
γ
γ γγ
γ
γ γ γ
φ γ γ γ
γ γ γ γ
∞
−
=
∞
−
=
=
≈ − − −
∏∫
∏∫
(A.2)
For special case of independent and identically distributed (i.i.d.) Nakagami-m channel, the MGF
can be reduced to [30]
( )
1 2 2
21
(2 )
0
1 , ,... 1
( , )
( ) 1 ( 1)
( ) !
j
m
SDC
T
p
ip mN mm
ps p
p i i i j j
NG m
s s e e d
pm i
γγ λ
γ
γ
φ γ γΩ
−∞ − Ω− Ω
= =
  
 ≈ + −  
Γ    
∑ ∑ ∏∫ (A.3)
where (.,.)G is the lower incomplete gamma function and
2
1
p
jj
iλ =
= ∑
Using the identity [52, Eq. (6.455.2)], after few algebraic manipulations, the closed-form MGF
expression can be obtained as shown in (5).
APPENDIX B
This section provides the derivation for the MGF of end-to-end SNR of ORS CAF relay system
with MRC protocol at the destination.
The effective MGF of (6) can be evaluated using the addition and differentiation properties of the
Laplace transform via a single integral expression given by
( )
,
, , ,
10
10
( ) ( ) ( )
( ) 1 [1 ( )][1 ( )]
ORS MRC
s d rT
s d s r r d
Ns
r
Ns
r
s s s e F d
s s e F F d
γ
γ γγ
γ
γ γ γ
φ φ γ γ
φ γ γ γ
−
∞
−
=
∞
−
=
=
≈ − − −
∏∫
∏∫
(B.1)

16
For special case of independent and identically distributed (i.i.d.) Nakagami-m channel, the MGF
can be reduced to
( )
( )
1 2 2
21
(2 )
0
1 , ,... 1
( ) 1 1 ( 1)
!
j
m
ORS MRC
T
p
ip mN m
m pp ss
m
p i i i j j
N
s s e e d
p i
γλ γ
γ
φ γ γΩ
−
− ∞− −Ω −Ω
= =
  
 ≈ + + −  
   
∑ ∑ ∏ ∫
(B.2)
Using the identity [52, Table 17.13], after few algebraic manipulations, the closed-form MGF
expression can be obtained as expressed in (7).
It is worth to mention that the expression in (7) is much more compact and simpler than the
equivalent expression in [30, Eq. (17)].
ACKNOWLEDGMENT
This work is supported in part by funding from the National Science Foundation NSF/HRD
0931679 and the US Air Force Research Laboratory (Contract #FA8750-09-1-0151).
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19
AUTHORS
Dr. Bhuvan Modi received PhD. degree from Prairie View A & M University, Texas A
& M University System, in 2012. He earned his M.S. degree in Electrical Engineering
from Lamar University, United States of America, M.S. degree in Electronics and
Communication Engineering from Dharmsinh Desai University, India, and the B.S.
degree in Electronics and Communication Engineering from North Gujarat University,
India, in 2009, 2002 and 2001, respectively. He is currently working as a Senior
Member of Technical Staff at AT&T Mobility Lab, Seattle, WA. He received ‘Student Travel Grant
Award’ to present his work at the IEEE MILCOM’11. Over last few years, Mr. Modi has published over a
dozen peer reviewed conference and journal articles. His current research interests include cross-layer
design/optimization for adaptive-link cooperative relay networks, Software Define Networking and 4G
VoLTE.
Dr. Oluwatobi O. Olabiyi received the B.Sc. degree in Electronic and Electrical
Engineering from Obafemi Awolowo University, Ile-Ife and M.S. and PhD degree in
Electrical Engineering from Prairie View A&M University, Texas. Over the last few
years, he has co-authored approximately two-dozen peer-reviewed conference and
journal articles. He was the recipient of the Roy G. Perry College of Engineering
Outstanding Masters Student of the Year Award (2011) and the National Society of
Black Engineer’s Golden Torch Award for Graduate Student of Year (2012). His research interests include
dynamic spectrum access, MIMO, cooperative communications, statistical signal processing, compressive
sensing, machine-learning and optimization techniques.
Dr. Annamalai is presently the Director of Center of Excellence for Communication
Systems Technology Research, a Texas A&M Board of Regents approved University
Research Center at the Prairie View A&M University, and a tenured faculty member
in the Department of Electrical and Computer Engineering. He has over 20 years of
research/teaching experience in wireless communications at Motorola, University of
Victoria, Air Force Research Laboratory, Virginia Tech and PVAMU with
approximately 200 peer-reviewed publications and 5 book chapters. Dr. Annamalai
has been honored by his colleagues on numerous occasions for his excellence in research including
winning the 2011 Roy G. Perry College of Engineering Outstanding Faculty (Research) Award, IEEE
Leon Kirchmayer Prize Paper award, ASEE/AFOSR Summer Faculty Fellowships, NSERC Doctoral
Prize, CAGS/UMI Distinguished Doctoral Dissertation Award, IEEE VTS/Motorola Daniel E. Noble
Fellowship, among others. He had served on the Editorial Boards of four IEEE journals/transactions in the
last 15 years, and has helped to organize a few major IEEE conferences on wireless communications
including serving in the capacity of Technical Program Chair of the 2002 IEEE Vehicular Technology
Conference in Vancouver, Canada. His current research interests include cooperative spectrum sensing,
compressive sensing, cross-layer design for scalable multimedia transmission and cooperative wireless
communications.

PERFORMANCE ANALYSIS OF THE LINK-ADAPTIVE COOPERATIVE AMPLIFY-AND-FORWARD RELAY NETWORKS WITH OPPORTUNISTIC RELAYING STRATEGY

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PERFORMANCE ANALYSIS OF THE LINK-ADAPTIVE COOPERATIVE AMPLIFY-AND-FORWARD RELAY NETWORKS WITH OPPORTUNISTIC RELAYING STRATEGY