We propose a novel near-capacity Multiple-Symbol Differential Decoding (MSDD) aided cooperative Differential Linear Dispersion Code (DLDC) scheme, which exhibits a high grade of system design flexibility in terms of the choice of activated relays and the DLDC's rate allocation. More specifically, the system has the freedom to activate a range of DLDCs depending on both the number of relays available in the network, as well as on their position, throughput and complexity considerations

Hanzo, Lajos

Ng, Soon

Xu, Chao

English

Southampton (e-Prints Soton)

IEEE SIGNAL PROCESSING LETTERS, VOL. 18, NO. 3, MARCH 2011 173Near-Capacity Irregular Convolutional CodedCooperative Differential Linear Dispersion CodesUsing Multiple-Symbol Differential DetectionChao Xu, Student Member, IEEE, Soon Xin Ng, Senior Member, IEEE, and Lajos Hanzo, Fellow, IEEEAbstract—We propose a novel near-capacity Multiple-SymbolDifferential Decoding (MSDD) aided cooperative DifferentialLinear Dispersion Code (DLDC) scheme, which exhibits a highgrade of system design ﬂexibility in terms of the choice of activatedrelays and the DLDC’s rate allocation. More speciﬁcally, thesystem has the freedom to activate a range of DLDCs dependingon both the number of relays available in the network, as well ason their position, throughput and complexity considerations.Index Terms—Cooperative communications, differential lineardispersion codes, irregular convolutional codes, relay selection.I. INTRODUCTIONCOOPERATIVE diversity was proposed in [1], wherethe single-element Mobile Stations (MSs) share theirantennas to form a Virtual Antenna Array (VAA) and as a ben-eﬁt, they typically experience uncorrelated fading. However, itbecomes unrealistic for the relays and the destination to esti-mate the channel of all the VAA links. To avoid the potentiallyexcessive complexity of coherent MIMO detection, non-coher-ently detected DPSK may be used in each of the single-antennalinks. Accordingly, Differential STBCs (DSTBCs) could befound in [2]. Furthermore, a Differential Linear DispersionCode (DLDC) based on the so-called Cayley transform wasproposed in [3] in order to strike a ﬂexible trade-off betweenthe achievable throughput and diversity gain.In the absense of channel estimation, Conventional Differ-ential Detection (CDD) generally suffers from a 3 dB perfor-mance penalty, provided that the Doppler frequency is not ex-cessive, while upon increasing the Doppler frequency a pro-nouncedirreducibleerrorﬂoorisformed.Multiple-SymbolDif-ferential Detection (MSDD) was proposed in [4] in order to re-duce the performance discrepancy. The MSDD observesconsecutive received symbols and makes a joint decision basedon( )informationsymbols.Thepricepaidisthatthecom-plexity imposed increases exponentially with . To mitigatethe complexity, Multiple-Symbol Differential Sphere Decoding(MSDSD) was proposed for Differential Space-Time Modula-tion (DSTM) including DSTBCs as well as DLDCs in [5]. AsManuscript receivedOctober 27, 2010; revised December 21, 2010; acceptedDecember 27, 2010. Date of publication January 10, 2011; date of current ver-sion January 27, 2011. This work was supported by the European Union’s Sev-enth Framework Programme ([FP7/2007-2013] ) under Grant 214625 and bythe RC-UK of the India-UK Advanced Technology Centre. The associate editorcoordinating the review of this manuscript and approving it for publication wasProf. Kostas Berberidis.The authors are with the School of Electronics and Computer Science, Uni-versity of Southampton, Southampton SO17 1BJ, U.K. (e-mail: cx1g08@ecs.soton.ac.uk; sxn@ecs.soton.ac.uk; lh@ecs.soton.ac.uk).Digital Object Identiﬁer 10.1109/LSP.2011.2104952a further advance, a soft-output MSDSD designed for DPSKwas proposed in [6] for the sake of turbo detection. A novelMSDSD aided cooperative Amplify-and-Forward (AF) designwas proposed in [7], where a low BER can only be achieved inthe high-SNR region.Against this background, the novelcontributions of this letterare: 1) we ﬁrst propose a soft-output MSDSD for the DSTBC/DLDC scheme, so that MSDSD may be applied for turbo detec-tion in cooperative Decode-and-Forward (DF) systems. 2) Wealsopropose a near-capacityMSDD/MSDSDaidedcooperativeDLDC scheme, which allows ﬂexible relay selection and coop-erative rate allocation.Thefollowingnotationisusedthroughouttheletter.ADLDCis described by the nomenclature of , whereand indicate the number of transmit and receive antennas,while and denote the number of channel uses and thenumber of transmitted symbols per block, respectively.Further-more, refers to the window length of the MSDD/MSDSD.II. SYSTEM OVERVIEWTheschematic ofthecooperative systemconsidered is shownin Fig. 1, where an Up-Link (UL) scenario is considered. Boththesourceandtherelaysareassumedtobesingle-antenna-aidedMobile Stations (MSs), while the destination is assumed to bea Base Station (BS) having two antennas. As shown in [8], ac-cording to free space path loss, the Reduced-Pathloss-Related(RPLR) power gain of the source-relay (SR) link with respectto the Source-Destination (SD) link and the RPLR powergain of the Relay-Destination (RD) link with respect to the SDlink have the relationship of(1)andtheterminologyoftheequivalenttransmitSNRatthesourcewas introduced in [8] as(2)In order to achieve an inﬁnitesimally low BER, turbo de-tection may be employed at both the relays and at the desti-nation. Similar to the classic Recursive Systematic Convolu-tional(RSC)codes,thedifferentialencoderoftheDPSK/DSTMhas a recursive structure. Hence theoretically a free distance ofmay be achieved by a combined RSC decoder and aMSDD/MSDSD having a detection window size as long as theencoding frame length. However, the detection window size ofMSDSD is severely limited because of its complexity. As an al-ternative mean, a Unity Rate Code (URC) may be employed asseen in Fig. 2. If the relays and the destination are able to afford1070-9908/$26.00 © 2011 IEEE174 IEEE SIGNAL PROCESSING LETTERS, VOL. 18, NO. 3, MARCH 2011Fig. 1. Block diagram of a relay-aided uplink system.Fig. 2. Schematic of the three-component serial-concatenated encoder at thesourceandrelays,andthecorrespondingthree-stageturbodetectionattherelaysand the destination.theIRregularConvolutionalCode(IRCC)decodingcomplexity,then near-capacity performance may be achieved.In the ﬁrst transmission period, the source transmitsIRCC/RSC coded as well as URC precoded DPSK sym-bols to both the relays and to the destination. At the relays, harddecisions are made after the three-stage turbo MSDD/MSDSD.Then the IRCC/RSC and URC re-encoded DLDC symbols aretransmitted by therelays during the second transmission period.At the destination, the same turbo detection process is carriedout for the coded DLDC symbols received from the relays. Theoverall throughput of the proposed cooperative scheme is givenby(3)where and are the rates of the IRCC/RSC employedat the source and at the relays, respectively. The variablesand denote the number of modulated bits per symbol of theDPSK modulation scheme employed at the source node, andthat of the DLDC employed at the relay node.The choice of the DLDC parameters and depends onhow many relays are available in the network as well as onhow many UL receive antennas are used at the BS. The DLDCthroughput speciﬁed by is determined by the positionoftherelays,whichspeciﬁesRPLRpowergains and .Our proposed DLDC selection designed for the cooperative DFscheme is detailed in Section IV.III. SOFT-DECISION AIDED MSDSD DECODERDESIGNED FOR DSTMDifferential encoding designed for DSTM schemes may beformulated in a way similar to classic DPSK, yielding(4)where the( )-elementunitary matrix carries thesourceinformation, while the transmission matrix has a size of( ).We assume that the Rayleigh fading envelope and phase re-main constant over channel uses and that the received signalis contaminated by Additive White Gaussian Noise (AWGN),hence the received signal may be modelled as(5)where the matrix has a size of ( ). The AWGN matrixhasthesamesize,azeromeanandavarianceof foreachdimension. The channel matrix is of size ( ), and itis generated according to Clarke’s fading model.As mentioned before, the MSDD/MSDSD observesconsecutive received signal blocks and makes ajoint decision based on ( ) consecutive informationblocks . The hard-output MSDSD designed for theDSTM of [5] should be modiﬁed in order to be used in turbodetection. Similarly to the soft-output DPSK MSDSD of [6],the Sphere Decoder (SD) aims to ﬁnd the optimum ( )blocks that leads to the minimum Euclidean dis-tance, which is formulated as(6)where denotes the decoding sphere radius, which is mini-mized by the SD. The coefﬁcient in (6) represents the pre-dictor coefﬁcients hosted by the corresponding elements in thelowertriangular matrix in[6,eq.(6)].Theaprioriprobabilityin(6)maybecalculatedbytheproductoftheaprioriindividualinformation block probabilities according to the a priori LLRsand the corresponding binary bit combinations.The most recent transmission matrix is a common mul-tiplier for all the transmission matrices. Hence we introduce theaccumulated information matrix in order to eliminate the inﬂu-ence of , which may be formulated as(7)Let us now deﬁne the Partial Euclidean Distance (PED) compo-nent seen in (6) as(8)with , and it lies within the decodingsphere. Each time the MSDSD performs sphere decoding, the( ) blocks giving the minimum decodingsphere radius are found. Therefore the MSDSD constitutesthe Max-Log-MAP approximation of the ML-MSDD, whereonly two optimum combinations are taken into account, whichis formulated as(9)XU et al.: NEAR-CAPACITY IRREGULAR CONVOLUTIONAL CODED COOPERATIVE DIFFERENTIAL LINEAR DISPERSION CODES 175TABLE ILOOKUP TABLE SUMMARIZING THE ￿￿￿ REQUIRED FOR ACHIEVINGAN INFINITESIMALLY LOW BER FOR THE THREE-STAGE TURBO DETECTEDIRCC-URC-DLDC(323Q)/DG3 MSDD SCHEME,W HEN ￿ ￿￿ ￿￿￿.where and denote the minimum Euclidean dis-tance, when is ﬁxed to 1 and 0, respectively. As a result,the reliability of the LLRs is degraded. Therefore, similar to thesoft-decision aided MSDSD designed for DPSK, the observa-tion windows are shifted only by one block at a time, while onlythe LLRs of the central data block are calculated each time, andhas to be an even number.IV. DESIGN AND PERFORMANCEIn this section, we propose a new relay selection and rateallocationdesignforthenear-capacityMSDDaidedcooperativeDLDC scheme, followed by our simulation results.BasedonEXITchartestimationandMonte-Carlosimulation,the required for achieving an inﬁnitesimally low BERat the destination is summarized in Table I. It has been widelyexploited [9] that a vanishingly low BER is achievable, whenan open EXIT chart tunnel is formed between the EXIT curvesof the inner and outer code. Furthermore, according to the areaproperties of EXIT charts [9], the area under the EXIT curveof the inner decoder is appropriately equal to the channel ca-pacity attained. Therefore, a near-zero area in the EXIT opentunnel implies a near-capacity performance. However, in prac-tice not all received frames can be error-freely decoded at theconvergence SNR estimated by the EXIT chart, since the EXITchart is only accurate for an inﬁnite interleaver length. In prac-tical Monte-Carlo simulations using a ﬁnite interleaver-length,normally about 0.5 dB higher SNR is required. We assume thattherearethreeavailablerelays,hencetheclassofDLDC(32TQ)and DG3 are of interest. Without loss of generality, we considerthe DSTM scheme employing BPSK, i.e., we have ( ),since increasing the number of is preferred compared to em-ploying a higher-level modulation scheme. Furthermore, sincethediversitygainofDLDCisdeterminedby [3],a setting of is ﬁxed.Table I demonstrates that a substantial design ﬂexibility maybe provided by the rich set of DSTM schemes having differentrates. It was demonstrated in [10] that having a ﬂexible coderateallocationwasbeneﬁcialforthecooperativeDFschemes.Inthis letter, we propose to allocate the code-rate by appropriatelychoosing the different modulation schemes. The design proce-duresproposedforourMSDDaidedcooperativeDLDCschemeare as follows.1) We ﬁrst determine the modulation scheme employed atthe source node based on the throughput considerationand the affordable complexity for the relays, then therequired at the relays to avoid error propagationis determined.2) The BS chooses the parameters and for DSTM ac-cording to the number of available relays, and then sets upthe corresponding lookup table. Table I represents the sce-nario of as well as for .3) The power gains and are determined by thepositions of the activated relays. Then the re-quired at the destination may be calculated by.4) Finally, the BS ﬁnd a suitable code rate for the DLDC inthe lookup table using the estimated .Itcanbeseenthattheclosertherelaysapproachthesourcenode,the higher becomes compared to , which leads to alower requiredatthedestination.Asaresult,accordingtoTableI,alowerDLDCcode-ratehastobechosenfortheweakRD link. By contrast, a higher-rate DLDC should be selected inthe opposite situation.We now present a design example. The modulation schemeof the SR link is ﬁrst ﬁxed to be DQPSK, and the MSDD withisemployedattherelays.TheEXITchartanddecodingtrajectory recorded for the SR links are shown in Fig. 3, whereour 36-component IRCC [11] has the weighting coefﬁcients ofThe bit interleaver length is set to . It can be seen in Fig. 3that is required for achieving a vanishinglylowBERattherelays.Iftherelayscannotaffordthecomplexityof decoding the 36-component IRCC and/or using MSDD, thena single-component RSC as well as the MSDSD designed inSection III may be employed, and the bit interleaver length maybe reduced to . It can be seen in Fig. 3 that employing asingle-component RSC and MSDSD requires a 0.8 dB higherSNR at the relays.Asanexample,weassumethattherearethreeavailablerelaysin the network, which are located in a position, where. According to the RPLR power gains relation-ship of (1), we have and ,which requires at the destination. There-fore, based on row and column of Table I, the DLDC(3232)using for MSDD and two inner iterations within theURC-MSDD composite decoder may be selected, as indicatedby the bold entry in Table I. As a result, according to (3), theoverall throughput of the cooperative scheme is 0.25. The EXITchart for the RD links is similar to the SR links of Fig. 3, andthe IRCC employed for the selected modulation scheme has theweighting coefﬁcients ofThe BER performance evaluated at the destination is por-trayed in Fig. 4. The maximum achievable rates indicated inFig. 4 are calculated based on the area property of the EXITchart [9]. It is shown in Fig. 4 that as a beneﬁt of the cooperative176 IEEE SIGNAL PROCESSING LETTERS, VOL. 18, NO. 3, MARCH 2011Fig. 3. EXIT chart of the three-stage turbo detected DQPSK scheme of Fig. 2for the SR links, when ￿ ￿￿ ￿￿￿. The 36-component IRCC having weightingcoefﬁcients and the MSDD with ￿ ￿￿are adopted, as well as a single inneriteration within the URC-MSDD composite decoder and a interleaver length of￿￿ are employed. The case of employing RSC and MSDSD with a interleaverlength of ￿￿ is also drawn.Fig. 4. BER performance of the proposed cooperative DLDC employingIRCC/RSC and MSDD/MSDSD, in comparison with their non-cooperativecounterparts, for ￿ ￿￿ ￿￿￿. A MSDSD aided cooperative turbo-codedDBPSK scheme is also drawn as a benchmark.diversity, the proposed near-capacity cooperative scheme pro-vides a 2.0 dB performance improvement compared to the con-ventional direct transmission operating without relaying. Fur-thermore, the low complexity cooperative scheme employingthesingle-componentRSCaswellasMSDSDalso outperformsits non-cooperative counterpart by 1.5 dB.As another benchmark, a cooperative turbo-coded DBPSKscheme with the same system throughput of 0.25 and the sameMSDSD window length of is also portrayed in Fig. 4.The schematics of the cooperative turbo-coded DBPSK wasproposed in [12], where the IRCC/RSC and URC blocks ofFig. 2 are replaced by a single half-rate turbo code. The numberof inner iterations within the turbo decoder is set to 2, and thenumber of outer iterations between the turbo decoder and theMSDSD is also set to 2. Fig. 4 shows that the non-cooperativeRSC and URC coded DQPSK scheme’s performance is compa-rable to the cooperative turbo-coded DBPSK, and all the pro-posed cooperative schemes outperform the turbo coded coop-erative scheme. This is because the three-stage turbo detectionemployed in our proposed scheme has an open tunnel leading tothe (1.0, 1.0) point of the EXIT chart, which results in a sharpturbo-cliff.Our proposed cooperative DLDC scheme becomes capableof outperforming its cooperative LDC coherent-detection-aidedcounterpart relying on realistic imperfect channel estimation,when the Gaussian-distributed Channel State Information(CSI) estimation noise becomes for the SR links, andfor the RD links. Viewing this somewhat surprisingfact from a slightly different angle, for the QPSK aided co-herent cooperative LDC scheme to maintain at least the sameperformance as DQPSK MSDSD aided cooperative DLDC, theCSI estimation error should be limited to for the SRlinks, and for the RD links.In conclusion, we have proposed a near-capacity MSDDaided cooperative DLDC scheme, relying on a ﬂexible relayselection and rate allocation design. We have demonstrated thatnear-capacity performance may be achieved by the employ-ment of our 36-component IRCC, and the proposed cooperativescheme performs better than the conventional direct transmis-sion regime operating without relaying and it also outperformsits cooperative turbo-coded DBPSK counterpart, which has thesame system throughput.REFERENCES[1] J. Laneman and G. Wornell, “Distributed space-time-coded protocolsfor exploiting cooperative diversity in wireless networks,” IEEE Trans.Inf. Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003.[2] G. Ganesan and P. Stoica, “Differential modulation using space-timeblock codes,” IEEE Signal Process. Lett., vol. 9, no. 2, pp. 57–60, Feb.2002.[3] B. Hassibi and B. Hochwald, “Cayley differential unitary space-timecodes,” IEEE Trans. Inf. Theory, vol. 48, pp. 1485–1503, Jun. 2002.[4] P.Ho andD.Fung, “Errorperformance ofmultiple-symboldifferentialdetection of PSK signals transmitted over correlated rayleigh fadingchannels,” IEEE Trans. Commun., vol. 40, pp. 1566–1569, Oct. 1992.[5] V. Pauli and L. Lampe, “On the complexity of sphere decoding fordifferential detection,” IEEE Trans. Inf. Theory, vol. 53, no. 4, pp.1595–1603, Apr. 2007.[6] V. Pauli, L. Lampe, and R. Schober, ““Turbo DPSK” using soft mul-tiple-symbol differential sphere decoding,” IEEE Trans. Inf. Theory,vol. 52, pp. 1385–1398, Apr. 2006.[7] L. Wang and L. Hanzo, “The amplify-and-forward cooperative up-link using multiple-symbol differential sphere-detection,” IEEE SignalProcess. Lett., vol. 16, pp. 913–916, Oct. 2009.[8] H. Ochiai, P. Mitran, and V. Tarokh, “Design and analysis of collabo-rative diversity protocols for wireless sensor networks,” in IEEE 60thVehicular Technol. Conf., Sep. 2004, vol. 7, pp. 4645–4649.[9] M.Tuchler,“Designofseriallyconcatenatedsystemsdependingontheblock length,” IEEE Trans. Commun., vol. 52, no. 2, pp. 209–218, Feb.2004.[10] L. Wang and L. Hanzo, “Optimum time resource allocation for tdma-baseddifferentialdecode-and-forwardcooperativesystems:Acapacityperspective,” IEEE Commun. Lett., vol. 14, pp. 506–508, Jun. 2010.[11] L. Kong, S. Ng, R. Tee, R. Maunder, and L. Hanzo, “Reduced-com-plexity near-capacity downlink iteratively decoded generalized multi-layer space-time coding using irregular convolutional codes,” IEEETrans. Wireless Commun., vol. 9, pp. 684–695, Feb. 2010.[12] M. Janani, A. Hedayat, T. Hunter, and A. Nosratinia, “Coded coop-eration in wireless communications: Space-Time transmission and it-erative decoding,” IEEE Trans. Signal Process., vol. 52, no. 2, pp.362–371, Feb. 2004.

Cayley differential unitary space-time codes,”

Coded cooperation in wireless communications: Space-Time transmission and iterative decoding,”

Design and analysis of collaborative diversity protocols for wireless sensor networks,”

Differential modulation using space-time block codes,”

Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,”

Errorperformance ofmultiple-symboldifferential detection of PSK signals transmitted over correlated rayleigh fading channels,”

M.Tuchler,“Designofseriallyconcatenatedsystemsdependingonthe block length,”

On the complexity of sphere decoding for differential detection,”

Optimum time resource allocation for tdmabaseddifferentialdecode-and-forwardcooperativesystems:Acapacity perspective,”

Reduced-complexity near-capacity downlink iteratively decoded generalized multilayer space-time coding using irregular convolutional codes,”

The amplify-and-forward cooperative uplink using multiple-symbol differential sphere-detection,”

Turbo DPSK” using soft multiple-symbol differential sphere decoding,”

Near-Capacity Irregular Convolutional Coded Cooperative Differential Linear Dispersion Codes Using Multiple-Symbol Differential Detection

Near-Capacity Irregular Convolutional Coded Cooperative Differential Linear Dispersion Codes Using Multiple-Symbol Differential Detection

Abstract

Similar works

Full text

Available Versions

Southampton (e-Prints Soton)