Abstract—This letter proposes a differential Space–Time Coding (STC) scheme designed for asynchronous cooperative networks, where neither channel estimation nor symbol-level synchroniza-tion is required at the cooperating nodes. More specifically, our system employs differential encoding during the broadcast phase and a Space–Time Spreading (STS)-based amplify-and-forward scheme during the cooperative phase in conjunction with inter-ference rejection direct sequence spreading codes, namely Loosely Synchronized (LS) codes. Our simulation results demonstrate that the proposed Cooperative Differential STS (CDSTS) scheme is ca-pable of combating the effects of asynchronous uplink transmis-sions without any channel state information. Index Terms—Asynchronous cooperation, cooperative diversity, differential space–time spreading, loosely synchronized codes. I

Chen, Sheng

Hanzo, Lajos

Sugiura, Shinya

English

Southampton (e-Prints Soton)

IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 2, FEBRUARY 2010 113Cooperative Differential Space–Time Spreading forthe Asynchronous Relay Aided CDMA Uplink UsingInterference Rejection Spreading CodeShinya Sugiura, Member, IEEE, Sheng Chen, Fellow, IEEE, and Lajos Hanzo, Fellow, IEEEAbstract—ThisletterproposesadifferentialSpace–TimeCoding(STC) scheme designed for asynchronous cooperative networks,where neither channel estimation nor symbol-level synchroniza-tion is required at the cooperating nodes. More speciﬁcally, oursystem employs differential encoding during the broadcast phaseand a Space–Time Spreading (STS)-based amplify-and-forwardscheme during the cooperative phase in conjunction with inter-ference rejection direct sequence spreading codes, namely LooselySynchronized (LS) codes. Our simulation results demonstrate thatthe proposed Cooperative Differential STS (CDSTS) scheme is ca-pable of combating the effects of asynchronous uplink transmis-sions without any channel state information.Index Terms—Asynchronous cooperation, cooperative diversity,differential space–time spreading, loosely synchronized codes.I. INTRODUCTIONCOOPERATIVE Space–Time Coding (STC) schemes [1]were proposed to achieve the best attainable diversitygain of uncorrelated elements, where a collection of single-an-tenna-aided nodes act as a virtual antenna array, having widelyseparated distributed antenna elements. On the other hand,attaining a high cooperative space–time diversity gain in apractical relay-aided network imposes further challenges.Firstly, many of the previously-proposed cooperative STCschemes assumed that perfect Channel State Information (CSI)of the Source-Relay (SR) links and/or of the Relay-Destination(RD) links is available at the destination receiver. However, therapidly changing topology of vehicles travelling at high speedsmakes it challenging to acquire accurate CSI, which resultsin a severe degradation of the achievable performance. Bycontrast, inspired by the differential STC philosophy developedfor collocated MIMO systems [2], a number of CooperativeDifferential STCs (CDSTCs) were proposed in [3], [4] in orderto achieve reliable symbol detection without any CSI.Another major challenge is the asynchronous nature of relaynodes in the network. The aforementioned cooperative STCsare all based on the assumption of perfect timing synchroniza-tion between the relay nodes, although in practice it is difﬁcultManuscript received August 27, 2009; revised October 01, 2009. First pub-lished October 13, 2009; current version published November 06, 2009. Thiswork was supported by the EU under the auspices of the Optimix project andof the EPSRC UK. The associated editor coordinating the review of this manu-script and approving it for publication was Dr. Tan F. Wong.S. Sugiura is with the School of Electronics and Computer Science, Univer-sity of Southampton, Southampton, SO17 1BJ, U.K., on leave from the ToyotaCentral Research and Development Laboratories, Inc., Aichi, 480-1192, Japan.S. Chen and L. Hanzo are with the School of Electronics and ComputerScience, University of Southampton, Southampton, SO17 1BJ, U.K. (e-mail:lh@ecs.soton.ac.uk).Digital Object Identiﬁer 10.1109/LSP.2009.2034236to acquire accurate symbol-level time synchronization withoutimposingahighadditionalsynchronizationoverheadandimple-mentation complexity. As noted in [5], the resultant time syn-chronization errors impose a signiﬁcant performance degrada-tion. To this end, a number of asynchronous cooperative STCswere proposed [6], [7], which invoke space–time equalizationor multi-carrier transmission techniques, assuming that the per-fect CSI and/or the relative transmission delays of the mobilesare available at the destination.Against this background, we ﬁrst propose a practical CDSTCscheme designed for asynchronous relay networks, where nei-ther channel estimation nor symbol-level synchronization is re-quired at any of the nodes. More speciﬁcally, our system em-ploys differential encoding during the broadcast phase and anSpace–Time Spreading (STS)-based [8] amplify-and-forwardscheme during the cooperative phase in conjunction with in-terference rejection spreading codes, namely Loosely Synchro-nized (LS) spreading codes [9].II. SYSTEM OVERVIEWConsider a collection of mobile nodes, each having a singleantenna element and communicating with each other or witha speciﬁc destination node via frequency-ﬂat Rayleigh fadingchannels, which corresponds to an uplink scenario. We assumethe employment of a Time Division aided CDMA (TD-CDMA)based channel allocation scheme, where DS-CDMA sourcenodes are supported in each of the time slots with the aid ofunique, user-speciﬁc DS-CDMA spreading codes. Morespeciﬁcally, each transmission of the source nodes is assistedby the preassigned source-speciﬁc relay nodes, and thesignal transmission involves two phases, i.e., the broadcastphase and the cooperative phase. Additionally, we introducenode-speciﬁc delays caused by their time synchronizationerrors, where the delays of the th source node and that of theassociated threlaynodeare representedby and ,respec-tively. Furthermore, the Channel Impulse Responses (CIRs)of the SR channels, the Source-Destination (SD) channel andthe RD channels are described by and, each modeled as complex Gaussian variables withzero means and variances of and , respectively.Here, and are the corresponding fading en-velopes, while and are the uniformly distributedphase-shift components.Without loss of generality, we focus our attention on the ﬁrsttime slot, where each of the sources communicates with acertain destination node with the aid of the source-speciﬁccooperating nodes selected from all the nodes, as illustrated inFig. 1. To be speciﬁc, we consider the case of relay1070-9908/$26.00 © 2009 IEEEAuthorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on November 9, 2009 at 03:56 from IEEE Xplore.  Restrictions apply. 114 IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 2, FEBRUARY 2010Fig. 1. Dual-phase transmission model of our CDSTS.nodes,wheretheresultantmaximumspace–timediversityorderprovided by the relay nodes is also four.A. Transmitted SignalDuring the broadcast phase of Fig. 1, each of the sourcenodes transmits the differentially-encoded symbols both tothe relay nodes and to the destination node. Letthe th source node be the source-of-interest in this systemmodel. First, the source bits are mapped to -bitPAM-modulated symbols and then the modulated symbolsare Serial-to-Parallel (S/P) converted to the symbol blocks, each containing four modulated symbols formulated as, where and represent thesymbol and the block indices, respectively. Then, based on thesymbol blocks , the corresponding differentially-encodedsymbol blocks are gener-ated as follows: [10]with(1)where the ﬁrst block is transmitted as areference of the next differentially-encoded block. To relate theblock index to the symbol index , let us deﬁne the th dif-ferentially-modulated symbol as , having the relation of. Furthermore, the time-domain wave-form transmitted by the th source can be written as, where is the rectangularwaveform, which is deﬁned over the interval and rep-resents the symbol duration of the broadcast phase.Next, the differentially-modulated symbols are spreadwith the aid of the source’s node-speciﬁc spreading code, where is the code lengthof the spreading code and is the chip duration, whilerepresents the th chip value. Here, we have the relation of. Note that the spreading factor of the spreadingcode is given by the number of nonzero chips.Having obtained the transmitted time-domain waveformas , thecorresponding symbols received at the th relayand at the destination are written as:and, where we haveand , eachgiven by the uniformly distributed random phase, while isthe operating carrier frequency. The noise componentsof the th relay and of the destination, namely has azero mean and variances of and . Furthermore,represents the transmission power of the source node, whileis that of each relay node, where the totaltransmission power is considered to be unity.B. Relayed SignalDuring the cooperative phase of Fig. 1, the relaynodes amplify-and-forward the received signals to the destina-tion node with the aid of the STS scheme. More speciﬁcally,each relay node constructs the STS codeword based on thepreassigned four spreading codes ,corresponding to the th source, which are expressed as, where is the code lengthof the spreading code and the symbol duration of the cooper-ating phase is given by . Let us furthermore deﬁnethe spreading factor of the codes as .First, the th relay node despreads the received signalwith the aid of the classic correlation operation using thespreading code , in order to obtain the despread symbolcorrespondingtothetransmittedsymbols ,whichis given by(2)(3)where is the Multi-User Interference (MUI)-relatedterm induced by the other source nodes’ signals(4)and is a Gaussian distributed complex variable havinga zero mean and a variance of .Let us then S/P convert the despread sym-bols to generate the block-indexed vectorwith the aid of therelation . Furthermore, the timedomain waveform of the despread symbols is givenby .Finally, the th relay constructs the following STS-relatedsignals with the aid of the STS mapping block of Fig. 1,which are given by(5)(6)Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on November 9, 2009 at 03:56 from IEEE Xplore.  Restrictions apply. SUGIURA et al.: COOPERATIVE DIFFERENTIAL SPACE–TIME SPREADING 115(7)(8)with the aid of the normalization factor. As a result of the quasi-si-multaneous cooperative transmission of the STS codewordof (5)–(8), the corresponding received symbols at thedestination node can be expressed as,where and has a zero meanand a variance of .III. CDSTS DETECTION ALGORITHMAt the destination node of Fig. 1, the symbols transmittedfrom the th source node are detected in a low-complexitymanner so that a high diversity gain is achieved without anyCSI estimation. First, the signals received at the broadcastphase are despread as follows:(9)(10)where we have the MUI-related component :(11)while the AWGN-related component is a Gaussian dis-tributed complex variable having a zero mean and a varianceof . For simplicity of the treatment, the despread symbolsare then rearranged at the detector into the followingvectorial form(12)with the aid of the symbol-to-block transformation. Next, the signals received during the co-operative phase are despread to form, which is given by(13)where canbe expressed as with the relations of(14)and isthecorrespondingMUIcomponent.Furthermore,thenoisecomponent isaGaussiandistributedcomplexvariable havinga zero mean and a variance of . Accordingto [10], let us denote the rearranged vectorial form of the de-spread signals as follows:(15)(16)(17)(18)where we have or RD. Finally, based on (15)–(18), thedetector evaluates(19)where represents the MUI-related term, originated from, , and , while is the AWGN-related termobeying in(3), in(10)and in(13).Finally,thesymbols aredetectedbythelow-complexityharddecisiondecoder evaluating (19).IV. BASIC PROPERTIES OF LS CODESAs represented by the term in (19), the attainableperformance of our CDSTS system is affected by the MUI,therefore dependent on the spreading codes employed. In orderto mitigate the performance degradation due to the MUI, weemploy LS codes as the spreading codes in our CDSTS system,which exhibit a so-called Interference Free Window (IFW),where the off-peak aperiodic auto-correlation values as well asthe aperiodic cross-correlation values become zero, resultingin zero ISI and zero MAI, provided that the maximum delay ofthe asynchronous transmissions is within the width of the IFW.Here we only highlight the basic characteristics and the pa-rameters of the LS codes employed, since the design of LScodes was detailed for example in [9] and in the referencestherein. To be speciﬁc, LS codes are constructed with the aidof a -dimensional Walsh-Hadamard matrix as wellas an orthogonal complementary code set of length . Morespeciﬁcally, by inserting zeros both at the beginning andin the center of the complementary code pair, we can generateAuthorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on November 9, 2009 at 03:56 from IEEE Xplore.  Restrictions apply. 116 IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 2, FEBRUARY 2010LS codes having an IFW of chip du-rations, where the corresponding code length of the LS codesis . According to [9], the parameter-basednotation of LS codes is given by LS .1V. PERFORMANCE AND CONCLUSIONWe consider a BPSK-modulated CDSTS system supportingsource nodes, each of which is supported bysource-speciﬁc relay nodes that are allocated prior to communi-cations. The synchronization delays of the source nodes andthose of the associated th relay nodes are uniformly dis-tributed in , where is the maximum delay value,ranging from 0 to 8 in our simulations. We assumed thatall the channels were nondispersive Rayleigh fading channels,while considering the geometrical gains ofand forthesimpliﬁedtreatmentoftherelayselection.As mentioned above, LS codes are employed as our DS-CDMAspreading codes, where the source nodes have the LS codes of, while the relay nodes em-ploy , indicating that thecor-responding width of the IFW is . Furthermore, the powerallocated to the souce and to the relay nodes was set to, as suggested in [4]. Fig. 2(a) shows the achievableBERperformanceofourCDSTSsysteminconjunctionwiththedifferent maximum delay values ofand . In addition to the above-mentioned LS codes, Goldcodes are also considered as spreading codes in order to showthe effects of diverse spreading codes on the achievable per-formance. Furthermore, we also characterized the noncooper-ative differential transmission scenario associated with ,where the source nodes communicate with the destination nodewithout relying on any cooperating nodes. Observe in Fig. 2(a)that for the case of , the LS code-basedCDSTSsystemattainedahighdiversitygain,outperformingthenoncooperative scenario, although an error ﬂoor was exhibitedfor the high-delay scenario of due to theeffects of the unsuppressed interfering signal components ar-riving outside the IFW. This also implies that the relays’ syn-chronization error-induced degradations were overcome, whiledispensing with the typical simplﬁying assumption of conven-tionalCDSTCschemes,whenassumingperfectly-synchronizedrelay nodes [5].Although the aforementioned systems assumed the presenceof frequency-ﬂat channels, our CDSTS system can be readilyemployedfortransmissionoverfrequency-selectivechannelsbyintroducing the concept of RAKE combining in (19). Fig. 2(b)shows the achievable BER performance of our CDSTS in afrequency-selective channel environment in conjunction withand 4 RAKE ﬁngers, where the maximum delay valuewas set to . Furthermore, we considered a corre-lated tapped delay line channel model for each channel, wherethe number of CIR taps was and the correlationfactor between the th tap and the th tap was set to. For comparison, we also simulated the noncooperative dif-ferentially-encoded transmission scheme using LS codes and1Note that while the size of the differentially-encoded symbol blocks ￿ ￿ ￿ ischosen to be identical to the number of relay nodes ￿ , the parameter ￿ hastosatisfytheconditionof￿ ￿ ￿ forthesourcenodesaswellas￿ ￿ ￿￿￿ for the relay nodes, indicating that increasing the number of source nodesper time slot ￿ has the following consequences: the number of cooperativenodes ￿ and the LS codes’ IFW width ￿ , therefore also the number of chipsin the LS codes increases. Consequently also the effective bit rate of the CDMAsystem is decreased in a ﬁxed-bandwidth scenario.Fig. 2. Achievable BER performance of our CDSTS system.the Gold code-based CDSTS benchmark scheme. It is seen inFig. 2(b) that both our LS code-based CDSTS arrangement andthe noncooperative scenario using LS codes beneﬁtted from anincreased path diversity gain upon increasing the number ofRAKE ﬁngers owing to the ideal auto-correlation character-istics of the LS codes. More speciﬁcally, our LS code-basedCDSTS is capable of gleaning both space–time diversity gainas well as path diversity gain.InthiscontributionweproposedapracticalCDSTCprotocol,whereneitherchannelestimationnorsymbol-levelsynchroniza-tion is required at the nodes. Our simulation results demonstratethat the proposed CDSTS scheme is capable of combating theeffects of asynchronous transmissions, provided that the max-imum synchronization delay of the relay nodes is within thewidth of the IFW.REFERENCES[1] J. Laneman and G. Wornell, “Distributed space–time-coded protocolsfor exploiting cooperative diversity in wireless networks,” IEEE Trans.Inform. 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A distributed space–time coding in asynchronous wireless relay networks,”

Accurate bit-error-rate analysis of bandlimited cooperative OSTBC networks under timing synchronization errors,”

Differential modulation for two-user cooperative diversity systems,”

Distributed differential space–time coding for wireless relay networks,”

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

Interference-free broadband single-and multicarrier DS-CDMA,”

Single and Multi-Carrier CDMA: Multi-User Detection, Space–Time Spreading, Synchronisation and Standards.

Space–time coded multi-transmission among distributed transmitters without perfect synchronization,”

Turbo detection of precoded sphere packing modulation using four transmit antennas fordifferentialspace–timespreading,”IEEETrans.WirelessCommun.,

Cooperative differential space-time spreading for the asynchronous relay aided CDMA uplink using interference rejection spreading code

Shinya Sugiura

Sheng Chen

Lajos Hanzo

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Cooperative differential spacetime spreading for the asynchronous relay aided CDMA uplink using interference rejection spreading code

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Cooperative differential space-time spreading for the asynchronous relay aided CDMA uplink using interference rejection spreading code

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