Cooperative relaying allows single antenna users to achieve diversity and coding gains by utilizing nearby users' transmitting capabilities. We consider a relay system employing constant envelope continuous phase frequency shift keying. Distributed space-time trellis codes are implemented with a novel multiple relay protocol

Martin, P.A.

Maw, R.L.

Taylor, D.P.

UC Research Repository

356 IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 5, MAY 2008Cooperative Relaying with CPFSK andDistributed Space-Time Trellis CodesRachel L. Maw, Philippa A. Martin, Senior Member, IEEE, and Desmond P. Taylor, Life Fellow, IEEEAbstract— Cooperative relaying allows single antenna users toachieve diversity and coding gains by utilizing nearby users’transmitting capabilities. We consider a relay system employingconstant envelope continuous phase frequency shift keying. Dis-tributed space-time trellis codes are implemented with a novelmultiple relay protocol.Index Terms— Cooperative relays, space-time trellis codes,continuous phase modulation.I. INTRODUCTIONCOOPERATIVE relaying can realize the advantages ofspace-time coding without requiring a user to have mul-tiple transmit antennas. Continuous phase modulation (CPM)is a non-linear modulation [1]. It has the advantage over linearmodulations of a constant envelope, which allows the use oflow cost and efficient non-linear power amplifiers. It has thusfar not been considered in a cooperative relaying context, buthas been shown to be a good alternative to linear modulationin space-time coded systems [2], [3], [4]. Continuous phasefrequency shift keying (CPFSK) is a special case of CPM [1].Here we consider CPFSK modulated cooperative relayingschemes.There are many possible cooperative relaying configura-tions [5], [6], [7], [8]. We consider half duplex schemes,where a relay can receive and transmit, but not at the sametime. They may be classified as either amplify and forward(AF) or decode and forward (DF) schemes. In AF schemes,the relays simply amplify received signals by a gain factorβ and retransmit them in subsequent time slots. In contrast,DF strategies require the relay terminals to have knowledgeof the source’s modulation format and coding to regeneratesignals. AF schemes are, therefore, more suited to ad-hocimplementation. We investigate single-user AF relay schemes.Three protocols for 1-relay systems transmitting over twotime slots are defined in [5] and are described in Table I. Herea system consists of 3 nodes, a source (S), relay (R) anddestination (D). In [9], the protocol I AF cooperative schemeis shown to be optimal in terms of the diversity/multiplextradeoff (DMT). In order to decode, the destination must knowβ and the channel gains, hSR, hSD and hRD, for the linksS → R, S → D and R → D, respectively. The DMT can beused as a design tool. It shows which scheme will be superiorgiven sufficient SNR, but not what SNR is sufficient [9].Protocol I AF is extended to allow multiple relays in [9].Each relay receives a source transmission in turn (every secondManuscript received February 1, 2008. The associate editor coordinating thereview of this letter and approving it for publication was G. K. Karagiannidis.The authors are with the Department of Electrical and Computer Engineer-ing, University of Canterbury, Private Bag 4800, Christchurch, New Zealand(e-mail: rlm57@student.canterbury.ac.nz, taylor@elec.canterbury.ac.nz).Digital Object Identifier 10.1109/LCOMM.2008.080163.TABLE IESTABLISHED SINGLE RELAY COOPERATIVE PROTOCOLS [5].Nodes Transmitting Nodes ReceivingTime Slot 1 2 1 2Protocol I S S, R R,D DProtocol II S R R, D DProtocol III S S,R R Dtime slot), then amplifies and forwards it in the next timeslot. A system with N relays requires 2N time slots foreach cooperation frame. Because only 12 the information isrepeated by the relays, the link cannot support multiplexinggains greater than 12 . In [10], [11] slotted AF (SAF) schemesare developed that have improved DMTs for N > 1. Thefocus is on the naive SAF protocol, where each relay listensin turn for 1 slot to receive the source and previous relay’stransmissions and then amplifies and forwards them in the nextslot. For N relays there are N+1 slots per cooperation frame.The last relays are receiving highly corrupted signals fromthe previous relays, as is the destination. This protocol can beoptimal in terms of the DMT with an infinite number of slots ifthe relays are physically isolated or if ordering or dumping ofrelays based on their channel quality is used [10]. Improvingcapacity by allowing multiple users to use the same relay slotis investigated in [12], but results in inter-user interferenceduring the communal slot.In Section II we propose novel AF protocols for multiplerelays. In Section III and IV we present and simulate a relayingscheme employing CPFSK and distributed space-time trelliscodes (DSTTCs). Conclusions are drawn in Section V.II. MULTIPLE RELAY PROTOCOLSWe propose a novel extension to the three protocols ofTable I for multiple relays, as illustrated by Table II. Hereeach protocol employs N relays and requires N +1 intervalsfor one cooperation frame. An interval can range from a singlesymbol period up to a complete data frame. Relays 1 to N arelabelled R1, . . . ,RN . The source transmits for the first N orN +1 intervals depending on the protocol. Each relay listensfor an interval in turn over the first N intervals. All relaysforward their amplified received signal to the destination in theN + 1-th interval. For EXT-I, NN+1 of the source informationis forwarded by the relays, allowing multiplexing gains upto NN+1 , the same as the naive SAF protocol. Beneficially,the proposed protocols do not suffer from the extensive errorpropagation inherent to the naive SAF protocol, as no relaylistens to other relays’ forwarded messages. The DMT isoptimized using EXT-1. In the case of 1 relay the protocols of1089-7798/08$25.00 c© 2008 IEEEAuthorized licensed use limited to: University of Canterbury. Downloaded on May 14, 2009 at 21:26 from IEEE Xplore.  Restrictions apply.MAW et al.: COOPERATIVE RELAYING WITH CPFSK AND DISTRIBUTED SPACE-TIME TRELLIS CODES 357TABLE IIPROPOSED COOPERATIVE RELAYING PROTOCOLS FOR SYSTEMS WITH N RELAYS.Nodes Transmitting Nodes ReceivingInterval 1 2 . . . N N+1 1 2 . . . N N+1Protocol EXT-I S S . . . S S,R1,R2, . . . ,RN R1,D R2,D . . . RN ,D DProtocol EXT-II S S . . . S R1,R2, . . . ,RN R1,D R2,D . . . RN ,D DProtocol EXT-III S S . . . S S,R1,R2, . . . ,RN R1 R2 . . . RN DTable II reduce to those of Table I. Note, the EXT-1 protocolhas been proposed for multi-user differential distributed space-time modulation in [13]. Using the approach of [13] all 3protocols in Table II can be extended to a multi-user system.III. SYSTEM MODELWe propose DSTTCs employing EXT-I and EXT-III basedon the space-time coded M -CPFSK system of [14], with mod-ulation index h = 1M . EXT-II is not considered because it doesnot utilize a source transmission in the final interval, whichlimits the rate of the DSTTC. In [14], CPFSK is modelled bythe Rimoldi decomposition [15], consisting of a continuousphase encoder (CPE) followed by a memoryless modulator. Ltfeedback free CPEs are combined into a single convolutionalencoder which has the Lt×2Lt generator matrix [14]ZLt(D)=⎡⎢⎢⎢⎣1−D D 0 0 0 · · · 00 0 1−D D 0 · · · 0...............0 0 0 1−D D⎤⎥⎥⎥⎦ (1)defined over the ring of integers modulo-M (ZM ), where Ltis the number of transmit antennas. By considering rate-Lt−1Ltspace-time codes (STCs) defined over ZM , the generatorsof the modulation, ZLt(D), and the STC, G(D), may becombined to form a trellis encoder with generator matrixJ(D) = G(D)ZLt(D) on ZM .Our distributed scheme employs N relays and instead oftransmitting from Lt co-located antennas as for traditionalspace-time coding (TSTC), the source transmits the coded dataover Lt = N + 1 intervals. Here an interval is the number ofsymbol periods, nf , required to transmit a data frame in aTSTC scheme. We consider a rate- NN+1 STC giving a systemthroughput of N log2 MN+1 bits per channel use (BPCU) or symbolperiod. Note the TSTC has throughput N log2(M) BPCU.The source has 1 transmit antenna and the relays each have1 transceiver antenna. Thus, only 1 memoryless modulator isrequired at S. Its input is formed by time-multiplexing theoutput of J(D) so that a frame of modulated data transmittedfrom the i-th antenna in the TSTC scheme is transmitted in thei-th interval for 1 ≤ i ≤ N+1. There are Lr receive antennasat D. The maximum achievable diversity is upper bounded byrLr, where r is the transmit diversity of the STC.The signal transmitted during the n-th symbol period of thei-th interval is given bysi(t,Xi,n) =√2ELtTcos(2πf1t + ψ˜(t,Xi,n)), (2)where the information carrying phase is defined as [15]ψ˜(t,Xi,n)=[2πh(X2i,n + X1i,nt− nTT)]mod 2π, (3)nT ≤ t ≤ (n+1)T in (2) and (3), f1 is the asymmetric carrierfrequency [15], E is the energy per symbol period, T is thesymbol period and Xi,n=[X1i,n X2i,n]is the output from thei-th CPE [14]. We normalize the signal transmitted from thei-th relay using the amplification factor βi =√ETET |hSRi |2+σn2for 1 ≤ i ≤ N , where σn2 is the noise power and hSRi isthe fade coefficient of the S → Ri link. The average transmitpower of each relay in the interval it transmits is then lessthan or equal to ET , the transmit power of the source.Perfect channel state information, hSRi , hSD, hRiD, isassumed at D, as is knowledge of the amplification factors βifor 1 ≤ i ≤ N . Because the coded data is stored at the relaysand transmitted simultaneously in the last interval, the trellisof J(D) is used for Viterbi decoding at D. If EXT-I is used,the decoding metric at D is augmented to use the informationreceived during the first N intervals, and the received signalat the j-th antenna at D isyj(t,X) =N∑i=1[βihRiD[hSRisi(t,Xi) + nRi(t)]]+ hSDN+1∑i=1si(t,Xi) + nj(t), j = 1, . . . , Lr,(4)where nRi(t) and nj(t) are the AWGN processes for the i-threlay and j-th antenna at D, respectively. The metric is thenM(y(t,X)|Xˆ) = −Lr∑j=1∫ nf (N+1)T0∣∣∣∣∣yj(t,X)−N∑i=1[βihRiDhSRisi(t, Xˆi)]− hSDN+1∑i=1si(t, Xˆi)∣∣∣∣∣2dt.(5)IV. NUMERICAL RESULTSIn the following simulations we use 4-CPFSK and the dataframes consist of 130 4-ary symbols. Quasi-static Rayleigh flatfading is assumed, so that the fading coefficients are constantover the cooperation frame of N + 1 intervals required tosend a data frame. They are modelled as complex Gaussianrandom variables with mean 0 and variance 12 per dimension.We let the signal to noise ratio (SNR) of the links Ri → Dfor 1 ≤ i ≤ N and S → D be equal and denoted SNRD =10 log10(EbN0)dB, where Eb is the bit energy and N0 is theone-sided noise power spectral density. We assume the SNRof the links S → Ri for 1 ≤ i ≤ N to be SNRR = SNRD+ 10 dB. This would be approximately true if the source andrelays were near each other and the destination was locatedfar away1. It was shown in [5] that TSTC design rules may1SNRR > SNRD is required for relaying to offer significant benefits [5].Authorized licensed use limited to: University of Canterbury. Downloaded on May 14, 2009 at 21:26 from IEEE Xplore.  Restrictions apply.358 IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 5, MAY 20085 10 15 20 2510−410−310−210−1100SNR D  (dB)Frame error rate  EXT−IEXT−IIINo RelayLr=1Lr=4Lr=2Fig. 1. FER of DSTTC with 4-CPFSK and 1 relay (1 BPCU).5 10 15 20 2510−410−310−210−1100SNR D  (dB)Frame error rate  EXT−IEXT−IIILr=2Lr=4Lr=1Fig. 2. FER of DSTTC with 4-CPFSK and 2 relays ( 43BPCU).be used to design DSTTCs (with appropriate power control).In the examples, we use the optimized codes of2 [4].Fig. 1 shows the frame error rate (FER) performance of1-relay schemes using EXT-I and EXT-III, where G(D) =[1 2+D1+2D], J(D) =[1−D D 2−D−D21+2D 2D+D21+2D]andr = 2. The performance with no relay is also shown. Eachscheme has a throughput of 1 BPCU, and is simulated withLr = 1, 2 and 4 antennas at D. For Lr = 1, EXT-III hasthe best performance and both cooperative schemes providegreater diversity than using direct transmission. For Lr = 2and 4, EXT-I outperforms EXT-III at low FER and bothstart to exhibit reduced diversity due to the amplification ofnRi over the Ri → D link. Increasing SNRR should delaythis reduction. At very low FER with Lr = 4 there is noimprovement using EXT-III instead of direct transmission.Fig. 2 shows the performance of cooperative relay schemes2Despite not having full rank, the STCs in [4] were shown to provideexcellent performance. For the same throughput, they outperform full rankdelay diversity using CPFSK.with 2 relays, where G(D) =[1 0 2D0 1 1 + 2D], J(D) =[1−D D 0 0 2D −D2 2D20 0 1−D D 1 + D − 2D2 D + 2D2]andr = 1. The system throughput is 43 BPCU. The relativeperformance of the two protocols is similar to that of the 1-relay systems. The performance of the system with no relayis not shown as it is unusably bad.V. CONCLUSIONWe have presented a distributed space-time trellis codedsystem employing CPFSK and a novel multi-relay protocol.Performance gains are achieved using AF cooperative relay-ing. As expected EXT-I provides the best performance forLr = 2 and 4. Surprisingly EXT-III is superior for Lr = 1 inthe simulated range of SNRD.REFERENCES[1] J. B. Anderson, T. Aulin, and C.-E. W. Sundberg, Digital PhaseModulation. New York: Plenum, 1986.[2] M. P. Fitz and X. Zhang, “A case for continuous phase modulation inspace-time modems,” in Proc. Inform. Theory Workshop, Oct. 2002, pp.61–64.[3] J. K. Cavers, “Space-time coding using MSK,” IEEE Trans. WirelessCommun., vol. 4, no. 1, pp. 185–191, Jan. 2005.[4] R. L. Maw, “Space-time coded systems with continuous phasemodulation,” Ph.D. dissertation, Univ. of Canterbury, New Zealand,2007. [Online]. Available: http://www.library.canterbury.ac.nz[5] R. U. Nabar, H. Bolcskei, and F. W. Kneubuhler, “Fading relay channels:performance limits and space-time signal design,” IEEE J. Select. AreasCommun., vol. 22, no. 6, pp. 1099–1109, Aug. 2004.[6] J. N. Laneman and G. W. Wornell, “Distributed space-time-codedprotocols for exploiting cooperative diversity in wireless networks,”IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003.[7] Y. Jing and B. Hassibi, “Distributed space-time coding in wireless relaynetworks,” IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3524–3536, Dec. 2006.[8] A. Nosratinia, T. E. Hunter, and A. Hedayat, “Cooperative communica-tion in wireless networks,” IEEE Commun. Mag., pp. 74–80, Oct. 2004.[9] K. Azarian, H. El Gamal, and P. Schniter, “On the achievable diversity-mulitplexing tradeoff in half-duplex cooperative channels,” IEEE Trans.Inform. Theory, vol. 12, no. 51, pp. 4152–4172, Dec. 2005.[10] S. Yang and J.-C. Belfiore, “Towards optimal amplify-and-forwardcooperative diversity scheme,” submitted to IEEE Trans. Inform. Theory.[11] ——, “On slotted amplify-and-forward cooperative diversity schemes,”in Proc. ISIT, Seattle, USA, July 2006, pp. 2446–2450.[12] O. Mun˜oz, A. Agustı´n, and J. Vidal, “Cellular-capacity gains of cooper-ative mimo transmission in the downlink,” in Proc. Int. Zurich Seminaron Commun., Feb. 2004, pp. 22–26.[13] G. Wang, Y. Zhang, and M. Amin, “Differential distributed space-timemodulation for cooperative networks,” IEEE Trans. Wireless Commun.,vol. 5, no. 11, pp. 3097–3108, Nov. 2006.[14] R. L. Maw and D. P. Taylor, “Space-time coded systems with continuousphase frequency shift keying,” in Proc. GLOBECOM, vol. 3, Nov. 2005,pp. 1581–1586.[15] B. E. Rimoldi, “A decomposition approach to CPM,” IEEE Trans.Inform. Theory, vol. 34, no. 2, pp. 260–270, Mar. 1988.Authorized licensed use limited to: University of Canterbury. Downloaded on May 14, 2009 at 21:26 from IEEE Xplore.  Restrictions apply.

Cooperative Relaying with CPFSK and Distributed Space-Time Trellis Codes

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Cooperative Relaying with CPFSK and Distributed Space-Time Trellis Codes

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