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Int. J. Electron. Commun. (AEÜ) 66 (2012) 1– 6

Contents lists available at ScienceDirect

International Journal of Electronics andCommunications (AEÜ)

jou rn al h omepage: www.elsev ier .de /aeue

n the performance of decode-and-forward relaying with multi-antennaestination

imanshu Katiyar ∗, R. Bhattacharjee1

ommunication and Advance DSP Group, Electronics and Electrical Engineering Department, Indian Institute of Technology Guwahati, North Guwahati, Guwahati 781039, India

r t i c l e i n f o

rticle history:eceived 9 December 2010ccepted 13 April 2011

a b s t r a c t

In recent times, relay based cooperative communication has emerged a viable means of communica-tion, dealing with harsh multi-path fading and improving link performance. In this paper, closed formexpressions of outage probability, average symbol error rate, average received SNR and channel capacity

eywords:ulti-antenna base stationaximum ratio combining

daptive decode and forward modeayleigh fading channel

have been derived, for the case when communication between the source and multi-antenna destination(base station) is supported by a single antenna adaptive decode and forward (DF) relay in Rayleigh fadingchannel. Comparative performance of such system with conventional single input multiple output (SIMO)system, for different path-loss conditions and various number of antenna elements on destination, havealso been studied. Numerical results show that, transmission through relay performs better than SIMOunder high path-loss conditions if the SNR is maintained above some threshold value.

. Introduction

SPATIAL diversity is a widely used technique in wireless commu-ications for combating multi-path fading. It is found that multiplentennas, employed at both the transmitter and receiver, offerarge gains in capacity [1]. From implementation point of view, stillhere are difficulties in accommodating multiple antennas in manyypes of wireless terminals. Cooperative relaying, is a technique inhich, multiple nodes share their antennas and other resources

2]. It creates virtual antenna array and is becoming an impor-ant mean to remove the burden of multiple antennas on wirelessodes. In a typical cellular communication setup, multiple anten-as can be used on the base-station which can communicate withingle antenna user node with the help of relay node. Such typef system is analyzed in [3], here authors investigate the effectf imperfect channel state information on the achievable diver-ity gain. In [4], Laneman developed distributed space-time codedooperative diversity protocols for improving spectral efficiency.utage probability of cooperative relay in statistically similar chan-els has been derived in [5] and several bounds are proposed forhe case when the statistics of channel are dissimilar. Approximate

nalysis of outage probability of selection cooperation for all SNRevels and arbitrary channel distributions is given in [6]. Selectionooperation in network scenario is discussed in [7], where multiple

∗ Corresponding author. Mobile: +91 9956956574.E-mail addresses: h.katiyar@iitg.ernet.in, katiyarhimanshu@gmail.com (H. Kati-

ar), ratnajit@iitg.ernet.in (R. Bhattacharjee).1 Fax: +91 3612582542; mobile: +91 9954498116.

434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.oi:10.1016/j.aeue.2011.04.007

© 2011 Elsevier GmbH. All rights reserved.

sources transmit their message and support each other to forwardsignals to their respective destinations. An end-to-end approximateerror performance of multi-antenna cooperative relay networkhas been carried out in [8]. Outage analysis of a system in whichcommunication between two single antenna nodes is supportedby a multi-antenna relay is analyzed in [9]. In [10], closed formexpressions for outage probability and BER have been derived whenmulti-antenna cooperative relay network operate in correlatedNakagami-m fading channel and both the relay and destinationperform maximum ratio combining (MRC) of signals. Closed formexpression of outage probability has been derived in [11], here com-munication between source and destination is supported by twomulti-antenna relay nodes. For best relay selection scheme, closedform expressions of outage and average channel capacity havebeen derived in [12]. Comparative outage performance of MRC andselection combining (SC) schemes for multiple relay network havebeen analyzed in [13]. In [14], outage performance of cooperativerelay network has been analyzed for Nakagami-m fading channel.Transmission rates are derived in [15] for various configurationsof relay, which placed between a multiple-input-multiple-output(MIMO) system. A closed form expression for the outage probabil-ity of MIMO system supported by MIMO relay is derived in [16].End-to-end symbol error probability of decode and forward relaysystem for M-ary phase-shift keying is derived in [17,18]. In [19],average bit-error rate performance is analyzed for uncoded decode-and-forward cooperative diversity networks. Analytical expression

for the end-to-end average bit error rate in multi-hop decode-and-forward routes is derived in [20].

In this paper we have considered a two hop cooperative relaysystem in which single antenna source and relay are communicat-

2 H. Katiyar, R. Bhattacharjee / Int. J. Electro

Ist Time Slot IInd Time Slot

Source (s)

Relay (r)

Destination (d)

Fig. 1. Two-hop cooperative relay communicating with multi-antenna base station.

ioowcpdpbaPcisoa

sstrNi

2

dTmtatnvrstrili

3.3. PDF of total received SNR

From the theorem on total probability, PDF of the received SNRcan be expressed as

ng with a multi-antenna base station. This work is extension ofur previous work [21], which gives the analytical expressions ofutage, symbol error rate and average received SNR of such net-ork in terms of infinite series. We have experienced problem of

onvergence with such expressions in different condition. In thisaper, a different approach has been adopted and the probabilityensity function (PDF) of the received SNR has been found out usingartial fraction method. Closed form expressions of outage proba-ility, average symbol error rate (SER), average received SNR andverage capacity of cooperative relay network are then derived.erformance of cooperative relay network is also compared withonventional SIMO system i.e. single antenna node communicat-ng with multi-antenna base station which performs MRC of theignals. Link performance have been evaluated at various SNR, vari-us path-loss conditions and different number of antenna elementst destination.

Rest of paper is organized as follows: In Section 2, we discuss theystem model of cooperative relay network in which single antennaource and relay are communicating with multi-antenna destina-ion. Closed form expressions of outage probability, SER, averageeceived SNR and average capacity have been derived in Section 3.umerical results and performance of such network are discussed

n Section 4. Finally, conclusions are drawn in Section 5.

. System model

As shown in Fig. 1, communication between source (s) andestination (d) takes place with the help of supporting relay (r).erminals s and r each has single antenna but the terminal d haveultiple antennas. As r operates in half duplex mode, s transmits to

he r and d in the first hop (i.e. s → r and s → d). If received SNR at r isbove a particular threshold (active mode), the message is assumedo be decoded without any error and retransmitted to the d in theext time slot (i.e. r → d). Signal received through direct path andia relay path are coherently combined at d. If the received SNR at

is below the required threshold (inactive mode), then r remainsilent and d receives the signal only through direct path. In this sys-em model, we are assuming that the channel between s → d and

→ d are independent and non-identically distributed, because ds receiving the signal from transmitting nodes, located at different

ocations. However, signals received at d are identically distributed,f they are coming from same place (i.e. from s or r). In this work,

n. Commun. (AEÜ) 66 (2012) 1– 6

we assume that received SNR at r (�sr) is exponentially distributed,whose PDF can be given as [22, Eq. (2.21)]

f�sr (�) = �sr exp (−�sr�) , (1)

where �sr =(

2�sr/�sd) /�, is path loss exponent, � is SNR at

reference point, �sr represents distance between node s and r, whichhas been normalized here by half the distance between s and d(i.e. �sd/2). Destination is equipped with multi-antenna array andperforms MRC, so PDF of received SNR at d can be written as [23]

f�ij (�) =�nij�n−1

(n − 1)!exp

(−�ij�

), (2)

where i ∈ {s, r}, j ∈{d}

, n is the number of antennas at d, �ij =(2�ij/�sd

) /�, �ij represents distance between node i and j. In first

hop, if received SNR at relay is above the required threshold, thenrelay decodes the message received from source. This condition,corresponds to mutual information (I), transmitted by the sourceis more than target data rate R (spectral efficiency) [4]

I = 12

log2 (1 + �sr)> R. (3)

In Eq. (3), we multiply logarithm with 1/2 because such systemoperates in two time-slots and utilize only 1/2 part of channel.

3. Mathematical analysis

3.1. Probability of relay transmission

Probability of relay being in the active mode can be written as

P [�sr > �] = 1 −∫ �

0

fsr (�)d� = P [I > R] , (4)

where � is the threshold. Substituting (1) in (4) and solving integralwe obtain

P [I > R] = exp (−�sr�) . (5)

Probability of relay in inactive mode is

P [I ≤ R] = 1 − P [I > R] = 1 − exp (−�sr�) . (6)

3.2. PDF of received SNR based on link condition

Let random variable � model the received SNR at d through relaylink (i.e. s → r → d). When relay is in inactive mode, conditional PDFof received SNR is given as

f�|I≤R(�)

= ı(�)

, (7)

where ı (·) is dirac delta function. For the case when relay is in activemode, conditional PDF of received SNR can be given as

f�|I>R(�)

= �nrd�n−1

(n − 1)!exp

(−�rd�

). (8)

f�(�)

= f�|I≤R(�)P [I ≤ R] + f�|I>R

(�)P [I > R] . (9)

Electro

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M

ws

M

h

rfa

f

3

P

s

P

wEo

P

w

3

(

S

,

H. Katiyar, R. Bhattacharjee / Int. J.

he MGF1 of f�(�)

, through relay link can be written as

srd(s) = P [I ≤ R] + P [I > R](

�rds + �rd

)n. (10)

n assuming the channels between s → r → d and s → d are inde-endent, MGF of equivalent link can be given as

T (s) = Msrd(s)Msd(s), (11)

here Msd(s) = �nsd/(s + �sd)

n is MGF of direct link. MT(s) can beimplified using method of partial fractions [24, Eq. (2.102)]

T (s) = P [I ≤ R](

�sds + �sd

)n+ P [I > R]

×[

n∑˛=1

A˛

(s + �sd)˛ +

n∑˛=1

B˛

(s + �rd)˛

], (12)

ere An−k+1 = (k−1)A

(−�sd)(k−1)! (�sd)

n(�rd)n, A (s) = 1

(s+�rd)n, Bn−k+1 =

(k−1)B

(−�rd)(k−1)! (�sd)

n(�rd)n, B (s) = 1

(s+�sd)n. Expression for PDF of

eceived SNR at d can be found out, by taking inverse Laplace trans-orm of MT(s). So the PDF of end-to-end received SNR can be writtens

�T

(�)

= P [I ≤ R](n − 1)!

�nsd�n−1 exp

(−�sd�

)+ P [I > R]

×[

n∑˛=1

A˛�˛−1

( ̨ − 1)!exp

(−�sd�

)+

n∑˛=1

B˛�˛−1

( ̨ − 1)!exp

(−�rd�

)]. (13)

.4. Outage probability

Outage probability (Pout), can be evaluated as [22, Eq. (1.4)]

out =∫ �

0

f�T(�)d�, (14)

o, Pout can be evaluated from (13), (14) and [24, Eq. (3.381.1)]

out = P [I ≤ R] (n, �sd�)

(n − 1)!+ P [I > R]

×[

n∑˛=1

A˛ (˛, �sd�)�˛sd ( ̨ − 1)!

+n∑˛=1

B˛ (˛, �rd�)�˛rd ( ̨ − 1)!

], (15)

here � = 22R − 1, (·, ·) is upper incomplete gamma function [24,q. (8.350.1)]. In case of SIMO, Pout can be evaluated with the helpf (2), (14) and [24, Eq. (3.381.1)]

out = (n, �sd�SIMO)(n − 1)!

, (16)

here �SIMO = 2R − 1.

.5. Average symbol error rate

Average SER for M-PSK modulated signal is defined as [22, Eq.5.1)] ∫ ∞ (√ ) ( )

ER =

0

Q c� f�T � d�, (17)

1 MGF =∫ ∞

0f�

(�)

exp(

−s�)d�.

n. Commun. (AEÜ) 66 (2012) 1– 6 3

where c = 2 sin2 (/M

). Average SER from (17), can be evaluated

from (13) and [25, Eq. (A8)]

SER = P [I ≤ R](n − 1)!

�nsd�{�sd, n

}+ P [I > R]

×[

n∑˛=1

A˛�{�sd, ˛

}( ̨ − 1)!

+n∑˛=1

B˛�{�rd, ˛

}( ̨ − 1)!

], (18)

where � {x, y}= (y)

xy

{√c

2x+c(2x+c)−y (y+0.5)2√ (y+1)(2x)−y

}2F1

(1, y + 0.5; y + 1; 2x

2x+c),

2F1·,·;·;· is Gauss hypergeometric function [24, Eq. (9.100)]. Incase of SIMO, average SER can be evaluated from (2), (17) and [25,Eq. (A8)]

SER =�

{�sd, n

}(n − 1)!�−n

sd

. (19)

3.6. Average received SNR

Average received SNR ( �̄), can be evaluated as [22, Eq. (1.1)]

�̄ = 12

∫ ∞

0

�f�T(�)d�. (20)

In (20), we multiply with 1/2, because average received SNR atmulti-antenna destination received in two time-slots. �̄ can beevaluated from (13), (20) and [24, Eq. (3.326.2)]

�̄ = 12

[P [I ≤ R]

n

�sd+ P [I > R]

×{

n∑˛=1

A˛˛

(�sd)˛+1

+n∑˛=1

B˛˛

(�rd)˛+1

}]. (21)

In case of SIMO, �̄ can be evaluated with the help of (2), (20) and[24, Eq. (3.326.2)]

�̄ = n

�sd. (22)

3.7. Average capacity

Average capacity is defined as [22, Eq. (5.1)]

C = 12

∫ ∞

0

log2(1 + �)f�T(�)d�. (23)

Average capacity from (23), can be evaluated with the help of (13)and [24, Eq. (4.337.5)]

C = 12

[�nsd

(n − 1)!� (�sd, n)

{1 − exp (−�sr�)

}+ exp (−�sr�)

×{

n∑˛=1

A˛� (�sd, ˛)( ̨ − 1)!

+n∑˛=1

B˛� (�rd, ˛)( ̨ − 1)!

}], (24)

here, �(˛, ˇ

)= (ˇ−1)!

˛ˇ loge2

ˇ−1∑�=0

1(ˇ−�−1)!

[(−1)ˇ−�−2˛ˇ−�−1 × exp (˛)Ei (−˛) +

ˇ−�−1∑ =1

( − 1)!(−˛)ˇ−�− −1

]Ei(•) is exponential integral [24, Eq. (27.5.3)]. In case of SIMO,

average capacity is defined as [22, Eq. (5.1)]

C =∫ ∞

0

log2(1 + �)f�sd(�)d�. (25)

4 H. Katiyar, R. Bhattacharjee / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1– 6

0 5 10 15 20 25 30 35 4010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

SNR (dB)

Out

age

Pro

babi

lity

AnalyticalSimulated

SIMO with BPSK

Relay with QPSKn=4

n=2

n=1

Fc

Aa

C

4

api(ihaiisSrrt

Fc

0 5 10 15 20 25 30 35 4010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

SNR (dB)

SE

R

AnalyticalSimulated

SIMO with BPSKRelay with QPSK

n=1

n=4 n=2

Fig. 4. SER ( = 3, � = 3) performance of cooperative relay network communicatingwith multi-antenna base station.

0 5 10 15 20 25 30 35 4010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

SE

RAnalyticalSimulated

SIMO with BPSK

Relay with QPSK

n=1

n=4

n=2

ig. 2. Outage performance ( = 3, � = 3) of cooperative relay network communi-ating with multi-antenna base station.

verage capacity from (25), can be evaluated with the help of (2)nd [24, Eq. (4.337.5)]

= �nsd� (�sd, n) . (26)

. Numerical results

In evaluating the performance of the system, we are assumingsymmetrical channel conditions (i.e. �sr = �rd /= �sd), where r islaced between s and d. R is spectral efficiency in bps/Hz which

s assumed to be unity for numerical evaluation. For various SNRsi.e. �) and various values of n and , end-to-end outage probabil-ty, symbol error rate, average received SNR and average capacityave been plotted in Figs. 2 and 3, Figs. 4 and 5, Figs. 6 and 7nd Figs. 8 and 9, respectively. Due to wastage of one time slotn cooperative relay network, spectrum efficiency of this systems just half of SIMO system if same modulation schemes is con-idered. So, for faithful comparison, SER performance of BPSK for

IMO is compared with the performance of QPSK for cooperativeelay network. For the simulation, vector of random variables ofeceived SNR (exponentially distributed) have been generated withhe help of [26, Eq. (7.41)]. From the generated random variables

0 5 10 15 20 25 30 35 4010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

SNR (dB)

Out

age

Pro

babi

lity

AnalyticalSimulated

n=4

SIMO with BPSK

Relay with QPSK

n=2

n=1

ig. 3. Outage performance ( = 5, � = 3) of cooperative relay network communi-ating with multi-antenna base station.

SNR (dB)

Fig. 5. SER ( = 5, � = 3) performance of cooperative relay network communicatingwith multi-antenna base station.

0 5 10 15 20 25 30 35 40−10

0

10

20

30

40

50

SNR (dB)

Ave

rage

SN

R (

dB)

AnalyticalSimulated

SIMO

Relay

n=4

n=1

n=2

Fig. 6. Average received SNR ( = 3, � = 3) at multi-antenna base station.

H. Katiyar, R. Bhattacharjee / Int. J. Electro

0 5 10 15 20 25 30 35 40−20

−10

0

10

20

30

40

50

SNR (dB)

Ave

rage

SN

R (

dB)

AnalyticalSimulated

Relay

SIMO

n=2

n=4n=1

Fig. 7. Average received SNR ( = 5, � = 3) at multi-antenna base station.

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

SNR (dB)

Ave

rage

Cap

acity

AnalyticalSimulated

Relay

n=1

SIMO

n=2

n=4

Fig. 8. Average capacity ( = 3, � = 3) of cooperative relay network communicatingwith multi-antenna base station.

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

SNR (dB)

Ave

rage

Cap

acity

AnalyticalSimulated

Relay

SIMO

n=1

n=4

n=2

Fig. 9. Average capacity ( = 5, � = 3) of cooperative relay network communicatingwith multi-antenna base station.

n. Commun. (AEÜ) 66 (2012) 1– 6 5

of received SNR for various links, relay compares the received SNRwith a particular threshold (�). If received SNR is greater than �,destination coherently combined the signals received through thedirect path and through the relay path else destination coherentlycombined the signals received only through the direct path. Withthe help of received SNR at destination, outage probability, sym-bol error rate, average received SNR and average capacity havebeen calculated. From Figs. 2 to 9, we observe that direct trans-mission is better at lower SNR because most of time relay will notdecode the message (i.e. relay will not participate) and unnecessarywastage of spectrum efficiency will take place. At higher SNR, relayassisted transmission is better than direct transmission as proba-bility of better participation of relay increases. Intersection pointof direct transmission curve and curve for transmission throughrelay increases with increase in antenna elements at destination.This is due to fact that slope of these performance curve increasesand advantage of cooperation will be visible at higher SNR. Athigher path-loss condition, communication through intermediaterelay node is superior to lower path-loss condition because signalsare intermediately boosted up. In such scenario, performance ofcooperative relaying is equivalent or may outperform SIMO sys-tem of same diversity order. From Fig. 5, it can be seen that at highpath-loss conditions, SER performance of cooperative relaying forQPSK with one antenna at destination becomes better than that ofSIMO with BPSK and having two antennas at the destination. Sim-ilar observations can be made in the outage, average received SNRand capacity plots.

5. Conclusion

In this paper, we have compared the outage probability, SER,average received SNR, average capacity of cooperative relay net-work having a multi-antenna base station with a conventionalSIMO system. Analytical expressions for each case have beenderived. Monte Carlo simulation (running simulator freely with105 samples) has been carried out and the analytical results arefound to match with the simulation results. We found that, supe-rior performance of cooperative relaying over conventional SIMOsystem depends on path-loss conditions, number of antenna ele-ments on destination and SNR conditions. For same performancelabel in some specific conditions, cooperative relaying can be usedto reduce the burden of large antenna array on base station. Cooper-ative relaying may outperform conventional SIMO system in higherpath-loss condition.

Acknowledgments

This work is partially supported by Institution of Electron-ics and Telecommunications Engineers (IETE), New Delhi (India),under the Grant IETE/J-282-8/BOR/2009. This work is also sup-ported by Department of Electronics and Communication Engg.,BBDNITM, Lucknow, Uttar Pradesh, India. Their supports are grate-fully acknowledged.

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technical reference. Upper Saddle River, New Jersey 07458: Prentice Hall;2004.

Himanshu Katiyar received his B.E. degree in Electronicsand Communication from M.J.P. Rohilkhand University,Bareilly, Uttar Pradesh, India, in 2001 and M.Tech. fromMadan Mohan Malviya Engineering College, Gorakhpur,Uttar Pradesh, India, in 2004. From 2004 to 2005 he waslecturer of Electronics and Communication EngineeringDept. at SRMSCET, Bareilly, Uttar Pradesh, India, and from2005 to 2006 he was lecturer of Electronics and Communi-cation Engineering Dept. at NIEC, Lucknow, Uttar Pradesh,India. At present he is Associate Professor of Electronicsand Communication Engineering Dept. at BBDNITM, Luc-know, Uttar Pradesh, India. He is currently pursuing hisPh.D. in area of wireless communication at Indian Institute

of Technology Guwahati (IITG), Assam, India. His research interests include almostall aspects of wireless communications with a special emphasis on MIMO systems,channel modeling, infrastructure-based multihop and relay networks, cooperativediversity schemes.

Dr. Ratnajit Bhattacharjee received his B.E. in Electronicsand Telecommunication Engineering (First Class Honors)from Gauhati University (REC (at present NIT) Silchar),M.Tech. (E and ECE Department, Microwave Engineeringspecialization) from IIT Kharagpur and Ph.D. (Engineer-ing) from Jadavpur University Kolkata. Presently he is anAssociate Professor in the Department of Electronics andElectrical Engineering, IIT Guwahati. Prior to joining IITGuwahati, he was a faculty member in REC (NIT) Silchar.His research interest includes Wireless communication,Wireless networks, Microstrip antennas, Microwave Engi-neering and Electromagnetics. He has published overninety research papers in journals, international and

national conferences. He has developed the web course on Electromagnetic The-ory under the NPTEL project of MHRD. At present he is developing the web courseon Advanced Mobile Communication under the phase II of the same project. He isinvolved with the ongoing mission project on Virtual labs at various capacities Hehas also been involved in several research projects. He has been a Co-investigatorfor the contracted research from NICT Japan in the area of Next Generation Wire-less Networks and is a member of the research team of the Tiny6 project dealingwith IPv6 and Sensor Networks. Presently he is also involved in an antenna system

development project from ISRO. In NIT Silchar, he was a coordinator for the settingup of Campus Wide Optical Fiber based network under the Centre for Excellencescheme. He was also associated in a number of sponsored projects in the field ofdevelopment of antenna system. He is a member of IEEE and life member of IndianSociety of Technical Education.