near-optimum detection scheme with relay selection technique for asynchronous cooperative relay...

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Published in IET CommunicationsReceived on 29th January 2013Revised on 29th December 2013Accepted on 17th January 2014doi: 10.1049/iet-com.2013.0967

T Commun., 2014, Vol. 8, Iss. 8, pp. 1347–1354oi: 10.1049/iet-com.2013.0967

ISSN 1751-8628

Near-optimum detection scheme with relay selectiontechnique for asynchronous cooperative relaynetworksWalid Mohamed Qaja1, Abdulghani M. Elazreg2, Jonathon A. Chambers1

1School of Electronic, Electrical and Systems Engineering, Loughborough University, Loughborough LE11 3TU, UK2Systems Engineering Department, Military Technological College, PO Box 626, 111A Sultanate of Oman, Muscat

E-mail: [email protected]

Abstract: A new near-optimum detection scheme for asynchronous wireless relay networks is proposed to cancel the interferencecomponent at the destination node caused by timing misalignment from the relay nodes. The detection complexity at thedestination node as compared with a previous sub-optimum detection scheme is reduced. Closed-loop extended orthogonalspace time block coding and outer convolutive coding are utilised to maximise end-to-end performance. A relay selectiontechnique is also proposed in this study for two dual-antenna relay nodes to enhance the system performance by selecting thebest links and the smallest time delay error among the relay nodes. Simulation results confirm that the proposed near-optimum detection scheme with relay selection is very effective at removing intersymbol interference at the destination nodeand achieving full cooperative diversity with unity data transmission rate between the relay nodes and the destination node.

1 Introduction

The need for robust personal communication systems anddevices has caused vast growth in the wirelesscommunications research area during the past few decades.In recent years, cooperative communication techniques havebeen a major focus of this effort because of their potentialadvantage in mitigating the practical difficulties ofimplementing actual antenna arrays [1]. These approachescombine physical single-input single-output links intovirtual multiple-input multiple-output systems [1]. Theapplication of space time block coding (STBC) in adistributed manner (termed distributed STBC or D-STBC)in such systems has shown significant improvement inperformance gain [2, 3].The majority of existing research related to D-STBC over

cooperative communication networks has assumed perfectsynchronisation (PS) among the cooperating nodes (relays)in which all the relayed symbols arrive at the destinationnode at the same time. This assumption, however, isimpractical and difficult to achieve because of differentlocations of the cooperative nodes and their distinct localoscillators. The effect of asynchronism among cooperativerelay nodes might lead to channel dispersion, which willdamage the orthogonality of the STBC causing significantdegradation in the overall system performance [4, 5].There has been some work in the literature that addresses

the issue of asynchronism in D-STBC among cooperatingnodes, mainly utilising an equalisation technique at thedestination as in [6, 7]. This technique increases theoverhead at the receiver. The near-optimum detection

scheme in [8] on the other hand effectively mitigates theasynchronism among relay nodes with simplenear-Alamouti decoding, but suffers from the limitation thatthe number of cooperating relay nodes must not exceed twothereby limiting the diversity order. In contrast, theapproach introduced in [9] for mitigating the effect ofimperfect synchronisation achieves fourth order diversity byutilising a parallel interface cancellation (PIC) detectionscheme for four relay nodes. This approach, however, doesnot achieve full data rate between the relay nodes and thedestination node because a complex D-OSTBC with 3/4data rate is utilised; moreover, the computationalcomplexity of the PIC iteration process required forovercoming the effects of interference is significant.The sub-optimum detection scheme in [10] was proposed

for the case of four relay nodes to mitigate asynchronismeffects utilising the closed-loop extended orthogonal STBC(CL EO-STBC) with phase rotated feedback as in [11].This scheme cancelled the interference components causedby asynchronism effectively with near-Alamouti simplicity,unity rate code and achieved the full diversity orderbetween the relay nodes and the destination node.Furthermore, the complexity of this scheme is only relatedto the size of utilised signal constellation. However, thisdetection scheme relied mainly on the existence of a directtransmission (DT) link between the source node and thedestination node which is unrealistic and can be difficult toachieve in practice.In this paper, a near-optimum detection scheme is

proposed for two dual-antenna cooperative relay nodes.The approach eliminates the interference components at the

1347& The Institution of Engineering and Technology 2014

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destination because of a time misalignment caused by theasynchronism in the transmission from the antennas of therelay nodes with the equivalent simplicity of the decodingas in [8, 10], but with the advantage of overcoming theirdrawbacks, that is, the achievement of a full diversity orderof four from the cooperating relay nodes to the destinationnode, as well as completely dispensing with the DT linkassumed in [10] and hence reducing the detectioncomplexity at the destination node and modelling a morerealistic wireless cooperative transmission scenario. Inaddition, a new relay selection (RS) technique for twodual-antenna relay nodes is considered in this paper toselect the best channel quality as well as the channel withthe minimum time misalignment.For the remainder of this paper, [.]T, [.]*, |.|, <{.}, ∠ and
{.}H denote transpose, conjugate, absolute value, real partof a complex number, phase angle and Hermitian (complexconjugate) transpose operations, respectively; CN(0, σ2)represents a circular complex Gaussian distribution withzero mean and variance of σ2 (i.e. 0.5σ2 per dimension).

2 System model

We consider the cooperative system model as depicted inFig. 1; with a single-antenna source and destination nodeand Rk two-antenna relay nodes, where k∈ 1,…,NR, andNR denotes the number of relay nodes in the network.There is no DT connection between the source node andthe destination node because it is assumed that the signalthrough the DT link fails to reach the destination nodebecause of path-loss effects [12]. Therefore the destinationnode relies only on the signal from the relay nodes.Furthermore, it is assumed that the separation betweenantennas is sufficient to have the required independentbranches for space-diversity application [13]. This systemcould potentially find application in emerging systemssuch as IEEE 802.16j WiMAX [14]. It is also assumedthat the source–relays and the relays–destination channelcoefficients are estimated perfectly at the destination (e.g.by using training symbols). Let fik denote the channelcoefficients from the source node to ith antenna of the kth

Fig. 1 Basic structure of general cooperative relay network with one sequipped with two antennas with outer convolutive coding


relay node and gik is the channel coefficients from the ithantenna of the kth relay node to the destination node andwe also assume that all channel coefficients fik and gik areconstant during the transmission of a signal code block (i.e. a quasi-static channel). The wireless network isassumed to transmit in an outdoor flat-fading environmentwhere there is insignificant multipath propagation;however, the lack of PS among the relays will affect thechannels from the cooperating relays to the receivermaking them dispersive. Furthermore, the asynchronismamong the virtual transmitting antenna array, as aconsequence of their different spatial locations, may breakthe orthogonality structure of the required STBC leadingto decoding failure. The problem of imperfectsynchronisation will also introduce intersymbolinterference (ISI) even in the flat-fading environment ifthe sampling time instants of the transmitter/receiver pulseshaping filters are not ideal [15, 16].Coding gain is exploited in this model by combining

outer convolutive coding at the source node with a Viterbidecoder at the destination node as shown in Fig. 1. Allrelay nodes are assumed to operate in half-duplex mode,which means all information transmission from the sourcenode to destination node occurs in two phases. In the firstphase, the information sequence s(n) = [s(1, n), s(2, n)]T,which is encoded by the convolutional encoder is thenpassed through the interleaver and mapped into quadraturephase shift keying (QPSK) symbols, where n denotes thediscrete pair index. Then, the source node broadcasts themto each antenna of each relay node Rk, k∈ 1,…,NR intwo different time transmission periods. In the secondphase, the decode-and-forward cooperation strategy is usedby the relay nodes. Moreover, using a cyclic redundancycode (CRC) scheme between the source node and therelay nodes as in [6–8] can ensure that error-free decodingis achieved at the relay nodes. Therefore it is assumedthat the relay nodes decode the source informationcorrectly. Then, the received signals at each relay nodeare processed using an STBC technique and thecomponents of the matrix code are effectively transmittedfrom each antenna of each relay node to the destinationnode in two different time transmission periods.

ource, NR relay nodes and one destination node, each relay node is

IET Commun., 2014, Vol. 8, Iss. 8, pp. 1347–1354doi: 10.1049/iet-com.2013.0967

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3 RS technique for two dual-antenna relaynodes
As mentioned previously, in a cooperative relay network, thecooperative relay nodes can assist the source node tobroadcast the signals to the destination node; however, thecooperative relay nodes have different locations so eachtransmitted signal from the source node to the destinationnode must pass through distinct paths causing differentattenuations within the signals received at the destinationnode which result in reducing the overall systemperformance. Therefore, to overcome this effect and benefitfrom cooperative communication, certain paths should beavoided by using selection techniques [17]. In this section,the conventional RS technique based on maximising theminimum instantaneous signal-to-noise ratio (SNR) is usedto ensure that the relay node with the best end-to-end pathsbetween the source node and the destination is used, asshown in Fig. 2a, to improve the system performance andprovide diversity gain on the order of the number oftransmitting antenna at the relay nodes equal to 2NRs

. Asmentioned in the previous section, each relay node isequipped with two antennas to assist the source node totransmit its signals to the destination node. The resultingSNRD at the destination node assuming maximum ratiocombining is given by

SNRD =∑k[NR

∑i[1,2

SNRSRikSNRRikD

1+ SNRSRik+ SNRRikD

(1)

where NR denotes the set of relay indices for the relay nodeschosen in the multi-RS scheme. SNRSRik

= |fik |2 s2s/s

2n

( )is

the instantaneous SNR of the paths between the sourcenode and the relay node antennas and SNRRikD

=|giik |2 s2

s/s2n

( )is the instantaneous SNR of the paths

between the relay node antennas and the destination node,where k∈ 1,…, NR and i∈ 1, 2. These expressions give theinstantaneous signal strength SNR between the source nodeand the relay node antennas, and the relay nodes antennasand the destination node. Then, the selected relay node is

Fig. 2 Source transmits to destination and neighbouring nodes overhea

a Set of relays with the best end-to-end path among NR candidates are selected to rmeasurementsb Relay with the best end-to-end path and the relay with the minimum time misalignto the destination node


chosen to maximise the minimum between them. Thetwo-antenna RS policy can be expressed as

V1k = min SNRSR1k, SNRR1kD

{ }

V2k = min SNRSR2k, SNRR2kD

{ }for k [ 1, . . . , NR (2)

and

R = maxk[1,...,NR

min{V1k , V2k}{ }

(3)

After the best relay node has been chosen as shown in Fig. 2a,then it can be used to forward the received signals towards thedestination node. In this paper, only two relay nodes in whicheach relay node is equipped with two antennas are selected toperform an appropriate encoding process to generatedistributed STBC at the destination node. The RS techniqueused in this paper is also utilised to minimise the timemisalignment among the set of selected relay nodes inaddition to selecting the best relay node with the smallesttime misalignment as shown in Fig. 2b. The procedure toperform this operation based on channel state information(CSI) at the destination node is as follows:

† Denote the set of available relay nodes by NR each ofwhich has two antennas.† Select the best group of relay nodes NRs

from the availableset of relay nodes NR using the max–min selection schemein (3).† Without loss of generality, the destination node is assumedto be synchronised with the best selected relay node, that is,t1 = t11 = t21 = 0 (Fig. 2b).† Without loss of generality, the time delays from eachantenna of each remaining relay nodes NRs−1 are assumedto be the same, because both antennas are co-located in thesame relay node tk = t1k = t2k≠ 0, k [ 2, . . . , NRs−1.† At this point the selection process is repeated among theremaining set of the best relay nodes NRs−1 where the relaynodes with minimum relative interference strength β areselected such that

r the communication

elay information via a distributed mechanism based on instantaneous channel

ment are selected assuming that the relay node with best SNR is synchronised


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b(l) = min b2, b3, . . . , bNRs−1

{ }for l [ −1, − 2, − 3 . . .

(4)

The relative interference strength β is normally β = 1 (i.e.0 dB) for tk = 0.5 T and β = 0.25 (i.e. −6 dB) for tk = 0.125T [10].

† Finally, the best relay node chosen above and the relaynode with the smallest time delay error are used to forwardthe received signals towards the destination node.

4 Distributed CL EO-STBC for twodual-antenna relay nodes

After selecting the best relay node and the relay node with thesmallest time delay error, the EO-STBC is distributed over thetwo dual-antenna relay nodes during the second broadcastingphase. The distributed open-loop EO-STBC can achieve fulldata rate at the expense of losing some diversity orderbetween the relay nodes and the destination node becauseof the interference factor between the estimated symbols.Therefore, in this section, a CL EO-STBC is considered fortwo dual-antenna relay nodes as shown in Fig. 3. Theapplication of a feedback scheme, [11], to the relay networkwill ensure full data rate together with full diversity orderequal to the number of employed antennas on thetransmitting relay nodes. The phases of the different codesymbols which are transmitted from the first antennas atboth relay nodes must be rotated by appropriate phaseangles U1 and U2, respectively, before they are transmitted,whereas the symbols from the second antennas of eachrelay node are kept unchanged as in (5).

U1s(1, n) s(1, n) U2s(2, n) s(2, n)−U1s

∗(2, n) −s∗(2, n) U2s∗(1, n) s∗(1, n)

[ ](5)

The application of phase rotations to the transmitted symbolsis equivalent to phase rotations of the corresponding channelcoefficients gik. This is important to enhance the effectivediversity between the relays and the destination at theexpense of some feedback overhead.

Fig. 3 Basic structure of distributed CL EO-STBC with outercoding using two-bit feedback based on phase rotation for anasynchronous wireless relay with two antennas in each relay nodeand one antenna in the source and the destination node with twophases for the cooperative transmission process and time delayoffset between the antennas of R2 and the destination node


As assumed in our previous discussions, the transmittedsymbols from the relay nodes will suffer from theasynchronism because of different propagation delays andhence will not arrive simultaneously at the destination node.This asynchronism will induce ISI at the destination andwill damage the orthogonality of the transmitted codewordas shown in Fig. 4.It is assumed that both antennas of R1 are fully

synchronised to the destination node, that is, ti1 = 0, i∈ 1,2. Therefore the received signal at the destination node viathe relay nodes in two different time transmission periodsbecause of time synchronisation error between the antennasof each relay node can be expressed as follows

rrd(1, n) = (U1g11 + g21)s(1, n)+ (U2g12 + g22)s(2, n)

+ Iint(1, n)+ wrd(1, n)(6)

rrd(2, n) = −(U1g11 + g21)s∗(2, n)+ (U2g12 + g22)s

∗(1, n)

+ Iint(2, n)+ wrd(2, n)

(7)

where Iint(1, n) and Iint(2, n) are the interference terms fromboth antennas of relay node R2 in two different timetransmission periods and are expressed as

Iint(1, n) = (U2g12(− 1)+ g22(− 1))s∗(1, n− 1)

+ (U2g12(− 2)+ g22(− 2))s(2, n− 1)(8)

Iint(2, n) = (U2g12(− 1)+ g22(− 1))s(2, n)

+ (U2g12(− 2)+ g22(− 2))s∗(1, n− 1)(9)

and wrd(1, n) and wrd(2, n) represent additive Gaussian noisewith zero-mean and unity variance at the destination node andgi1 and gi2, i∈ 1, 2, denote complex channel coefficients fromthe antennas of each relay node and the destination node. Asshown in Fig. 4, the effect of ISI from the previous symbols isrepresented by gi2(l ), i∈ 1, 2, and l∈−1, −2. We note thatthat gi2(−2) is generally a much smaller coefficient [8, 10].Therefore the strengths of gi2(l ) can be expressed as a ratio as

bi2(l) =|gi2(l)|2|gi2|2

for i = 1, 2 and l = −1, − 2 (10)

where β12(l ) = β22(l ) = β(l ) denotes a sample of a pulseshaping waveform and the effect of the time delay ti2, i∈ 1,

Fig. 4 Representation of misalignment of received signals at thedestination node which induces ISI in the case of two relay nodeseach relay node is equipped with two antennas


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2 [8, 10], between transmission from the antennas of the relaynode R1 and the antennas of the relay node R2 at thedestination node.The received signals rrd(1, n) and r∗rd(2, n) conjugated for
convenience in (6) and (7) can be represented in vectorform as

rrd(n) = Hs(n)+ I int(n)+ wrd(n) (11)

where

H = U1g11 + g21 U2g12 + g22U∗

2 g∗12 + g∗22 −U∗

1 g∗11 − g∗21

[ ](12)

wrd(n) = wrd(1, n), w∗rd(2, n)

[ ]Tis an additive Gaussian noise

vector, with elements having distribution CN 0, s2w

( ), at the

destination node and I int(n) = Iint(1, n), I∗int(2, n)

[ ]Tis the

interference vector containing terms from the antennas ofR2 at the destination node, which can be modelled as in (8)and (9).On the basis of (11), it is well known from estimation

theory that the matched filter is the optimum front-endreceiver to obtain statistics for detection in the sense that itpreserves information. Similar to [18] the matched filteringis performed by pre-multiplying (11) by HH. Therefore theconventional distributed CL EO-STBC detection can becarried out as follows

y(n) = [y(1, n), y(2, n)]T = HHrrd(n)

= ( |U1g11|2 + |g21|2 + |U2g12|2 + |g22|2( )︸��︷︷��︸

ld

+ 2< U1g11g∗21 + U2g12g

∗22

( )))︸��︷︷��︸

la

s(n)+HHI int(n)

+HHwrd(n)

(13)

where λd is the conventional diversity gain for the antennas ofboth relay nodes and one receive antenna at the destinationnode, λa is the array performance gain and U1 = eju1 andU2 = eju2 are determined by two feedback informationangles θ1 and θ2 which are obtained by maximising λa,which corresponds to a type of array gain. It is clear that ifλa > 0, the designed closed-loop system can obtainadditional performance gain, which leads to an improvedSNR at the destination node. The design criterion of thetwo-bit feedback scheme can be found in [11]. That is, eachelement of the feedback performance gain λa should be realand positive and can be achieved by

u1 = −/(g11g∗21)

u2 = −/ g12g∗22

( )(14)

The exact values of the phase angles in (14) are real valuedand would require infinite precision for perfect precision,which in practice it is not possible to use because of thelimited feedback bandwidth. Hence, these angles should bequantised first before they get fed back to the transmittingantennas. For each phase angle, a two-bit feedback requiresfour phase level angles to be chosen from the set of {θ1,θ2} ec = [0, p/2, p or 3p/2]. The selection of the discrete


feedback information that corresponds to the phaseadjustment of the first antennas of each of the two relays isperformed according to

u1 = argmaxu1ec < (g11g∗21)e

ju1{ }

(15)

and

u2 = argmaxu2ec < (g12g∗22)e

ju2{ }

(16)

The selection that gives the largest values of (15) and (16) willprovide the largest array gain and achieve full diversityadvantage.To detect which symbols were actually transmitted from

each antenna of each relay, the least squares (LS) methodcan be employed as follows to estimate s(t, n)

s(t, n) = argminst[S

|y(t, n)− lst|2 for t [ 1, 2 (17)where

l =∑2i=1

∑2k=1

(|gik |2)︸��︷︷��︸ld

+ 2< g11g∗21U1 + g12g

∗22U2

( )︸��︷︷��︸

la

(18)

The SNR is related to the channel gain λ as

SNR = l

4

s2s

s2w

(19)

where s2s is the total transmit power of the desired signal and

s2w is the noise power at the destination node. The detection

algorithm in (9) will not give optimal results because of theinterference component HHIint(n) in (11).

5 Near-optimum detection for distributed CLEO-STBC for two dual-antenna relay nodes

In this section, the proposed near-optimum detection schemecan be utilised to combat the impact of Iint(n) in (9), where s(t,n− 1), with t∈ 1, 2, is in fact already known if the detectionprocess has been initialised properly. As in (6), Iint(1, n) =(U2g12(−1) + g22(−1))s*(1, n − 1) + (U2g12(−2) + g22(−2))s(2, n − 1) then the component (U∗

2 g∗12(− 2)+ g∗22(− 2))s

(1, n− 1) can be removed before applying the lineartransformation in (11) and can be rewritten as follows

y(n) = [y(1, n), y(2, n)]T = HHrrd(n)

= Ds(n)+ z(n)s∗(2, n)+ v(n)(20)

where D = HHH = l 00 l

[ ], v(i) =HHw(n)

r′rd (n) = rrd(1, n)− Iint(1, n)r∗rd(2, n)− (U∗

2 g∗12(−2)+ g∗22(−2))s(1, n− 1)

[ ]

and

z(n) = z(1, n)z(2, n)

[ ]= HH 0

(U∗2 g

∗12(−1)+ g∗22(−1))

[ ]

Hence, (20) can then be rewritten as

y(1, n) = ls(1, n)+ z(1, n)s∗(2, n)+ v(1, n) (21)


Fig. 5 Probability of error performance comparison of theperfectly synchronised, with and without RS, conventional detectorfor distributed CL EO-STBC and outer convolutive coding usingtwo relay nodes each relay node has two antennas

Fig. 6 Probability of error performance of asynchronousdistributed CL EO-STBC with RS and randomly selected minimumtime misalignment against fixed time misalignment without RS

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and
y(2, n) = ls(2, n)+ z(2, n)s∗(2, n)+ v(2, n) (22)

y(2, n) in (22) is only related to s(2, n) and therefore s(2, n)can be detected by using the LS method as follows

s(2, n) = arg minsm[S

y(2, n)− lsm − z(2, n)s∗m∣∣ ∣∣2 (23)

Then, the detection of s(1, n) can be carried out using the LSmethod by substituting s(2, n) detected in (21), as follows

s(1, n) = arg minsm[S

|y(1, n)− lsm − z(1, n) s∗ (2, n)|2 (24)

The above procedure totally mitigates the interferenceinduced by different time delays from the antennas of thesecond relay node at the destination node. The optimality ofthe above procedure in terms of ML detector can beachieved if there is no decision feedback error s(t, n−1),t∈ 1, 2, therefore the above procedure is termednear-optimum detection. Moreover, the above analysis hasshown that the detection complexity of this approach isonly dependent upon the constellation size as comparedwith detection schemes presented in [9] which also dependson the number of PIC iterations. Also, the above detectionapproach does not rely on the detection result of the DTlink as compared with the sub-optimum detection approachin [10] and by reducing the timing error among the relaynodes when equipped with two antennas on each relaynode, the complexity is significantly reduced. Furthermore,the fourth order diversity with coding gain and unity datatransmission rate between the relay nodes and thedestination node are exploited by this approach with thesame decoding complexity as [8].

6 Simulation results

In this section, we show some simulation results for ourproposed near-optimum scheme assuming perfect detectionat relays (with two dual-antenna relay nodes). In simulation,we assume that all channels are quasi-static Rayleigh fadingfrequency flat channels, all simulations are coded usingQPSK symbols and the average bit error rate (BER) isplotted against the SNR. The two-bit feedback EO-STBCwith outer convolutive coding under PS and with RS isincluded as reference in all figures. The SNR is defined asSNR = s2

s/s2n (dB), and all relays transmit at 1/2 power.

The destination node has full knowledge of the CSI. InFig. 5, we show performance of the RS scheme discussedin Section 5 for perfectly synchronised distributed CLEO-STBC relay network. We can observe that there is asignificant improvement in the BER when the RS scheme isapplied, for example, at BER = 10−3, there is approximatelya 2 dB gain with RS.Fig. 6 shows the performance of the distributed CL

EO-STBC network when time misalignment is introduced.The perfectly synchronised distributed CL EO-STBC withRS is also included in the figure as a reference. In thisfigure, the performance comparison in terms of BER ismade between the asynchronous transmission with RS aswell as the minimum selection of time misalignment (β)in the range of [−6… 6] dB and without RS with fixedtime misalignment of −6 dB. We can note that theperformance improvement is due to the RS scheme


adopted, for example, ∼9 dB SNR is required to achievea BER of 10−3 whereas, 12 dB is required for achievingthe same value of BER when the RS scheme is notadopted. We also show the performance of asynchronousdistributed CL EO-STBC network with RS and differenttime misalignment values in Fig. 7. We have β in therange of [−6… 6], [−3… 6], and [0… 6] dB. The effectof selecting the smallest time misalignment is clear on theerror performance where a 9 dB SNR attains a BER of10−3 in the case of selecting the smallest value of β (i.e.in the range of [−6… 6] dB, whereas, with the increasingβ value, the BER becomes worst. In Fig. 8, we show theeffect of applying the RS scheme with selecting theminimum time misalignment on the distributed CLEO-STBC for four single-antenna relay nodes [10] ascompared with our proposed distributed CL EO-STBC fortwo dual-antenna relay nodes. We can see that our


Fig. 7 Probability of error performance of asynchronousdistributed CL EO-STBC with RS and randomly selected minimumtime misalignment with different ranges

Fig. 9 Probability of error performance of the proposednear-optimum detection scheme for distributed CL EO-STBCusing two dual-antenna relay nodes for different randomlyselected minimum time misalignment

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proposed network significantly outperforms the scheme in[10] when applying the RS with minimum delayalgorithm. The results in this figure shows that no matterwhat SNR is employed, a BER of 10−3 is not attainablewith [10]. Fig. 9 shows the effectiveness of the proposednear-optimum detection scheme in mitigating the effect ofasynchronism. The proposed scheme completely eliminatesthe effect of ISI because of time misalignment andenhancing the diversity order. The results also show thatthe smaller the time misalignment, the better theperformance in terms of BER. For example, at a BER of10−3, the proposed near-optimum scheme with RS andminimum time misalignment (in the range [−6… 6] dB)requires ∼4.7 dB of SNR and in the range [−3… 6] dBrequires ∼5 dB of SNR, whereas the conventionalperfectly synchronised distributed CL EO-STBC scheme

Fig. 8 Probability of error performance of asynchronousdistributed CL EO-STBC with RS and randomly selected minimumtime misalignment for the case of two dual-antenna relay networkagainst four single-antenna relay network [10]


requires ∼4 dB of SNR for achieving the same value ofBER.Table 1 illustrates the comparison between the proposed

near-optimum and previous work in [8, 10]. It can be seenthat the cooperative diversity order of four can be obtainedby using the proposed near-optimum and sub-optimumdetection scheme in [10] for CL EO-STBC, whereas in thenear-optimum detection scheme in [8] cooperative diversityorder cannot exceed more than two by utilising theAlamouti code. However, the sub-optimum detection [10]requires the existence of the DT link between the sourcenode and the destination node for a successful detection. Incontrast, the proposed near-optimum detection scheme doesnot require the DT link between the source node and thedestination node. In all our simulations no errorpropagations were encountered.

7 Conclusions

In this paper, a near-optimum detection approach with RS andminimum time misalignment selection was proposed andanalysed by utilising distributed CO EO-STBC with phaserotation [11] and outer convolutive coding for wireless relaynetworks over frequency flat fading under imperfectsynchronisation. A system with two dual-antenna relaynodes was demonstrated in particular.Through simulation results and analysis process, it was

shown that this near-optimum approach is effective atremoving ISI at the destination node caused by timemisalignment among relay nodes with computationaldetection complexity at the destination node dependent onlyon the constellation size and without the need for the DTlink as compared with the previous work in [10].Furthermore, the fourth order diversity with coding gainand unity data transmission rate between the relay nodesand the destination node are exploited by the proposedapproach that employed two dual-antenna relay nodes withthe equivalent decoding complexity as in [8].Moreover, it has been shown through simulation results

that the max–min RS method enhanced the overall systemperformance by choosing the best links as well as the


Table 1 Comparison of proposed near-optimum scheme with previous detection scheme in [8, 10]

Detection scheme Near-optimum detection in [8] Sub-optimum detection in [10] Proposed near-optimum detection

number of relay nodes 2 4 2number of antennas at relay nodes 1 1 2number of time misalignments 1 3 2complexity at destination low high lowcomplexity at relay node low low highDT link not needed needed not neededcooperative diversity order 2 4 4

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cooperating node with the smallest time delay error to relaythe transmitted symbols. The minimum time misalignmentselection method followed in this paper is performed afterselecting the best relay in terms of instantaneous SNR;therefore, it does not degrade the overall end-to-endperformance.

8 Acknowledgment

We thank again the associate editor and the anonymousreviewers for their very useful comments which haveimproved the clarity of our manuscript.

9 References

1 Lin, K., Sadek, A., Su, W., Kwasinski, A.: ‘Introduction in cooperativecommunications and networking’ (Cambridge University Press,New York, 2009, 1st edn.), Ch. 1, pp. 3–44

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17 Bletsas, A., Khisti, A., Reed, D., Lippman, A.: ‘Simple cooperativediversity method based on network path selection’, IEEE J. Sel. AreasCommun., 2006, 24, (3), pp. 659–672

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near-optimum detection scheme with relay selection technique for asynchronous cooperative relay...

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