Int. J. Electron. Commun. (AEU) 64 (2010) 988 -- 991

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Int. J. Electron. Commun. (AEU)

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LETTER

Performance ofMRC combiningmulti-antenna cooperative relay network

Himanshu Katiyar∗, R. Bhattacharjee1Communication and Advance DSP Group, Electronics and Communication Engineering Department, Indian Institute of Technology Guwahati, North Guwahati, Guwahati 781039, India

A R T I C L E I N F O A B S T R A C T

Article history:Received 8 April 2009Accepted 29 July 2009

Keywords:Outage probabilityBit error rate for BPSKMRC combiningMulti-antenna relayDecode and forward mode

Performance of cooperative relaying employing infrastructure based fixed relays having multiple antennashas been investigated. Employing MGF based approach, closed form expression for outage probability andbit error rate performance of BPSK signal have been derived, when relay and destination are assumed toperform MRC combining of the signals. The effect of relay placement on the system performance has alsobeen studied under different path loss conditions.

© 2009 Elsevier GmbH. All rights reserved.

1. Introduction

Cooperative relaying was introduced to make use of the broad-cast nature of the wireless channel and create virtual antenna ar-rays with communicating nodes having single antennas. It providesspacial diversity to combat multi-path fading. Different aspects ofsuch scheme have been investigated in [1–5]. Recently, use of multi-antenna relay nodes (infrastructure based fixed relay) in a coopera-tive network has been proposed and a probability density function(PDF) based approach for calculating error rate for network contain-ing fixed multi-antenna relay nodes have been presented in [6].

This paper presents outage analysis for a cooperative relayingscheme that includes a multi-antenna relay. Here, multi-antennarelay and destination performs MRC combining of signals. A momentgenerating function (MGF) based approach has been developed forevaluation of probability of outage and average bit error rate forBPSK. Link performance has been evaluated including the effects ofrelay placement and different path loss condition.

2. Cooperative relay

As shown in Fig. 1, our decode and forward (DF) cooperativerelay network consists of multi-antenna relay (r), placed between

∗ Corresponding author. Mob.: +919954249653.E-mail addresses: h.katiyar@iitg.ernet.in, katiyarhimanshu@gmail.com

(H. Katiyar), ratnajit@iitg.ernet.in (R. Bhattacharjee).1 Tel.: +913612582503; fax: +913612582542.

1434-8411/$ - see front matter © 2009 Elsevier GmbH. All rights reserved.doi:10.1016/j.aeue.2009.07.007

source (s) and destination (d). Relay node is equipped with one trans-mitting antenna and n receiving antennas.1

Due to half-duplex nature of the relay, the source transmits tothe relay and destination in first time slot (i.e. s → rk and s → d). Amulti-antenna relay receives signal from the source throughmultiplelinks and perform MRC combining. After MRC combining, if receivedSNR is above the threshold of the decoder, the message is decodedand retransmitted to the destination in the next time slot. If receivedSNR at the relay is below the required threshold, the destinationreceives signal only through the direct path. When the SNR at relayis above threshold, signals received via direct path and via relay pathare coherently combined at d.

2.1. Mathematical modeling

The relationship between the transmitted signal xi at ithnode/antenna and received signal yj at jth node/antenna can bewritten as

yj =√Piaijxi + zj, (1)

here i ∈ {s, r0}, j ∈ {rk, d}, xi is the signal vector, drawn from a whitecomplex Gaussian code-book, of independent and identically dis-tributed (i.i.d.) complex Gaussian random variable (RV) i.e. N(0, 1),

1 In this paper, symbol r0 represents transmitting antenna of r and rk representsthe kth receiving antenna of r.

H. Katiyar, R. Bhattacharjee / Int. J. Electron. Commun. (AEU) 64 (2010) 988 -- 991 989

r0 Ist Hop

r1

rk

2nd Hop

rn-1

ro

Fig. 1. Two-hop cooperative relaying with multi-antenna relay system.

Pi is the power transmitted by ith node,2 distribution of zj is com-plex Gaussian with zero mean and Nj/2 variance per dimension i.e.N(0,Nj). So un-faded signal to noise ratio received at jth node isgiven as �j =Pi/Nj. aij is modeled as zero-mean, circularly symmetriccomplex Gaussian RV with variance 1/�ij. |aij| is Rayleigh distributedand �ij = |aij|2 is exponentially distributed,3 so its PDF is given as

f�ij (�) = �ij exp(−�ij�). (2)

Parameter �ij = (2 × �ij/�sd)�/(��j). Here � = (GiGj/�

�ij )(�/4�)2 � is

carrier wavelength, � is path loss exponent, �ij represents distancebetween node/antenna i and j, which is normalize by half of thedistance between s and d (i.e. �sd/2). For the system model underconsideration, antenna gains (Gi, Gj) so chosen such that � becomeunity. In first hop, if received SNR at relay is above the requiredthreshold, then relay decodes themessage received from source. Thiscondition, corresponds to mutual information (I), transmitted by thesource is more than target data rate R (spectral efficiency) [2]:

I = 12log2

⎛⎝1 +

n−1∑k=0

�srk

⎞⎠>R. (3)

In Eq. (3) we multiply logarithmwith 12 because such system operate

in two time-slots and utilize only 12 part of channel.

2.1.1. Probability of relay transmissionFor identically distributed Rayleigh fading (i.e. ∀�srk=�sr) between

s → r, probability of relay transmission (active mode) is given by4

[3]

P[I >R] = P

⎡⎣n−1∑

k=0

�srk >�

⎤⎦= exp(−�sr�)

n−1∑k=0

(�sr�)k

k!, (4)

here �=22R−1. Probability of relay will not transmit (inactive mode)

P[I�R] = 1 − P[I >R]. (5)

2 Here we assume that PT =Ps +Pr , Ps =Pr =0.5×PT and SNR(db)=10 log10(PT /Nj)is total transmitted signal to noise ratio.

3 We assume that all transmitter have no prior knowledge of CSI and all receiverhave CSI through training sequence transmitted along message. Receiver employcoherent detection, so in subsequent analysis we need only consider the fadingcoefficient magnitude.

4 We assume that transmitted data to be encoded with CRC such that the relayswill be able to decide whether it decoded correctly or not.

2.1.2. PDF of received SNR based on link conditionLet random variable � models the channel SNR of s → r and

r0 → d, which takes care of the fading on both links involving therelay. When relay is inactive, then probability of received SNR at d,through s → r → d link is modeled as

f�|I�R() = �(). (6)

For the case when relay is active, then probability of received SNRat d, through s → r → d link is given by

f�|I>R() = �r0d exp(−�r0d). (7)

2.1.3. PDF of total received SNRFrom theorem on total probability, PDF of received SNR can be

expressed as [7]

f�() = f�|I�R()P[I�R] + f�|I>R()P[I >R]. (8)

The MGF5 of f�(), through relay link is given as

Msrd(s) = P[I�R] + P[I >R] × �r0d

s + �r0d. (9)

For the case, when channel between s → r → d and s → d areindependent and destination performs MRC, the MGFs of direct pathand relay path have been multiplied i.e.

MT (s) = Msrd(s) × Msd(s), (10)

here Msd(s) = �sd/(s + �sd) is MGF of direct link.

2.2. Outage probability

Outage probability (Pout), can be evaluated, by taking inverseLaplace transform of MT (s)/s, evaluated at � i.e.

Pout = [1 − exp(−�sd�)]

⎡⎣1 − exp(−�sr�) ×

n−1∑k=0

(�sr�)k

k!

⎤⎦

+[1 + 1

�sd − �r0d{�r0d exp(−�sd�) − �sd exp(−�r0d�)}

]

× exp(−�sr�)n−1∑k=0

(�sr�)k

k!. (11)

Accuracy of this expression is crosschecked with the help of numer-ical technique, which is given in [9, Eq. (11)].

2.3. Bit error rate

Bit error rate (BER) for BPSK modulated signal is define as [10,Eq. (9.15)]

BER = 1�

∫ �/2

0MT

(1

sin2()

)d. (12)

5 MGF = ∫∞0 f�() exp(−s)d [8, Eq.(2)].

990 H. Katiyar, R. Bhattacharjee / Int. J. Electron. Commun. (AEU) 64 (2010) 988 -- 991

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Relay distance from source (m)

Out

age

Pro

babi

lity

(Pou

t)

Theoritical n=2Numerical n=2Theoritical n=4Numerical n=4Theoritical n=6Numerical n=6

Fig. 2. Outage probability of multi-antenna relay network (�=2.5) at various locationbetween s and d.

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relay distance from source (m)

Out

age

Pro

babi

lity

(Pou

t)

Theoritical n=2Numerical n=2Theoritical n=4Numerical n=4Theoritical n=6Numerical n=6

Fig. 3. Outage probability of multi-antenna relay network (�=4.5) at various locationbetween s and d.

After some algebraic manipulations with the help of [11,Eq. (3.653.2)], BER for this system can be found as

BER = 12

[1 − 1√

1 + �sd

]⎡⎣1 − exp(−�sr�)n−1∑k=0

(�sr�)k

k!

⎤⎦

+ 12

⎡⎣�sd

⎛⎝1 − 1√

1 + �r0d

⎞⎠− �r0d

(1 − 1√

1 + �sd

)⎤⎦

× 1�sd − �r0d

exp(−�sr�)n−1∑k=0

(�sr�)k

k!. (13)

Accuracy of expression in (13) is crosschecked with the help of nu-merical integration of (12).

3. Numerical results

This section presents the performance of relay based system inwhich s is communicating with d, supported by multi-antenna r. Thes and d are considered to be located at (0,0) and (0,100), respectively.Spectral efficiency (R) and noise variance at r and d are assume tounity. End to end MGF of this system is established in (10) and closeform expression for Pout and BER are established in (11) and (13).Path loss exponent (�) between s to r, s to d and r to d is consideredto be same. Pout and BER is calculated, for the case when SNR=10(db).

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

Relay distance from source (m)

BE

R

Theoritical n=2Numerical n=2Theoritical n=4Numerical n=4Theoritical n=6Numerical n=6

Fig. 4. BER of multi-antenna relay network (� = 2.5) at various location between sand d.

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

100

Relay distance from source (m)

BE

R

Theoritical n=2Numerical n=2Theoritical n=4Numerical n=4Theoritical n=6Numerical n=6

Fig. 5. BER of multi-antenna relay network (� = 4.5) at various location between sand d.

r is located at distance which ranges from 2 to 98. In Figs. 2 and 3,we plot the Pout and in Figs. 4 and 5, we plot BER for various values ofn and �. We observed that the performance of such system suffersif relay is placed near the source, because path loss between r tod is close to that between s to d and therefore spectrum efficiencysuffers. In this scenario, advantage of having multiple antennas relayis negligible because signal strength in any path (i.e. s–rk link) issufficiently high, so most of time relay is able to decode the messageand the overall performance depends on that of r–d link. As locationof relay is moved near the destination, system performance againsuffers. This is due to large path-loss, resulting poor received SNRat relay and most of time relay node will not be able to decode themessage. Under such conditions installation of multiple antennason relay improves the system performance. From Figs. 2 to 5, weobserve that performance of system improves with increase in thenumber of antenna elements and for relay placement towards d.

H. Katiyar, R. Bhattacharjee / Int. J. Electron. Commun. (AEU) 64 (2010) 988 -- 991 991

4. Conclusion

Cooperative relay network employing multiple antenna relay hasbeen investigated and MGF based method has been used for analy-sis. Analytical expressions for outage probability and average BER forBPSK, are derived. Validity of these expressions are verified throughnumerical technique. Result shows that the number of antenna ele-ments on relay and the location of the relay plays a vital role on theperformance of such system.

References

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[5] Beres E, Adve R. Selection cooperation in multi-source cooperative networks.IEEE Trans Wireless Commun 2008;7:118–27.

[6] Adinoyi A, Yanikomeroglu H. Cooperative relaying in multi-antenna fixed relaynetworks. IEEE Trans Wireless Commun 2007;6:533–44.

[7] Beaulieu NC, Hu J. A closed-form expression for the outage probabilityof decode-and-forward relaying in dissimilar Rayleigh fading channels. IEEECommun Lett 2006;10:813–5.

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Himanshu Katiyar received his B.Tech. degree inElectronics and Communication from M.J.P. Rohilk-hand University, Bareilly, Uttar Pradesh, India, in2001 and M.Tech. from Madan Mohan Malviya En-gineering College, Gorakhpur, Uttar Pradesh, India,in 2004. From 2004 to 2005 he was lecturer ofElectronics and Communication Engineering Depart-ment at SRMSCET, Bareilly, Uttar Pradesh, India, andfrom 2005 to 2006 he was lecturer of Electron-ics and Communication Engineering Department atNIEC, Lucknow, Uttar Pradesh, India. He is currentlypursuing his Ph.D. in area of wireless communica-tion at Indian Institute of Technology (IIT), Guwa-hati, Assam, India. His research interests include al-most all aspects of wireless communications with a

special emphasis on MIMO systems, channel modeling, infrastructure-based multi-hop and relay networks, cooperative diversity schemes. He has been selected forIETE Research Fellowship.

Ratnajit Bhattacharjee received his B.E. in Electron-ics and Telecommunication Engineering (First ClassHonors) from Gauhati University (REC (at presentNIT) Silchar), M.Tech. (E and ECE Department,Microwave Engineering specialization) from IITKharagpur and Ph.D. (Engineering) from JadavpurUniversity Kolkata. Presently he is an Associate Pro-fessor in the Department of Electronics and Com-munication Engineering, IIT Guwahati. Prior to join-ing IIT Guwahati, he was a faculty member in REC(NIT) Silchar. His research interest includes wire-less communication, wireless networks, microstripantennas, microwave engineering and electromag-netics. He has published over 60 research papersin journals, international and national conferences.

He has developed the web course on Electromagnetic Theory under the NPTELproject of MHRD. He has also been involved in several research projects. He hasbeen a co-investigator for the contracted research from NICT Japan in the area ofNext Generation Wireless Networks and currently a member of the research teamof the Tiny6 STIC project (funded by French ministry of Foreign Affairs), which dealswith IPv6 and Sensor Networks. 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.