Xiao andNi EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 DOI 10.1186/s13638-014-0236-7

RESEARCH Open Access

Performance analysis of two-user cooperativeARQ protocol over Rayleigh fading channelHailin Xiao1* and Ju Ni2

Abstract

In this paper, we present a two-user cooperative automatic repeat request (C-ARQ) protocol which combinescooperative diversity at the physical layer and ARQ at the link layer. In this scheme, distributed Alamouti space-timeblock coding (DASTBC) is applied to achieve cooperative diversity, and ARQ is used to improve the data link layerreliability. To analyze the performance of the proposed protocol, we derive the average frame error rate (FER) andthroughput with multiple phase shift keying (MPSK) over a Rayleigh fading channel. Numerical simulation resultsshow that the performance gain of average FER with ARQ retransmission is about 2 dB more than the case withoutARQ retransmission in the same conditions. Moreover, the combined DASTBC and quadrature phase shift keying (QPSK)with ARQ retransmission will lead to an approximate 3 Mbits/s increase in transmission rate.

Keywords: Cooperative communication; Multiple phase shift keying; ARQ; Space-time block coding

1 IntroductionMultiple antennas are often used to combat channelfading in wireless communication system [1]. However,implementing multiple antennas at a mobile station isimpractical for most wireless applications due to thelimited size of the mobile unit [2,3]. Relay-assistedcommunication is suitable to solve the problem andplays a main role in the future generation cellular sys-tems and ad hoc networks [4]. One form of relay-assisted communication is cooperative diversity [5,6].Its principle is to exploit the broadcast nature of wire-less transmission and creates a virtual antenna arraythrough cooperating users. Each transmitting node hasits own message and is responsible for transmitting theinformation of its partner(s). Therefore, a virtual an-tenna array is obtained through the use of the relay'santennas without complicated signal design or addingmore antennas into the nodes. In [7], a cooperativediversity scheme between users has been used not onlyto obtain higher throughput but also to decrease time-varying channel sensitivity. In [8], multiple-source coopera-tive message has been sent to a common destination,and it is shown to offer full spatial diversity with better

* Correspondence: xhl_xiaohailin@163.com1School of Information and Communication, Guilin University of ElectronicTechnology, Guilin 541004, Guangxi, ChinaFull list of author information is available at the end of the article

© 2015 Xiao and Ni; licensee Springer. This is aAttribution License (http://creativecommons.orin any medium, provided the original work is p

bandwidth efficiency. In [9], differential relay strategiesover downlink channel in a two-user cooperative com-munication system have been proposed, which are ableto achieve performance gain in association with theproposed criterion. Recently, various techniques suchas distributed space-time coding [10,11] and modula-tion [12] have been developed to realize cooperativediversity. For achieving a diversity gain, the Alamoutispace-time block code (STBC) has been used incooperative system in a distributed manner [13]. Thesecooperative diversity schemes have been shown to be ableto achieve significant performance gains over the amplify-and-forward and decode-and-forward protocols [14].Automatic repeat request (ARQ) protocol is com-

monly used in the communication system to improvethe reliability, which requests retransmissions for thosepackets received in error [15]. Recently, the ARQ proto-col has been applied in cooperative diversity system toachieve higher link reliability; it is called cooperativeARQ [16]. Cooperative ARQ (C-ARQ) protocol permitsnodes other than the source and the destination to activelyhelp deliver the correct data [3,17,18]. In [3], the authorshave analyzed the diversity multiplexing trade-off (DMT)for ARQ-based opportunistic cooperative communicationover Nakagami fading channels. In [17], the authors havedesigned the ARQ protocol for two-user cooperative di-versity systems in wireless networks. In [18], a cross-layer

n Open Access article distributed under the terms of the Creative Commonsg/licenses/by/4.0), which permits unrestricted use, distribution, and reproductionroperly credited.

Figure 1 Two-user cooperative diversity system.

Xiao and Ni EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 Page 2 of 6

C-ARQ has been studied, and the performance of spectralefficiency over Nakagami fading channel has been evalu-ated. In [19], a coordinated hybrid automatic repeatrequest (HARQ) approach has been proposed, which canimprove the network outage probability and the users'fairness. Despite that these studies are not relevant tothe average frame error rate (FER) and throughput ofcooperative ARQ, they can serve as references [20].In this paper, we present a two-user C-ARQ protocol

which combines cooperative diversity at the physical layerand ARQ at the link layer. To analyze the performance ofthe protocol, we derive the average FER and throughput

Figure 2 Two-user cooperative ARQ protocol based on [15].

with multiple phase shift keying (MPSK) over a Rayleighfading channel. Numerical simulation results show thatthe performance gain of average FER with ARQ retransmis-sion is about 2 dB more than the case without ARQ retrans-mission in the same conditions. Moreover, the combineddistributed Alamouti space-time block coding (DASTBC)and quadrature phase shift keying (QPSK) with ARQretransmission will lead to an approximately 3 Mbits/sincrease in transmission rate.

2 System modelWe consider a cellular system in which two cooperativeusers transmit their information to the same destination(D) as depicted in Figure 1 [17]. Both users and destinationare equipped with a single antenna. The system adoptstime division multiple access (TDMA) scheme, and boththe half-duplex users share the same frequency band. Thus,to ensure half-duplex operation, we further divide eachchannel into orthogonal subchannels. Under the aboveorthogonality constraints, we can now conveniently, andwithout loss of generality, characterize our channel modelsusing a time-division notation; frequency division counter-parts to this model are straightforward due to the sym-metry of the channel allocations. Specifically, using systemcommunication, we can provide the powerful benefits ofdiversity without the need for physical arrays, although at aloss of spectral efficiency due to half-duplex operation andpossibly at the cost of additional received hardware.In this paper, we extend a two-user cooperative diver-

sity system by exploiting the proposed ARQ protocols asfollows. A whole cooperative frame is divided into threesub-frames. The first sub-frame is allocated for user 1(U1) to transmit its data packet. The second sub-frameis assigned to user 2 (U2) to transmit its data packet.The third sub-frame is shared between both users and isused to relay each other's message to the destination.The cyclic redundancy checksum (CRC) is used to facili-tate error detection. If one user receives a correct sub-frame of its partner, it will relay the received informationin cooperative sub-frame. Otherwise, the relaying user willdo nothing in the third sub-frame. To utilize DASTBC toachieve diversity, U1 relays the packet of U2 with a nega-tive conjugate form. Similarly, U2 transmits a conjugatepacket of U1. Then, the destination uses maximum ratiocombine (MRC) to receive data packets.The inter-user channels and the user-destination chan-

nels are independent of each other. All channels are as-sumed to experience block Rayleigh fading, i.e., they arefixed during a frame and change independently in thenext frame, where each frame contains a fixed Nf num-ber of bits. Each frame at the physical layer may containmultiple packets from the data link layer. Details of thepacket and frame can be found in [21]. If each packetincludes Np symbols, after M-ary digital modulation of

Xiao and Ni EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 Page 3 of 6

rate Rn bits/symbol, each packet is mapped to a bit blockcontaining Np × Rn bits. As in HIPER-LAN/2 and IEEE802.11a standards [22], each sub-frame is given by:

N f ¼ N c þ Nb Np � Rn ð1Þwhere Nc is the pilot and control parts and Nb is thenumber of packets per frame which depends on thechosen modulation and coding pair [23,24].

3 Two-user cooperative ARQ protocolFor a better description of the two-user cooperativeARQ protocol, we focus on a whole cooperative frame.The destination feeds back CRC checking results of re-ceived packets, where an acknowledgement (ACK) or anegative acknowledgement (NACK) message is informedto both users in the ARQ process. It is assumed that thefeedback channel is error free and has no latency, anderror detection based on CRC is perfect. We considerthat the destination has only one ARQ opportunity in awhole cooperative frame. The protocol works as followsand is shown in Figure 2:

1) If the receiver decodes the messages of U1 and U2correctly. The destination simultaneously transmitsan ACK message to U1 and U2. The system willstart the next cooperative frame.

2) If the receiver does only decode the messages of U1correctly. The destination drops the erroneous packetsand feeds back two messages in half time slots offeedback duration, an NACK for U2 and ACK for U1.Then, retransmission will be performed by U2 in thenext cooperative frame, while U1 will transmit its nextpacket in that frame. And vice versa, if the receiverdoes only decode the messages of U2 correctly, areciprocity ARQ process is also executed.

3) If the receiver does not decode the messages of U1 andU2 correctly. The destination dumps both erroneouspackets and feeds back a NACK message to informboth users to retransmit their incorrect packets in thenext frame.

4 Performance analysisIn this section, to analyze the performance of the protocol,we derive the average FER and throughput with MPSKover the Rayleigh fading channel.

4.1 Average frame error rateThe frame error is determined by the signal-to-noise ra-tio (SNR). For the flat Rayleigh fading channel, the prob-ability density function (PDF) of instantaneous SNR γ isgiven by:

f γ γð Þ ¼ 1�γe−

γ�γ ð2Þ

where �γ represents the average SNR. For MRC diversityreception with two independent Rayleigh fading signals,the PDF of the output SNR is given by [25]:

f γ γð Þ ¼ 1�γ 1−�γ 2

½ exp ð− γ

�γ 1Þ− exp ð− γ

�γ 2Þ� ð3Þ

where �γ 1 and �γ 2 �γ 1≠�γ 2ð Þ are the average SNR ofthe two independent diversity branches, respectively. If�γ 1 ¼ �γ 2, the PDF of the output of SNR is given by:

f γn γð Þ ¼ 1�γ n

exp −γn�γ n

� �; n ¼ 1; 2 ð4Þ

where the output SNR can be obtained by the selectioncombing diversity reception [25].

The average FER (FERM—

) with M-ary digital modula-tion can be expressed as:

FERM—

¼Z ∞

0PeðbjγÞM f γ γð Þdγ ð5Þ

where Pe(b|γ)M is the bit error ratio (BER) in nonfading

channel and fγ(γ) is the PDF of the output SNR. ForMPSK modulation, the BER is given by [26]:

PeðbjγÞM ¼ Q

ffiffiffiffiffi2γ

pð Þ M ¼ 2≈2Q

ffiffiffiffiffi2γ

psin π=Mð Þð Þ M > 2

�ð6Þ

where Q(⋅) is Q function and can be written as [22]:

Q xð Þ ¼ 1π

Z π=2

xexp −x2=2 sin2θ

� �dθ ð7Þ

With (2), (5), and (6), the average FER with MPSKmodulation can be calculated as:

FER2n

—¼

Z ∞

0PeðbjγÞM 1

�γe−

γ�γdγ

¼ 1π

Z π2

0

Z ∞

0exp½−ð 1

sin2θþ 1

�γnÞdγdθ�

¼ �γn

2ð1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi�γn

�γn þ 1

sÞ M ¼ 2ð Þ

ð8Þ

FERMn

—

¼Z ∞

0PeðbjγÞM 1

�γ ne−

γ�γndγ

¼ �γ nð1−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

sin2 π=Mð Þ�γn

sin2 π=Mð Þ�γ n þ 1

sÞ M > 2ð Þ

ð9Þ

where �γn is the average SNR of the two independentdiversity branches, respectively. Substituting (3) and (6)into (5), the average FER with MRC and MPSK modula-tion are given by:

Þ

Figure 3 Average FER without ARQ retransmission under �γ1¼2�γ2 (1) and �γ1 ¼ 3�γ2 (2).

Xiao and Ni EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 Page 4 of 6

FER2MRC

—¼ 1

π �γ 1−�γ 2ð ÞZ

0

�2π

ð �γ 1 sin2θ

�γ 1 þ sin2θ−

�γ 2 sin2θ

�γ 2 þ sin2θÞdθ

¼ 12 �γ 1−�γ 2ð Þ ½�γ 1ð1−

ffiffiffiffiffiffiffiffiffiffiffiffiffi�γ 1

�γ 1 þ 1

sÞ−�γ 2ð1−

ffiffiffiffiffiffiffiffiffiffiffiffiffi�γ 2

�γ 2 þ 1

sÞ� M ¼ 2ð

ð10Þ

FERMMRC

—

¼ 1�γ 1−�γ 2ð Þ ½�γ 1ð1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisin2 π=Mð Þ�γ 1

sin2 π=Mð Þ�γ 1 þ 1

sÞ

−�γ 2ð1−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

sin2 π=Mð Þ�γ 2

sin2 π=Mð Þ�γ 2 þ 1

sÞ� M > 2ð Þ

ð11ÞFor each whole cooperative frame, we analyze its

average FER with ARQ and without ARQ. If there is noARQ retransmission, two users will not retransmit theirrespective data packet. The average FER at the destin-ation can be derived as follows:

FERM—

¼ FERM1

—

þ FERM2

—

þ 1−FERM1

—�

� 1−FERM2

—� FERM

MRC

—

ð12Þ

According to three cases of the proposed C-ARQprotocol, the average FER at the destination are respect-ively given by the following:

Case 1: U1 and U2 transmit correct packets.

FERM—

¼ FERM1

—

þ FERM2

—

þ ð1−FERM1

—

Þ2� ð1−�����FERM

2 Þ2 FERMMRC

—ð13Þ

Case 2 (U1): U1 transmits erroneous packets.

FERM—

¼ FERM1

—

þ FERM2

—

þ ð1−FERM1

—

Þ2� ½1−ðFERM

2

—

Þ2� FERMMRC

—

ð14Þ

Case 2 (U2): U2 transmits erroneous packets.

FERM—

¼ FERM1

—

þ FERM2

—

þ ½1−ðFERM1

—

Þ2�� ð1−FERM

2

—

Þ2 FERMMRC

—

ð15Þ

Case 3: U1 and U2 transmit erroneous packets.

FERM—

¼ FERM1

—

þ FERM2

—

þ ½1−ðFERM1

—

Þ2�� ½1−ðFERM

2

—

Þ2� FERMMRC

—

ð16Þ

4.2 Throughput analysisThroughput is defined as the ratio between the numberof information bits correctly transmitted by a user andthe time that the channel is allocated to that user in amulti-user system [18,27]. Hence, the throughput can becalculated as follows:

Throughput Mð Þ ¼ Pf

tN f ð17Þ

where Pf is the average FER at the destination. Eachframe lasts t seconds.

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

SNR(dB)

Thr

ough

put(

Mbi

ts/s

)

Case 3Case 2(U2)

Case 2(U1)

Case 1

Simulation

QPSK

BPSK

Figure 5 Throughput with ARQ retransmission under �γ1 ¼ 2�γ2.

Figure 4 Average FER with ARQ retransmission under �γ1 ¼ 2�γ2.

Xiao and Ni EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 Page 5 of 6

5 Numerical simulation resultsIn this section, numerical simulation results are providedto present the average FER performance analysis of thetwo-user C-ARQ protocol. We set the number ofpackets Nb = 1,000. Each packet is set to be 1,000 sym-bols (Np = 1,000), and the pilot and control parts are setto be 4 symbols (Nc = 4). Each channel realization is gen-erated as random matrix whose elements are assumed tobe circularly symmetric complex Gaussian with zeromean and unity variance. Ten thousand channel matricesare generated with Monte Carlo simulations. For each sce-nario, 1,000,000 simulation runs are used to obtain eachsimulated point. The transmitters have normalized band-width W = 1 M (it is straightforward to extend the resultsto the cases with different bandwidths).Figure 3 illustrates the average FER without ARQ re-

transmission under �γ 1 ¼ 2�γ 2 and �γ 1 ¼ 3�γ 2. We considerthese cases by fixing one of the users' channels to thedestination at a relatively high SNR, i.e., �γ 1 ¼ 20 dB. Wevary the quality of U2's channel to destination. We ob-serve that numerical simulation results are consistentwith analytical solutions. It can be seen that the averageFER performance degrades as the asymmetric averageSNR between the two diversity branches increases. More-over, with the increase of the modulation order M, theaverage FER performance gets worse.Figure 4 illustrates the average FER with ARQ retrans-

mission under �γ 1 ¼ 2�γ 2. The figure shows that numericalsimulation results are consistent with analytical solutionsin all cases. As expected, case 3 has a bad average FER per-formance in the same condition. Comparing Figure 4 with

Figure 3, the performance of average FER with ARQretransmission is much better than the case without ARQretransmission, and it is shown that the performance gainis about 2 dB at an average FER of 10−4.Figure 5 shows the throughput with ARQ retransmission

under �γ1 ¼ 2 �γ2 . It can be seen that the throughput ofBPSK modulation is worse than QPSK modulation atthe high SNR. The cooperative transmission with BPSKand ARQ retransmission performs best when the SNRis low, because BPSK is more robust to channel fading.Moreover, we observe that ARQ retransmission can achievesufficient throughput gain. The combined DASTBC and

Xiao and Ni EURASIP Journal on Wireless Communications and Networking (2015) 2015:11 Page 6 of 6

QPSK with ARQ retransmission will lead to an approxi-mately 3 Mbits/s increase in transmission rate.

6 ConclusionsIn this paper, we have presented a two-user C-ARQ proto-col. To analyze the performance of the protocol, we havederived the average FER and throughput over a Rayleighfading channel. Numerical simulation results are pre-sented to validate the proposed theoretical analysis. Al-though we limit two users for simplicity, the proposedscheme can be extended to include more than two users,and the proposed protocol can provide useful basic toolsfor designing more complicated ARQ protocols. Moreimportantly, our results in this paper offer important ana-lytical method in cooperative communication system.

Competing interestsThe authors declare that they have no competing interests.

AcknowledgementsThe work of H. Xiao and J. Ni is supported by the National Natural ScienceFoundation of China (Grant No.: 61472094; 61261018; 61362007), GuangxiNatural Science Foundation (Grants No.: 2014GXNSFGA118007 and2013GXNSFFA019004).

Author details1School of Information and Communication, Guilin University of ElectronicTechnology, Guilin 541004, Guangxi, China. 2Library of Guilin University ofElectronic Technology, Guilin 541004, Guangxi, China.

Received: 19 August 2014 Accepted: 24 December 2014

References1. EV Belmega, S Lasaulce, Energy-efficient precoding for multiple-antenna

terminals. IEEE Trans. Signal Process. 59(1), 329–340 (2011)2. H Xiao, S Ouyang, ZP Nie, Design and performance analysis of compact

planar inverted-L diversity antenna for handheld terminals. Wireless Pers.Commun. 52(4), 709–717 (2010)

3. JS Harsini, M Zorzi, Effective capacity for multi-rate relay channels with delayconstraint exploiting adaptive cooperative diversity. IEEE Trans. Wireless C.11(9), 3136–3147 (2012)

4. NH Tran, LJ Rodriguez, T Le-Ngocand, HR Bahrami, Precoding and symbolgrouping for NAF relaying in BICM systems. IEEE Trans. Vehicular. Technol.62(6), 2607–2617 (2013)

5. SS Ikki, MH Ahmed, Performance analysis of cooperative diversity withincremental best relay technique over Rayleigh fading channels. IEEE Trans.Commun. 59(8), 2152–2161 (2011)

6. T Liu, L Song, Y Li, Q Huo, B Jiao, Performance analysis of hybrid relay selectionin cooperative wireless systems. IEEE Trans. Commun. 61(3), 779–788 (2013)

7. C-H Choi, U-K Kwon, Y-J Kim, G-H Im, Spectral efficient cooperativediversity technique with multi-layered modulation. IEEE Trans. Commun.58(12), 3480–3490 (2010)

8. H Ding, J Ge, DB da Costa, Z Jiang, A new efficient low complexity schemefor multi-source multi-relay cooperative networks. IEEE Trans. Vehicular.Technol. 60(2), 716–722 (2011)

9. MR Bhatnagar, A Hjørungnes, Differential relay strategies over downlinkchannel in two-user cooperative communication system. Wireless Pers.Commun. 53(1), 1–14 (2010)

10. J Wu, H Hu, M Uysal, High-rate distributed space-time-frequency coding forwireless cooperative networks. IEEE Trans. Wireless Commun. 10(2), 614–625(2011)

11. A Nasri, R Schober, M Uysal, Performance and optimization of network-codedcooperative diversity systems. IEEE Trans. Commun. 61(3), 1111–1122 (2013)

12. MR Bhatnagar, Decode-and-forward-based differential modulation forcooperative communication system with unitary and nonunitaryconstellations. IEEE Trans. Vehicular Technol. 61(1), 152–165 (2012)

13. A Bansal, MR Bhatnagar, A Hjørungnes, Decoding and performance boundof demodulate-and-forward based distributed Alamouti STBC. IEEE Trans.Wireless Commun. 12(2), 702–713 (2013)

14. YF Chen, R Shi, M Long, Performance analysis of amplify-and-forward relayingwith correlated links. IEEE Trans. Vehicular Technol. 62(5), 2344–2349 (2013)

15. I Stanojev, O Simeone, U Spagnolini, Y Bar-Ness, RL Pickholtz, Cooperative ARQ viaauction-based spectrum leasing. IEEE Trans. Commun. 58(6), 1843–1856 (2010)

16. M Mardani, JS Harsini, F Lahouti, B Eliasi, Link-adaptive and QoS-provisioningcooperative ARQ—applications to relay-assisted land mobile satellitecommunications. IEEE Trans. Vehicular Technol. 60(7), 3192–3206 (2011)

17. C Zhang, W Wang, G Wei, Design of ARQ protocols for two-user cooperativediversity systems in wireless networks. Comput. Commun. 32(6), 1111–1117(2009)

18. N Marchenko, C Bettstetter, Cooperative ARQ with relay selection: ananalytical framework using semi-Markov processes. IEEE Trans. VehicularTechnol. 63(1), 178–190 (2014)

19. B Makki, T Svensson, T Eriksson, M Alouini, Coordinated hybrid automaticrepeat request. IEEE Commun. Lett. 18(11), 1975–1978 (2014)

20. M Behrooz, T Eriksson, T Svensson, On an HARQ-based coordinated multi-pointnetwork using dynamic point selection. EURASIP J. Wireless Commun. Netw.2013(209), 1–11 (2013)

21. Q Liu, S Zhou, GB Giannakis, Cross-layer combining of adaptive modulationand coding with truncated ARQ over wireless links. IEEE Trans. WirelessCommun. 3(5), 1746–1754 (2004)

22. A Doufexi, S Armour, M Butler, A Nix, D Bull, J McGeehan, P Karlsson, Acomparison of the HIPERLAN/2 and IEEE 802.11a wireless LAN standards.IEEE Commun. Mag. 40(5), 172–180 (2002)

23. J Wang, OY Wen, S Li, Near optimum pilot and data symbols powerallocation for MIMO spatial multiplexing system with zero-forcing receiver.IEEE Signal. Process. Lett. 16(5), 358–361 (2009)

24. X Rui, J Hou, L Zhou, Decode-and-forward with full-duplex relaying. Int. J.Commun. Syst. 25(5), 270–275 (2012)

25. L Fang, G Bi, AC Kot, New method of performance analysis for diversityreception with correlated Rayleigh-fading signals. IEEE Trans. Vehicular.Technol. 49(5), 1807–1812 (2000)

26. JG Proakis, Digital Communications, 4th edn. (McGraw-Hill, New York, 2001)27. H Zheng, A Lozano, M Haleem, Multiple ARQ process for MIMO systems.

EURASIP J. Appl. Signal. Process. 2004(5), 772–782 (2004)

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