A novel iterative soft interference cancellation (SIC) aided beamforming receiver is developed for high-throughput quadrature amplitude modulation systems. The proposed SIC based minimum symbol error rate (MSER) multiuser detection scheme guarantees the direct and explicit minimization of the symbol error rate at the output of the detector. Adopting the extrinsic information transfer (EXIT) chart technique, we compare the EXIT characteristics of an iterative MSER multiuser detector (MUD) with those of the conventional minimum mean-squared error (MMSE) detector. As expected, the proposed SIC-MSER MUD outperforms the SIC-MMSE MUD. Index Terms—Beamforming, iterative multiuser detection, minimum symbol error rate, quadrature amplitude modulation

Chen, Sheng

Hanzo, L.

Tan, S.

English

A novel iterative soft interference cancellation (SIC) aided beamforming receiver is developed for high-throughput quadrature amplitude modulation systems. The proposed SICbased minimum symbol error rate (MSER) multiuser detection scheme guarantees the direct and explicit minimization of the symbol error rate at the output of the detector. Adopting the extrinsic information transfer (EXIT) chart technique, we compare the EXIT characteristics of an iterative MSER multiuser detector (MUD) with those of the conventional minimum mean-squared error (MMSE) detector. As expected, the proposed SIC-MSER MUD outperforms the SIC-MMSE MUD

Southampton (e-Prints Soton)

IEEE SIGNAL PROCESSING LETTERS, VOL. 15, 2008 301Iterative Multiuser Minimum Symbol Error RateBeamforming Aided QAM ReceiverShuang Tan, Sheng Chen, and Lajos HanzoAbstract—A novel iterative soft interference cancellation (SIC)aided beamforming receiver is developed for high-throughputquadrature amplitude modulation systems. The proposed SIC-based minimum symbol error rate (MSER) multiuser detectionscheme guarantees the direct and explicit minimization of thesymbol error rate at the output of the detector. Adopting the ex-trinsic information transfer (EXIT) chart technique, we comparethe EXIT characteristics of an iterative MSER multiuser detector(MUD) with those of the conventional minimum mean-squarederror (MMSE) detector. As expected, the proposed SIC-MSERMUD outperforms the SIC-MMSE MUD.Index Terms—Beamforming, iterative multiuser detection, min-imum symbol error rate, quadrature amplitude modulation.I. INTRODUCTIONITERATIVE detection principle, originally proposed in thecontext of turbo codes [1], [2], has found its way into iter-ative detector designs [3]–[6]. Most studies consider the min-imummean-squareerror(MMSE)softinterferencecancellation(SIC) aided iterative multiuser detector (MUD) [4]–[6]. How-ever, the MMSE algorithm does not guarantee the minimiza-tion of the system’s error rate. In [7] and [8], the bit error rate(BER), rather than the mean-square error, was minimized atthe MUD’s output for binary phase shift keying and quadraturephase shift keying signals. Yeh and Barry [9] have succeededin directly minimizing the detector’s symbol error rate (SER)for quadrature amplitude modulation (QAM) signals. Recently,a minimum SER (MSER) beamforming aided receiver has beendeveloped for QAM systems [10]. The concept of extrinsic in-formation transfer (EXIT) charts was introduced in [11]. Thissemi-analytic technique uses the mutual information (MI) be-tween the inputs and outputs of the concatenated receiver com-ponents in order to analyze their achievable performance. EXITcharts were employed in turbo equalization in [5], while in [12],they were used for examining the convergence properties of aturboMUD.ThenoveltyofthiscontributionisthatiterativeSICaidedMSERbeamformingisproposedforQAMsignals,anditsperformance is studied with the aid of EXIT charts.II. SYSTEM DESCRIPTIONThe system supports number of QAM users, and each usertransmits on the same angular carrier frequency . The receiverisequippedwithalinearantennaarrayconsistingof elements,which has a uniform element spacing of half wavelength. As-Manuscript received October 1, 2007; revised December 17, 2007. The as-sociate editor coordinating the review of this manuscript and approving it forpublication was Prof. Richard J. Kozick.The authors are with the School of Electronics and Computer Science, Uni-versity of Southampton, Southampton SO17 1BJ, U.K.Digital Object Identiﬁer 10.1109/LSP.2008.917792Fig. 1. Iterative multiuser beamforming receiver structure.sume that the channel is non-dispersive. Then the symbol-rate-sampled received signal can be expressed asfor , whereisthechannelcoefﬁcientofuser , isthe thsymbolofthe th user, is a complex-valued additive white Gaussiannoise process with , and is the rel-ative time delay at array element for the user signal, withbeing the direction of arrival for user . The received signalvector is given by, where ,, and the system ma-trix , with the steering vectors, .The iterative multiuser beamforming receiver’s structureis shown in Fig. 1, which consists of two stages, namely,the soft-input soft-output (SISO) interference cancellationaided beamforming MUD, followed by parallel single-userSISO channel decoders. The two stages are separated bythe usual bit-based deinterleavers and interleavers .The proposed SISO beamforming MUD ﬁrst determines thebeamformer weight vector according to the speciﬁcdesign criterion and provides an estimated symbol cor-responding to the transmitted symbol with the aid oflinear transformation . Let us deﬁne as theth bit of the -QAM symbol ,whereas is the same bit but in a different position ofthe bit-based interleaving block after the deinterleaver. ,, and denote the a priori, a posteriori, and extrinsicinformation in terms of logarithmic likelihood ratio (LLR),and the subscripts and are associated with the MUD andchannel decoder, respectively. Then the SISO beamformingMUD delivers the a posteriori information of bitexpressed in terms of its LLR as [6](1)where represents the a priori LLR of the in-terleaved and encoded bits , while rep-resents the extrinsic information delivered by the SISO MUD,1070-9908/$25.00 © 2008 IEEE302 IEEE SIGNAL PROCESSING LETTERS, VOL. 15, 2008Fig.2. Interference-affectedexpectation￿ ^ s oftheestimatedsignal ^ s whens = s and the decision boundaries.based on the received signal and the a priori informationabout the encoded bits of all users, except for the th bit of thedesired user . The extrinsic information is then deinterleavedand fed into the th user’s channel decoder, as the a priori in-formation in the next iteration.As seen in Fig. 1, between the banks of channel decoders andinterleavers,wecomputetheextrinsicLLRbasedontheaprioriinformation provided by the SISO MUD for theSISO decoder as [6],where theextrinsicinformation is gleaned from thesurroundingencoded bits, excluding the speciﬁc bit considered [6]. After in-terleaving, the extrinsic information delivered by the channeldecoders is fed back to the SISO MUD, as the a priori informa-tion concerning the encoded bits of all the users for exploitationduring the next iteration.III. SISO INTERFERENCE CANCELLATIONGiven the a priori LLRs, the mean and variance based onthe a priori information of the th user’s symbols are deﬁnedas [5]: and , where thesymbol-index was dropped for notational convenience.When using the SIC principle, the estimated symbol of usercan be expressed as [5]: , where.A. SISO Interference Cancellation Using the MMSE MUDClassically, the MMSE solution for the beamformer’s weightvector is expressed as [6](2)where is the average symbol energy, denotes theidentity matrix, and ,i nwhich denotes a diagonal matrix. The conditional prob-ability density function (PDF) , where isthe th legitimate value of the QAM con-stellation, may be assumed to be Gaussian distributed and thecorresponding extrinsic output LLR is given by [6](3)where denotes the th bit of , ,, and the a priori probability ofthe thbitinsymbol is.B. SISO Interference Cancellation Using the MSER MUDIn [10], the MSER algorithm is investigated when the MUDhas access to no a priori information. Under this condition,the subset PDFs conditioned on the different values of the esti-mated satisfy the shifting properties and are symmetricallydistributed [10]. However, when the MUD is provided with apriori information, these properties are invalid and the MSERmethod of [10] cannot be applied directly to our iterativesystem. Hence, we derive a new a priori information aidedMSER MUD. Deﬁne a symbol in the -QAM constellation as, whereand . Assumethat the th symbol combinationis transmitted, in which the desired user transmits symbol. Fig. 2 shows the estimated and its marginalPDFs. The PDF of is Gaussian distributed with a mean, as seen in Fig. 2. When the thuser transmits symbol , the conditional PDF of is aGaussian mixture deﬁned by(4)where is the proba-bility of transmitting the th possible symbol combination ,given the a priori information of the other users, exceptfor user .B yd e ﬁning for ,the decision boundaries of are determined by forthe in-phase component and by for the quadraturecomponent, as seen in Fig. 2. Fig. 2 only portrays the scenarioof the inner constellation point, which is enclosed by bound-aries. The points at the edge of the constellation may have openboundaries in one or two directions.TAN et al.: ITERATIVE MULTIUSER MINIMUM SYMBOL ERROR RATE BEAMFORMING AIDED QAM RECEIVER 303Assume that the th user transmits symbol . Thein-phase component’s conditional error probability ofcan be shown to be (also see [10])(5)Similarly, the quadrature component’s conditional error proba-bility of can be shown to be(6)The average error probabilities of the in-phase and quadraturecomponents are given, respectively, by(7)(8)The resultant SER can be formulated as, and the MSER solution is deﬁned as the one thatminimizes the upper bound of the SER given by(9)In order to arrive at an optimum MSER solution, we need thegradients of and in the context of the simpliﬁed con-jugate gradient algorithm [7], which can be derived from thegradients of the Q-functions in (5) and (6), leading to(10)and(11)where .The marginal conditional PDFs andcan both be assumed to be Gaussian dis-tributed. The means and variances of the in-phase and quadra-turecomponentsof aregivenby ,, and(12)(13)where ,, withand .Usingthe Gaussian distribution assumption, the extrinsic informationdelivered by the MSER MUD can be expressed as(14)when is mapped to the real part of , and(15)304 IEEE SIGNAL PROCESSING LETTERS, VOL. 15, 2008Fig. 3. EXIT charts and simulated trajectories of the iterative MMSE andMSER receivers supporting K =316QAM users at E =N =7 :5 dB.when is mapped to the imaginary part of , wheredenotes the th bit of and.IV. EXIT CHART ANALYSISThe EXIT chart analysis computes the MI between the LLRsand the corresponding bits [11]. An EXIT chart is shown inFig. 3 for the simulated system investigated in Section V. Letdenote the MI between the a priori values and the cor-responding bit-sequence, while denote the MI between theextrinsic values and the corresponding bit-sequence. TheEXIT function of the channel decoder is deﬁned by, which maps the input variable to the output vari-able , and the value of in the range character-izes the quality of the output LLRs of the decoder components.In the multiuser scenario, the MUD’s EXIT curve recorded forthe desired user depends on all the other users’ channeldecoder output MI. In our simulations, all the users’ signal-to-noise ratios (SNRs) are identical. Hence, the turbo MUD canaverage all the users’ MIs in order to simplify the EXIT chartfunction to .The output of one of the two constituent components is theinput of the other; hence, both transfer functions are shown inthe same EXIT plane having coordinate axes of ,. The staircase-shaped lines in Fig. 3, connectingthe MI points evaluated during each iteration, are referred to asthe detection trajectory. An inﬁnitesimally low BER may be at-tained, when there is a so-called open tunnel between the EXITcurves of the decoder and the MUD. This graphical represen-tation gives us an immediate insight into the number of de-tection iterations required for attaining the best possible BERperformance.V. SIMULATION RESULTSThe system employs a two-element antenna array to support16QAM users. All the users have the same transmitpower. Each user employs a different randomly generated inter-leaver. The interleaver length of each user is 2 bits. Allthe users have the same channel coefﬁcients of ,, and employ the same rate-1/2 and constraint-length4 non-systematic convolutional code using the octally repre-sented generators (15, 17). The arrival angles of the users’ sig-nals are 68 ,1 5, and , respectively.Fig. 4. SER comparison of the MMSE and MSER iterative beamforming re-ceivers for the 16QAM system supporting K =3users.Fig.3showstheEXITcurvesandthesimulatedtrajectoriesoftheiterativeMMSEandMSER16QAMbeamformingreceiversat . For this system, the MMSE and MSERMUDs have almost the same output value at both the axesat and . Between these two points of in-tersection, the MMSE MUD has the lower EXIT curve, and theMSER’s EXIT curve reaches a higher value. Fig. 4 showsthe SER versus SNR performance of the MMSE and MSERbeamforming receivers, in contrast to the single-user perfor-mance. It can be seen that after iterations, both the itera-tive systems approach the single-user performance. The MSERsystem has a lower operating SNR threshold, which is 0.8 dBlower than that of the MMSE system.REFERENCES[1] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limiterrorcorrectingcodinganddecoding:Turbocodes,”inProc.ICC1993,Geneva, Switzerland, May 1993, vol. 2, pp. 1064–1070.[2] S.Benedetto,D.Divsalar,G.Montorsi, andF.Pollara,“Serialconcate-nationofinterleaved codes:Performanceanalysis, design,anditerativedecoding,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 909–926, May1998.[3] C. Douillard, A. Picart, M. Jézéquel, P. Didier, C. Berrou, and A.Glavieux, “Iterative correction of intersymbol interference: Turbo-equalization,” Eur. Trans. Commun., vol. 6, pp. 507–511, Sep.–Oct.1995.[4] M. Tüchler, A. C. Singer, and R. Koetter, “Minimum mean squarederror equalization using a priori information,” IEEE Trans. SignalProcess., vol. 50, no. 3, pp. 673–6820, Mar. 2002.[5] M. Tüchler, R. Koetter, and A. C. Singer, “Turbo equalization: Prin-ciples and new results,” IEEE Trans. Commun., vol. 50, no. 5, pp.754–767, May 2002.[6] X. Wang and H. V. Poor, “Iterative (Turbo) soft interference cancella-tion and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47,no. 7, pp. 1046–1060, Jul. 1999.[7] S. Chen, N. N. Ahmad, and L. Hanzo, “Adaptive minimum bit errorrate beamforming,” IEEE Trans. Wireless Commun., vol. 4, no. 2, pp.341–348, Mar. 2005.[8] S. Chen, L. Hanzo, N. N. Ahmad, and A. Wolfgang, “Adaptive min-imum bit error rate beamforming assisted receiver for QPSK wirelesscommunication,” Digit. Signal Process., vol. 15, no. 6, pp. 545–567,Mar. 2005.[9] C.-C. Yeh and J. R. Barry, “Adaptive minimum symbol-error rateequalization for quadrature amplitude modulation,” IEEE Trans.Signal Process., vol. 51, no. 12, pp. 3263–3269, Dec. 2003.[10] S. Chen, H.-Q. Du, and L. Hanzo, “Adaptive minimum symbol errorrate beamforming assisted receiver for quadrature amplitude modula-tion systems,” in Proc. VTC 2006-Spring, Melbourne, Australia, May2006, vol. 5, pp. 2236–2240.[11] S. ten Brink, “Convergence behavior of iteratively decoded parallelconcatenated codes,” IEEE Trans. Commun., vol. 40, no. 10, pp.1727–1737, Oct. 2001.[12] K. Li and X. Wang, “Exit chart analysis of turbo multiuser detection,”IEEE Trans. Wireless Commun., vol. 4, no. 1, pp. 300–311, Jan. 2005.

Adaptive minimum bit error rate beamforming assisted receiver for QPSK wireless communication,” Digit.

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Adaptive minimum symbol error rate beamforming assisted receiver for quadrature amplitude modulation systems,” in

Adaptive minimum symbol-error rate equalization for quadrature amplitude modulation,”

codes:Performanceanalysis, design,anditerative decoding,”

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Exit chart analysis of turbo multiuser detection,”

Iterative (Turbo) soft interference cancellation and decoding for coded CDMA,”

Iterative correction of intersymbol interference:

Minimum mean squared error equalization using a priori information,”

Near Shannon limit errorcorrectingcodinganddecoding:Turbocodes,”inProc.ICC1993,

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Iterative Multiuser Minimum Symbol Error Rate Beamforming Aided QAM Receiver

Iterative Multiuser Minimum Symbol Error Rate Beamforming Aided QAM Receiver

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