Physical Communication 4 (2011) 190–195

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Physical Communication

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Full length article

Performance of two-hop infrastructure based multi-antennaregenerative relaying in Rayleigh fading channelHimanshu Katiyar a,∗, R. Bhattacharjee b

a Electronics and Communication Engg. Department, BBDNITM, Lucknow, Indiab Communication and Advance DSP Group, Electronics and Electrical Engg. Department, Indian Institute of Technology Guwahati, India

a r t i c l e i n f o

Article history:Received 13 December 2010Received in revised form 6 June 2011Accepted 7 June 2011Available online 15 June 2011

Keywords:Outage probabilityAverage error rateSelection combiningMulti-antenna relayRegenerative modeRayleigh fading channel

a b s t r a c t

Cooperative relaying is considered as an effective technique to enlarge the coveragearea and enhance the system capacity for the future wireless systems. In this paper,an infrastructure based multi-antenna cooperative relay network has been investigated.Closed form expressions of outage probability and average error rate have been derived,when the relay and the destination perform selection combining of the signals. The relayis assumed to operate in the adaptive decode and forward mode. The effect of number ofantennas installed on the relay and their placement has also been studied.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Cooperative relaying has emerged as an effective tech-nique to combat the effect of path loss and multi-pathfading. Here, relay nodes share their antennas and otherresources to create a virtual array through distributedtransmission and signal processing. In their pioneeringwork [1], Laneman et al. analyzed various aspects of co-operative relay systems. End-to-end error performance ofselection cooperation has been discussed in [2]. Closedform expressions of outage probability and channel capac-ity with tight approximation over a sufficiently wide rangeof signal to noise ratio (SNR) have been presented in [3].In [4], the authors have analyzed the various cooperativeprotocols for a decode and forward relay network. Errorperformance of distributed space–time coding for coop-erative relay networks is analyzed in [5]. In [6], various

∗ Corresponding author. Tel.: +91 5222702502; fax: +91 3612582542.E-mail addresses: katiyarhimanshu@gmail.com,

h.katiyar@iitg.ernet.in (H. Katiyar), ratnajit@iitg.ernet.in(R. Bhattacharjee).

1874-4907/$ – see front matter© 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.phycom.2011.06.002

relaying strategies for wireless networks have been stud-ied. In [7], Laneman et al. develop and analyze distributedspace–time coded cooperative diversity protocols forimproving spectral efficiency. Outage probability of coop-erative relaying in statistically similar channels has beenpresented in [8]. In the same paper several bounds are pro-posed for the cases when the statistics of the channels aredissimilar. In [9], outage performance of dual-hop oppor-tunistic relaying has been studied and performance hasbeen compared to that of a single-hop single inputmultipleoutput (SIMO) system under Rayleigh fading conditions.Recently, use of multi-antenna relay nodes (infrastruc-ture based fixed relay) in a cooperative network has beenproposed and a probability density function (PDF) basedapproach for calculating approximate error rate of infras-tructure based fixed relay with multiple receive antennasand single transmit antenna has been presented in [10].In [11], closed form expressions of outage probability andbit error rate (BER) for binary phase shift keying (BPSK)are derived for the case when communication betweensource and destination is supported by amulti-antenna re-lay, and both relay and destination perform maximum ra-tio combining (MRC) of signals in Rayleigh fading channel.

H. Katiyar, R. Bhattacharjee / Physical Communication 4 (2011) 190–195 191

Fig. 1. Two-hop cooperative relay network.

Outage probability and average error rate of two-hopmulti-antenna relay based system have been analyzed re-spectively in [12,13] for the case when the relay performsselection combining (SC) of signals and the destinationperforms MRC of signals. In [14], closed form expressionsfor outage probability and BER have been derived for amulti-antenna cooperative relay network which operatesin correlated Nakagami-m fading channel and both the re-lay and destination perform MRC of signals. A closed formexpression of outage probability has been derived in [15],here communication between source and destination issupported by two multi-antenna relay nodes. Outage per-formance of a system in which communication betweensource and destination is supported by arbitrary numberof relays has been derived in [16,17], where the desti-nation performs MRC and SC of the received signals, re-spectively. For opportunistic relay network, closed formexpressions of outage probability and average capacityhave been derived in [18], when relays operate in adaptivedecode and forward mode. User cooperation in the uplinkof a cellular network is discussed in [19] and symbol er-ror rate for Nakagami-m fading channel has been derived.Adaptivemulti-node incremental relaying technique in co-operative communications with amplify-and-forward re-lays has beenproposed in [20]. Here, the authors found thatadaptivemulti-node incremental relaying outperforms theconventional MRC in terms of outage probability. Perfor-mance of relay based network operating above 10 GHz hasbeen studied in [21–23].

This paper presents the outage and average errorperformance of a basic three node system in whichcommunication between two single antenna nodes issupported by a multi-antenna relay. Here, the relay isassumed to operate in an adaptive decode and forwardmode andperforms SC of signals received throughmultipleantennas. Destination performs SC of signals received fromsource and/or relay in two different time-slots. Sourceand destination are assumed to be equipped with a singleantenna because they are tiny wireless nodes where it isdifficult to install multiple antennas. Hardware complexityfor the relay is not an important issue here because theyare considered to be infrastructure type fixed nodes. So, inthe system model under consideration, the relay terminalhas multiple receiving antennas and a single transmittingantenna. Installation of multiple receiving antennas atthe relay improves the probability of its participation.However, we are considering single transmitting antennaat the relay to avoid the signal processing complexity at

the destination side. Fading channels between differentpairs of nodes (i.e. source–relay and relay–destination)have been considered to have non-identical statisticalparameters, whereas identical fading parameters areassumed for the channels between antenna elements ofrelays. The assumptions about the statistical parameterspertain to the location of the nodes. Receiving antennasof the relay are located at the same place (i.e. at relay),so there is higher probability that the channels seen bythese relay antennas are identically distributed whereasthe destination receives signals through paths which arelikely to be nonidentical as the source and relay are locatedat different places. Link performance has been evaluatedincluding the effect of number of antennas installed onrelay and its placement between source and destination.

The rest of the paper is organized as follows: Section 2briefly discusses the system model for the multi-antennacooperative relay network. Closed form expressions ofoutage probability and average error rate in Rayleighfading environment are derived in Section 3. Numericalresults are discussed in Section 4. Finally, conclusions aredrawn in Section 5.

2. Systemmodel

In this work, we analyze the performance of aregenerative cooperative relay network shown in Fig. 1.Here, a multi-antenna relay (R) is placed between source(S) and destination (D). The relay node is assumed to beequipped with one transmitting antenna and n receivingantennas.1Due to thehalf-duplex nature of operation of therelay, S transmits toR andD in the first time-slot (i.e. S → Rand S → D). Relay R receives the signals from S throughmultiple links and performs SC. After SC if the received SNRis above a particular threshold, R forwards the message inthe second time-slot and S remains in inactive in that timeslot. If R cannot perform the decode and forward operationdue to poor channel condition, it remains silent and S re-transmits the signal in the second time slot. Destination Dcan select the better of the two copies of the signal receivedin the first time-slot (i.e. S → D) and in the second time-slot (i.e. S → D or R → D). It is assumed that appropriatemechanism has been built in the system so that S aftera small delay comes to know that R could not decodethe message successfully. In practice, this can be achievedby broadcasting only a single bit of information by Rwhich reflects the status of R and therefore the spectrumefficiency of the systemwill be effected onlymarginally. Inour previous work presented in [12–14,11], we assumedthat S is busy only for the first time-slot and remains silentin second time-slot. In such a system model, if R cannotparticipate due to poor channel conditions, diversity ordersuffers. Such a system model is useful for the case whenS has limited battery power or fading does not changeindependently from first time-slot to second time-slot. Inthis work, we have assumed that the fading parameterbetween twonodes changes independently fromone time-slot to another time-slot. Statistical parameters of fading

1 In this paper, symbol Ro represents transmitting antenna of R and Rkrepresents the kth receiving antenna of R.

192 H. Katiyar, R. Bhattacharjee / Physical Communication 4 (2011) 190–195

channel between different pair of nodes are assumed tobe non-identical, whereas identical fading parameter isassumed for the channel between antenna elements ofrelays. So the PDF of received SNR (γij) can be writtenas [24]

fγij (γ ) =λnijγ

n−1

(n − 1)!exp

−λijγ

, (1)

here i ∈ {S, Ro} , j ∈ {Rk,D}, λij =ℓij/ℓSD

ψ/ω,ψ is

the path loss exponent, ℓij represents distance betweennode i and j, which is normalized by reference distanceℓSD/2, ω is SNRat the reference point. In this systemmodel,we are assuming a scenario of independent and identicallydistributed (i.i.d.) fading between S → R (i.e.λSRk = λ̄SR forall k). So, the average received SNR atD due to S → D, R →

D transmissions will beϖSD (=2/λSD) andϖRD (=1/λRoD),respectively and average received SNR at R due to S → Rtransmission will beϖSR

=1/λ̄SR

∑nk=1 1/k

[25, Eq. (8)].

In first hop, if the received SNR at R after SC is abovethe threshold, relay decodes the message received fromthe source. In this condition, mutual information (I),transmitted by the S is grater than target data rate η(spectral efficiency) [7]:

I =12log2

1 + max

γSRk

> η. (2)

In Eq. (2), we multiply the logarithm by 1/2 because sucha system operates in two time-slots and utilizes only 1/2part of the channel. When R is inactive, SNR received atD due to the transmission from R can be modeled by therandom variable (RV) γ inactive

RoD and its PDF is given as

fγ inactiveRoD

(θ) = δ (θ) , (3)

where δ (·) is a Dirac delta function. Similarly, PDF ofRV γ inactive

sd models the received SNR at D due to thetransmission from S when S is inactivefγ inactive

SD(θ) = δ (θ) . (4)

When R is active, SNR received atD due to the transmissionfrom R can be modeled by RV γ active

RoD and its PDF is given as

fγ activeRoD

(θ) = fγRoD (θ) = λRoD exp−λRoDθ

. (5)

Similarly, the PDF of RV γ activeSD models the received SNR at

D due to the transmission from S when S is active, can bemodeled asfγ active

SD(θ) = fγSD (θ) = λSD exp (−λSDθ) . (6)

3. Mathematical analysis

In this section, we first outline the steps involved infinding out the PDF of total received SNR based on the linkconditions. With the PDF of received SNR known, outageprobability and average error rate expressions are derived.

3.1. Probability of relay in inactive mode

Probability that R will not transmit (inactive mode) isgiven by

P [I ≤ η] = Pmax

γSRk

≤ χ

, (7)

here χ = 22η− 1 is the threshold and η is the spectrum

efficiency. So, (7) can be written as

P [I ≤ η] =1 − exp

−λ̄SRχ

n. (8)

Probability that the relay will transmit (active mode) isgiven byP [I > η] = 1 − P [I ≤ η] . (9)

3.2. PDF of received SNR based on link condition

Let the random variable Θ models the received SNRat D due to transmission from S or R the in second time-slot. When, R is active and re-transmits the message, Sbecomes inactive.When R is inactive, S becomes active andre-transmits the message. So, the conditional PDF of RVΘwhen R is not active is given byfΘ|I≤η (θ) = fγ inactive

RoD+γ active

SD(θ) . (10)

For the case when R is active, S remain silent. So, theconditional PDF of RVΘ can be given asfΘ|I>η (θ) = fγ active

RoD+γ inactive

SD(θ) . (11)

3.3. PDF of total received SNR

In the first time-slotD receives the signal through directlink only. So, the cumulative distribution function (CDF) ofthe direct link can be calculated with the help of (1)

Fγ1 (θ) =

∫ θ

0fγSD (θ) dθ = 1 − exp (−λSDθ) . (12)

From the theorem on total probability, the PDF of thereceived SNR in the second time-slot can be written as

f (2)Θ (θ) = fΘ|I≤η (θ) P [I ≤ η] + fΘ|I>η (θ) P [I > η] . (13)So, the CDF of the received SNR in the second time-slot canbe calculated with the help of (13)

Fγ2 (θ) =

∫ θ

0f (2)Θ (θ) dθ

= P [I ≤ η] {1 − exp (−λSDθ)}

+ P [I > η]1 − exp

−λRoDθ

. (14)

End-to-end link in the first and second time-slots areindependent, so the PDF of equivalent link is given as

fΘT (θ) =ddθ

Fγ1 (θ) Fγ2 (θ)

. (15)

So, (15) can be simplified asfΘT (θ)

= 2λSD {exp (−λSDθ)− exp (−2λSDθ)}

× P [I ≤ η] + P [I > η]λRoD exp

×−λRoDθ

+ λsd exp (−λSDθ)

−λSD + λRoD

exp

−

λSD + λRoD

θ. (16)

3.4. Outage probability (Pout)

Outage occurs when received SNR falls below a certainspecified threshold. Here, for the given thresholdχ , we cancalculate outage probability as follows [26, Eq. (1.4)]

H. Katiyar, R. Bhattacharjee / Physical Communication 4 (2011) 190–195 193

Pout =

∫ χ

0fΘT (θ) dθ. (17)

Outage probability can be calculated with the help of (8),(9), (16), (17) and [27, Eq. (3.381.1)]

Pout = {1 − 2 exp (−λSDχ)+ exp (−2λSDχ)}

×1 − exp

−λ̄SRχ

n

+

1 −

1 − exp

−λ̄SRχ

n

×

1 − exp

−λRoDχ

− exp (−λSDχ)

+ exp−

λSD + λRoD

χ

. (18)

3.5. Average error probability (Pe)

Average error probability is a standard performancemeasure of diversity systems operating over fadingchannels. The average error rate for M-PSK modulatedsignals is define as [26, Eq. (5.1)]

Pe =

∫∞

0Q

√cθ

fΘT (θ) dθ, (19)

here c = 2 sin2 (π/M). Average error probability can beevaluated with the help of (8), (9), (16), (19) and[28, Eq. (A8)]

Pe = 2λSD {µ (λSD, 1)− µ (2λSD, 1)}

×1 − exp

−λ̄SRχ

n

+

1 −

1 − exp

−λ̄SRχ

n

×

λRoDµ

λRoD, 1

+ λSDµ (λSD, 1)

−λSD + λRoD

µ

λSD + λRoD, 1

(20)

where, µ {x, y} =Γ (y)xy

c

2x+c(2x+c)−yΓ (y+0.5)2√πΓ (y+1)(2x)−y

2F1 (1, y

+0.5; y + 1; 2x2x+c

, 2F1 (·, ·; ·; ·) is a Gauss hypergeomet-

ric function [27, Eq. (9.100)] and Γ (·) is a gamma func-tion [27, Eq. (8.310.1)].

4. Numerical results

In evaluating the performance of this system, thefollowing scenario is considered: S and D have beenassumed to be located at (0, 0) and (0, 100), respectively,while R is located at a distance (from S) ranging from 10to 90. η and ψ are assumed to be 1 and 5, respectively.Average received SNR is calculated for ω = 5 and plottedin Fig. 2. Outage probability has been calculated for variousvalues of n and plotted in Fig. 3. Similarly, the average errorrate for BPSK signals (i.e. M=2) have been plotted in Fig. 4,for various values of n. For the case when R is placed at(0, 70), outage and average error rate are plotted in Fig. 5,with respect to n. For the simulation, vector of randomvariables of received SNR (exponentially distributed) hasbeen generated with the help of [29, Eq. (7.41)]. Aftergenerating vector of random variables for various links,

Fig. 2. Average received SNR (ψ = 5) of ϖSR,ϖSD and ϖRD , when R isplaced at various locations between S and D.

Fig. 3. Outage probability atψ = 5, when R is placed at various locationsbetween S and D.

Fig. 4. Average error rate (BPSK) at ψ = 5, when R is placed at variouslocations between S and D.

SC is performed at the relay and the received SNR iscompared to a particular threshold (χ ). If the receivedSNR is greater than χ , the destination performs SC ofsignals received through the direct path and through therelay path else the destination performs SC of the signals

194 H. Katiyar, R. Bhattacharjee / Physical Communication 4 (2011) 190–195

Fig. 5. Outage probability with respect to antennas installed on R, here Ris placed at (0, 70).

received through the direct path in two different time-slots. From the vector of random variables of receivedSNR at destination, outage probability and average errorrate at the destination have been calculated. It is observedthat the performance curves overlap for various valuesof n, when R is placed near S because average receivedSNR at R is sufficiently high and most of the time themessage is decoded by R (independent of n). In this case,D receives lower average SNR due to transmission from Rand systemperformance suffers. As the location of Rmovestowards D, average received SNR at D becomes higher if Rsupports the transmission. However, system performanceagain suffers beyond a certain distance as R now receivespoor average SNR and fails to decode the message, hencediversity order of the system reduces. Placement of R nearthe mid-point of the S–D link gives superior performance.Installation of more receiving antennas on R improves therelay participation, hence system performance improves.In this case, R can be placed at a much larger distance fromS to improve system performance.

5. Conclusion

In this paper, outage probability and average errorrate of a cooperative relay network employing a multipleantenna relay in Rayleigh fading environment, has beeninvestigated. Analytical expressions of outage probabilityand average error rate have been found. The analysisincludes the case where the source retransmits the samemessage in the time slot meant for the relay transmissionif the relay fails to decode the message sent by thesource in its time-slot. Monte Carlo simulation (runningthe simulator freely with 105 samples) has been carriedout and the analytical results are found to match thesimulation results. Results shows that placement of relayafter themid-point of S–D link gives superior performance.Outage and error performance improves if a higher numberof receiving antennas are placed on the relay and itsplacement is shifted more towards destination as thenumber of antennas are increased.

Acknowledgments

This work is partially supported by Institution ofElectronics and Telecommunications Engineers (IETE),

NewDelhi (India), under the grant IETE/J-282-8/BOR/2009.This work is also supported by Department of Electronicsand Communication Engg., BBDNITM, Lucknow, UttarPradesh, India. Their support is gratefully acknowledged.

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Himanshu Katiyar received his B.E. degreein Electronics and Communication Engineer-ing from M.J.P. Rohilkhand University, Bareilly,Uttar Pradesh, India in 2001, M.Tech degreefrom Madan Mohan Malviya Engineering Col-lege, Gorakhpur, Uttar Pradesh, India in 2004and Ph.D. degree in the area of wireless com-munication at the Indian Institute of Technol-ogy (IIT), Guwahati, Assam India in 2011. From2004–2005 he was lecturer of Electronics andCommunication Engineering Dept. at SRMSCET,

Bareilly, Uttar Pradesh, India and from 2005–2006 he was lecturer of

Electronics and Communication Engineering Dept. at NIEC, Lucknow, Ut-tar Pradesh, India. At present he is Associate Professor of the Electron-ics and Communication Engineering Dept. at BBDNITM, Lucknow, UttarPradesh, India. Hewas awarded from IETE research fellowship and hewasproject investigator (from September, 2009 to December, 2010) of an IETEsponsored research project. He has published over seventeen researchpapers in journals, international and national conferences. His researchinterests include almost all aspects of wireless communications with aspecial emphasis on MIMO systems, channel modeling, infrastructure-based multihop and relay networks and cooperative diversity schemes.

R. Bhattacharjee received his B.E. in Electron-ics and Telecommunication Engineering (FirstClass Honors) from Gauhati University (REC (atpresent NIT) Silchar), M. Tech. (E and ECE De-partment, Microwave Engineering specializa-tion) from IIT Kharagpur and Ph.D. (Engineering)from Jadavpur University Kolkata. Presently heis an Associate Professor in the Department ofElectronics and Electrical Engineering, IIT Guwa-hati. Prior to joining IIT Guwahati, he was a fac-ulty member in REC (NIT) Silchar. His research

interest includesWireless communication,Wireless networks,Microstripantennas, Microwave Engineering and Electromagnetics. He has pub-lished over ninety research papers in journals, international and nationalconferences. He has developed theweb course on Electromagnetic Theoryunder the NPTEL project of MHRD. At present he is developing the webcourse on Advanced Mobile Communication under phase II of the sameproject. He is involved with the ongoingmission project on Virtual labs atvarious capacities He has also been involved in several research projects.He has been a Co-investigator for the contracted research fromNICT Japanin the area of Next Generation Wireless Networks and is a member ofthe research team of the Tiny6 project dealing with IPv6 and Sensor Net-works. Presently he is also involved in an antenna system developmentproject from ISRO. In NIT Silchar, hewas a coordinator for the setting up ofthe Campus-wideOptical Fiber based network under the Centre for Excel-lence scheme. He was also associated in a number of sponsored projectsin the field of development of antenna system. He is amember of IEEE anda life member of the Indian Society of Technical Education.