We investigate and propose a new amplify-and-
forward cooperative relay networks scheme in
which a full-rate and full-diversity extended-
orthogonal space-time block coding (EOSTBC)
scheme is used. Utilizing a feedback channel,
a simple phase rotation is applied at the relay
nodes to extract full diversity and array gain. A
feedback quantization approach which reduces
the overhead in the feedback channel for prac-
tical systems is also proposed. The performance
of the proposed scheme, with and without opti-
mum power allocation strategy, is investigated.
Average bit error rate simulations confirm the
utility of the scheme. The results also confirm
the improvement in bit error rate (BER) perfor-
mance over quasi-orthogonal space time block
codes (QOSTBC)

Jonathon Chambers (1251609)

Nasr E.M. Eltayeb (7203647)

Shakiru K. Kassim (7200722)

English

Loughborough University Institutional Repository

   This item was submitted to Loughborough’s Institutional Repository (https://dspace.lboro.ac.uk/) by the author and is made available under the following Creative Commons Licence conditions.      For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/  International Symposium on Information Theory and its Applications, ISITA2008Auckland, New Zealand, 7-10, December, 2008A Two-Hop Amplify-and-Forward Scheme for ExtendedOrthogonal Space Time Coding in Cooperative NetworksNasr ELTAYEB, Shakiru KASSIM and Jonathon CHAMBERSFaculty of EngineeringDept. of Electronic and Electrical EngineeringLoughborough University, LE11 3TU, United KingdomE-mail: {n.e.eltayeb, s.k.kassim, j.a.chambers}@lboro.ac.ukAbstractWe investigate and propose a new amplify-and-forward cooperative relay networks scheme inwhich a full-rate and full-diversity extended-orthogonal space-time block coding (EOSTBC)scheme is used. Utilizing a feedback channel,a simple phase rotation is applied at the relaynodes to extract full diversity and array gain. Afeedback quantization approach which reducesthe overhead in the feedback channel for prac-tical systems is also proposed. The performanceof the proposed scheme, with and without opti-mum power allocation strategy, is investigated.Average bit error rate simulations confirm theutility of the scheme. The results also confirmthe improvement in bit error rate (BER) perfor-mance over quasi-orthogonal space time blockcodes (QOSTBC).1. INTRODUCTIONCooperative communication has recently gained a lotof interest due to its ability to realize the performancegains of multiple-input multiple-output (MIMO) wire-less systems, with distributed single antenna termi-nals forming virtual antenna arrays. More importantly,with the increasing interests in ad hoc networks, re-searchers have been looking for methods to exploit spa-tial diversity using the available “free” mobile termi-nals working as relays (because the fading paths fromtwo mobiles are statistically independent, this gener-ates spatial diversity), as well as splitting the availabletime slot into two phases [1][4]. The source node trans-mits during the first phase, while relays transmit dur-ing the second phase, sending a version of the receivedsignal to the intended destination, thereby increase di-versity order against fading and interference. Becauseoriginal signals need two hops before arriving at des-tination in these system models, we can name themdual-hop cooperative systems.In this paper, we consider a relay network with two-step protocol and apply EO space-time code [7] amongthe relays. The problem we are interested in is: “Canwe increase the reliability of a wireless network by usingEO space-time codes among the relays?” More specif-ically, the focus of this paper is on end-to-end BERanalysis of wireless relay networks. We investigate inthe diversity gain and array gain that can be achievedin wireless relay network by having parallel relays co-operate distributively. Here, by diversity gain we meanthe negative of the exponent of the SNR or transmitpower in the BER formula at hight SNR wich is consis-tent with the diversity gain definition in MIMO systemsOn the assumption that relays are in full co-operation and adequately spaced to avoid interference,we demonstrated that with and without signal powercontrol between the relaying stages, the proposedclosed-loop EOSTBC (CL-EOSTBC) scheme outper-forms closed-loop QOSTBC (CL-QOSTBC) scheme.The organization of this paper is as follows. Thesystem model is described in Section 2. In Section 3 weprovide the power allocation strategy for the two-stagerelay network. The results are verified by simulationsin Section 4 using both QOSTBC and EOSTBC basedon phase rotation feedback methods. In Section 5 wegive the conclusions.2. SYSTEM MODELIn our model Fig.1, we consider a simple two-stagerelay network, with a single source and destinationcommunicating via cooperating relay nodes in paral-lel. All participating nodes communicate using a sin-gle antenna configuration over a quasi-static flat fadingAuthorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on September 30, 2009 at 11:56 from IEEE Xplore.  Restrictions apply. r1r2r3r4Relays: rjSource: s Destination: dRxTxhs,1hs,2hs,3hs,4hd,1hd,2hd,3hd,4Figure 1: A simple two-hop cooperative relay networkarchitecture:Amplify-and-Forward scheme.channels hi,j , where i ∈ {s, d} represents the channelfrom the source or destination to a particular relay nodej ∈ {1, 2, · · · , N} up to the maximum number of partic-ipating relays N. In the context of this work all randomchannel parameters hi,j are assumed to be zero meancircular complex Gaussian (ZMCSCG) random vari-able with unity variance (i.e Rayleigh fading). In thisscheme we use a simple two-step protocol over two timeframes, i.e time division multiple access (TDMA). Inthe first time frame the source node broadcasts√Psskto the relay nodes over a number of symbol intervals de-pending on the size of the STBC coding matrix; wherePs is the source transmit power and s ∈ Z is the trans-mitted symbol. Assuming perfect cooperation amongrelay nodes, i.e. perfect synchronization the distributedchannel vector hsr can take the form,hs,i = [hs,1hs,2 · · ·hs,N ]T (1)At the relay nodes, the received signals at the ithrelay is denoted as yi, which is corrupted by both thefading hs,i and the noise ns,i.yi =√Pshs,is+ ns,i (2)In the next time-frame each relay node syn-chronously re-transmits a scaled version of the receivedsignals in the first time-frame with the same power con-straint as in the first hop, according to a pre-allocatedcolumn of a STBC matrix, whereas the source remainssilent. In this implementation the EOSTBC scheme [6]with four participating relays is used,G = γi[y1 y1 y2 y2−y∗2 −y∗2 y∗1 y∗1](3)where γi, denote the average transmission power at ev-ery relay nodes and (.)∗ denotes complex conjugate op-eration. However in [2], Akhter et al. note that fullorder diversity cannot be accomplished due to inter-ference factor between estimated symbols, illustratedby the βˆ terms below, which after combining at thedestination receiver results in a matrix of the followingform,HHrdHrd =[αˆ+ βˆ 00 αˆ+ βˆ](4)For a more detailed analysis the interested reader is re-ferred to [2] and [3]. However, Eltayeb et al. [7] showedthat a simple phase rotation θ and φ on the complexsymbols transmitted from nodes 1 and 3 ensure thatnot only the βˆ term is positive but also maximizedduring the transmission period, which will provide 4thorder diversity and array gain, at the expense of requir-ing a feedback channel.Following similar approach, a coding matrix wasdesigned for the QOSTBC [8] as:Q = γiy1 y2 y3 y4−y∗2 y∗1 −y∗4 y∗3−y∗3 −y∗4 y∗1 y∗2y4 −y3 −y2 y1 (5)where γi is the transmit power in each relay. Bothschemes explore a phase feedback from the destinationnode to the relays in order to exploit the full diversity,hence CL-EOSTBC and CL-QOSTBC.The received signal rd at the destination can bedescribed asrd =N=4∑i=1hd,iyi + nd,i (6)where hd,i is the channel gain between the relay ri anddestination d, yi is the encoded received signal plusnoise at relay ri of si and nd,i is the complex Gaussiannoise with mean zero and varianceN0/2 per-dimension.3. Resource-Allocation StrategyIn this section, we discuss the optimum power al-located among the source and the relays to maximizethe received SNR at the destination.Under the assumption of full data exchange, each ofthe K relaying stages experiences independent BERs,which are denoted here as Pb,v∈(1,K)(e), caused by in-dependent SERs Ps,v∈(1,K)(e). A bit from the sourceterminal is received correctly at the target only whenat all stages, the bit has been transmitted correctly.The end-to-end BER can therefore be expressed as,Pb,e2e(e) = 1−K∏v=1(1− Pb,v(e)) (7)Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on September 30, 2009 at 11:56 from IEEE Xplore.  Restrictions apply. which at low BER or sufficiently high SNRs at everystage, can be written as,Pb,e2e(e) =K∑v=1Pb,v(e)=K∑v=1Ps,v(e)log2(Mv)(8)where Mv is the modulation order at the vth stage.To maximize the capacity and hence to minimizethe end-to-end BER we allocate optimal power to eachstage, the total transmission power available in the sys-tem satisfy the following power constraint,β1 +n=4∑i=1βi = P (9)where α1P and αiP , i = 1, · · · , 4 are the power allo-cated to the source and the ith relay, respectively, andtheir sum should not exceed the overall network powerconstraint P as shown in (9).If the source transmits B bits per frame, where theframe is defined as D = B/log2(M), to the target overk relaying stages, the normalized end-to-end through-put Θ (Bits/Hz) can be expressed as,Θ = minv∈(1,K){αvRvlog2(Mv)}.(1− Pb,e2e(e))B (10)where Rv is the STBC rate of the vth stage, Mv is themodulating index, αv is the optimized frame durationof the vth stage under the constraint that Σkv=1αv = 1,Pb,e2e(e) is the end-to-end BER and min{.} signifiesthe dependence of the throughput on the weakest linkin the chain.The end-to-end throughput is maximized by minimiz-ing the end-to-end BER through optimally assigningfractional power allocated to each relaying stage withour assumption that the fractional frame duration isoptimized.The elegant analysis presented in [4] simplifies BERby invoking its upper bound which occurs when (8) isupper bounded by its largest argument θ = pi/2.P (e) =1pi∫ piM−1M0φρ(GPSKsin2θ)dθ (11)where M is the constellation size and GPSK ≡sin2(pi/M) and thus the presented BER of the vth re-laying stage for M -PSK 1 can be upper bounded as,1The result can be applied to other binary and M-ary signalsin a straightforward way (see e.g. [4]).Pb,e2e(e) ≤K∑v=1Mv − 1Mvlog2(Mv)(1 + βvGPSKRvγvtvSN)−q(12)Pb,e2e(e) ≤K∑v=1Av(1 +Bvβv)−q(13)This upper bound was then utilized to determinethe effective fractional allocated power βv∈(1,K) thatobeysβv =[αw( q−1v A−1v Bqvvq−1w A−1w Bqww) 1qmax+1]−1(14)where qmax = argmax(q1, · · · , qk) and w is the previousrelaying stage.The constant Av and Bv are obtained by comparing(13) with (12) to arrive atAv =Mv − 1Mvlog2(Mv)(15)Bv =GPSKvRvγvtvSN(16)where the fractional frame durations αw need to bechosen such as to maximize (10) under the constraint∑Kv=1 αv = 1. This is clearly achieved byαw =∏Kw=1,w 6=vRw.log2(Mw)∑Kk=1∏Kw=1,w 6=kRw.log2(Mw)(17)The performance of the algorithm is assessed bymeans of simulation for M-PSK schemes only. We ex-plicitly show the end-to-end BER versus the SNR forvarious 2-stage communication scenario deploying thedemonstrated fractional power allocation strategy in(14), which is also compared against a non-optimumpower allocation scheme.4. SIMULATION RESULTSIn this section we provide simulation results for ourproposed scheme. We consider a QPSK modulation inour simulations. For all our simulation results we as-sume perfect CSI and equal signal-to-noise ratio (SNR)at all receiving terminal, i.e. a terminal knows perfectlythe channel state information of the link preceding it.We assume that the channel is quasi-static flat fadingtime-invariant during the transmission of one symbolperiod. We also assume that the channel is quasi-staticflat fading time-invariant during the transmission ofone symbol period.Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on September 30, 2009 at 11:56 from IEEE Xplore.  Restrictions apply. 0 5 10 15 2010−410−310−210−1100SNR,[dB]End−to−End BERNon optimum QOSTBCOptimum QOSTBCNon optimum EOSTBCOptimum EOSTBCFigure 2: Comparison between optimum andnon-optimised end-to-end BER for variousconfigurations of a two-stage relaying net-works over frequency-flat fading channels.2 4 6 8 10 12 14 16 1810−410−310−210−1100SNR,[dB]End−to−End BEROptimized EOSTBC (Perfect feedback)Optimized EOSTBC (quantized feedbackI)Non optimized EOSTBC (Perfect CSI)Figure 3: Optimum end-to-end BER of theproposed scheme of two-stage relaying net-work with feedback quantization approach.A simple relay network based on quasi-orthogonalSTBC (QOSTBC) scheme using an AAF protocol atthe relays was proposed in [9]. Figure 2 compares ourproposed relay network based on extended-orthogonalSTBC (EOSTBC) scheme for both optimum and non-optimum scenarios with an optimum and non-optimumQOSTBC implementation and illustrates the perfor-mance improvements achieved by phase rotation at therelay nodes, i.e nodes 1 and 3. From the figure we cansee that the performance of the proposed system is al-ways better than the that of the relay network basedQOSTBC at any power or SNR. Also we can see fromfigure 2 that the difference of the slope of the non-optimum and optimum curves of the two systems areincreasing as the total transmit power goes higher.A further important issue for real-world applica-tions is what happens to the over all performance of theoptimum relay network based EOSTBC scheme if thepower control routine fails to operate properly. Therewill be only 0.5dB loss in the performance of the pro-posed scheme which still significantly performs betterthan the QOSTBC relaying link with optimum powerallocation; therefore ensuring a more robust transmis-sion scheme in the event of power control failure.Finally, the simulation result of a practical scenarioof a quantized method is depicted in Figure 3. We no-tice that the performance gain of the quantized schemeand the ideal feedback scheme are perfectly match-ing and still considerably better than the non-optimumcase.5. COCLUSIONIn this paper, we study the optimal power alloca-tion among the source and the relays in a wireless re-lay network. We consider AAF relay network for bothQOSTBC and EOSTBC. The optimal power allocationfor these schemes were demonstrated. Simulation re-sults show that the optimum power allocation can bringthe proposed scheme a considerable received SNR gainscompared to equal power allocation. This implies thatthe optimum power allocation scheme is very effectivein optimizing the system performance and reducing theoverall consuming power of a wireless network.References[1] A. Sendonaris, E. Erkip, and B. Aazhang: “Usercooperation diversity-part I: System descrip-tion,” IEEE Trans. Commun., vol.51, no.11,pp.1927–1938, Nov. 2003.[2] J. Akhtar and D. Gesbert; “Extended Or-thogonal Block Codes With Partial Feedback,”IEEE Transactions on Wireless Communica-tions, vol.3, no.6, , pp.1959–1962, Nov. 2004.Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on September 30, 2009 at 11:56 from IEEE Xplore.  Restrictions apply. [3] Y. Yu S. Kerouden, and J. Yuan; “Closed-LoopExtended Orthogonal Space-Time Block Codesfor Three and Four Tranmsit antennas,” IEEESignal Processing Letters, vol.13, no.5, pp.273–276, May. 2006.[4] M. Dohler: “Virtual Antenna Array” PhD The-sis, University of London, Nov. 2003.[5] Y. Jing and B. Hassibi: “Distributed space-timecoding in wireless relay networks” IEEE Trans-actions on Communications, vol.5, no.12, Dec.2006.[6] J. N. Laneman, D. N. C. Tse, and Gr. W.Wornell:“Cooperative diversity in wireless networks: Ef-ficient protocols and outage behavior,” IEEETrans. Inform. Theory, vol.50, no.12, pp.3062–3080, Dec. 2004.[7] N. M. Eltayeb, S. Lambotharan, and J. A. Cham-bers: “A Phase Feedback Based Extended Space-Time Block Code for Enhancement of Diver-sity,” IEEE VTC Conference, 65th, pp.2296–2299, April 2007.[8] H. Jafarkhani: “A Quasi-Orthogonal Space-TimeBlock Code”, IEEE Trans. Commun., vol.49,pp.1–4, Jan. 2001.[9] S.K.Kassim, M.Hayes, N.M. Eltayeb, J.A. Cham-bers,“Exploitation of Quasi-Orthogonal SpaceTime Block Codes in Virtual Antenna Arrays:Part II Monte Carlo-Based throughput Evalu-ation,” IEEE Vehicular Technology Conference,66th, pp.242-246, May 2008.Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on September 30, 2009 at 11:56 from IEEE Xplore.  Restrictions apply. 

A two-hop amplify-and-forward scheme for extended orthogonal space time coding in cooperative networks

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A two-hop amplify-and-forward scheme for extended orthogonal space time coding in cooperative networks

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