A generic sphere-detection (SD) scheme is proposed, which substantially reduces the detection complexity by decomposing it into two stages, namely the generic iterative search-centre-update phase and the reduced-complexity search around it. This two-stage philosophy circumvents the high complexity of channel-coded soft-decision aided SDs

Chen, S.

Hanzo, L.

Wang, L.

Xu, L.

English

Southampton (e-Prints Soton)

Generic iterative search-centre-shiftingK-best sphere detection for rank-deﬁcientSDM-OFDM systemsL. Wang, L. Xu, S. Chen and L. HanzoA generic sphere-detection (SD) scheme is proposed, which substan-tially reduces the detection complexity by decomposing it into twostages, namely the generic iterative search-centre-update phase and thereduced-complexity search around it. Thistwo-stage philosophy circum-vents the high complexity of channel-coded soft-decision aided SDs.Motivation: The sphere detector (SD) constitutes acomputationallyefﬁ-cient solution to the maximum likelihood (ML) detection problem inuncoded multiple-input, multiple-output (MIMO) systems [1, 2].However, when employed in an iterative detection aided channelcoded system, the SD has to generate soft information for every trans-mitted bit, which requires the observation of a high number of hypoth-eses about the transmitted MIMO symbol, resulting in a potentiallyexcessive complexity. To answer the question concerning how to main-tain a near-ML performance with the aid of a small set of symbolhypotheses as posed in [1], we propose the centre-shifting scheme forSDs based on the novel discovery that, in contrast to the conventionalSD [1, 2], the SD’s search for the ML solution may be conﬁned to areduced search space centred at a point other than the MMSE solution.Generic iterative centre-shifting SD: Conventionally, in the scenarioof (M   N)-element spatial-division-multiplexing (SDM) orthogonal-frequency-division-multiplexing (OFDM) MIMO systems using a con-stant modulus modulation constellation size of Mc, the ML solutioncan be found according to [2]:^ sML ¼ arg min  s[MMcð^ s   ^ xcÞHðHHH þ s2wICÞð  s   ^ xcÞð 1Þby creating a reduced-size search space in the transmit MIMO-symboldomain centred on the MMSE solution x ˆc ¼ (HHH þ sw2I)HHy bychoosing an appropriate value for the maximum number of bestMIMO-symbol candidates K retained at each search level in the so-called K-best SD. Note that H is an (N   M)-dimensional frequency-domain channel transfer factor (FDCHTF) matrix with each columnrepresenting the unique FDCHTF of the corresponding transmitantenna and sw2 is the noise variance. This unique FDCHTF allowsthe separation of the M SDM streams, even if using N 4 M receiverantennas in the rank-deﬁcient scenario considered.During our investigations, we realised that it would be desirable to setthe SD’s search centre x ˆc to a high-probability MIMO signal constella-tion point, which may be expected to be closer to the true ML solutionthan the MMSE solution, because this would allow usto reduce the SD’ssearch space by opting for a small value of K and hence reduce its com-plexity. Our proposition is that the search centre be obtained by a moresophisticated detector, rather than by the conventional MMSE detector.This generic proposition turns the SD into a high-ﬂexibility detector,which can be beneﬁcially combined with arbitrarily sophisticated orlow-complexity linear or nonlinear detectors. In other words, the totalaffordable computational complexity can be ﬂexibly split between theSD’s search-centre calculation phase and the search phase. We willdemonstrate that an improved performance against complexity trade-off emerges, if the search-centre calculation is iteratively updated,especially by the improved estimates of a channel decoder.Fig. 1 Receiver architecture of generic iterative centre-shifting K-best SDschemeBased on these observations, we surmise that the generic centre-shift-ing scheme applied for the SD is expected to become signiﬁcantly morepowerful, if it is employed in the scenario of the iterative detection aidedchannel coded system of Fig. 1. This is because the iterative process ofobtaining a more accurate search centre is further aided by the channeldecoder, which substantially improves the total error-correction capa-bility of the iterative receiver. In comparison to the conventional SD-aided iterative receiver of [1], the generic search-centre-shifting receiverproposed in Fig. 1 has an additional functional block for calculating theiteratively updated search centre x ˆc. As an application example of thegeneric centre-shifting scheme, the MMSE soft-interference-cancella-tion (SIC-MMSE) algorithm of [3] is used. Hence, every time thesearch centre xc is updated, the SD is required to regenerate the candidatelist [1], which is used to calculate the extrinsic LLRs delivered to theouter channel decoder of Fig. 1.Fig. 2 BER performance improvement achieved by SIC-MMSE-aided itera-tive centre-shifting K-best SD receiver in scenario of (8   4)-element rank-deﬁcient 4-QAM SDM/OFDM systemApplication example: As shown in Fig. 2, the SIC-MMSE-aided iterativecentre-shifting K-best SD using K ¼ 16 is capable of approaching the per-formance of the iterative SD dispensing with centre-shifting and henceusing a large search space of K ¼ 1024, at a BER of 1025 in the highlyrank-deﬁcient 4QAM scenario of (8   4) MIMO elements. Furthermore,for a ﬁxed value of K, such as for example K¼ 32 and for the sametarget BER of 1025, we can observe that the iterative gain over the non-iterative soft-input-soft-output (SISO) receiver was doubled to about6 dB by the SIC-MMSE-aided centre-shifting scheme, when comparedto that achieved by the iterative SD dispensing with centre-shifting.Moreover, observe in Fig. 3 that the candidate list generation com-plexity of the SIC-MMSE centre-shifting-aided receiver, which is quan-tiﬁed in terms of the number of partial Euclidean distance (PED)evaluations, is well below that of the receiver using no centre-shiftingfor the SNR range spanning 2–12 dB. This statement is valid, if ouraim is to achieve the near-ML BER performance quantiﬁed in Fig. 2by setting K ¼ Ncand ¼ 16 in the presence of the centre-shifting scheme.Fig. 3 Candidate-list-generation-related computational complexity histo-gram of SIC-MMSE-aided iterative centre-shifting K-best SD (K ¼ 16)receiver in scenario of an (8   4)-element rank-deﬁcient 4-QAM SDM/OFDM systemELECTRONICS LETTERS 10th April 2008 Vol. 44 No. 8Conclusions: The proposed near-ML SD ﬁnds the search-centre usingan arbitrarily sophisticated or low-complexity detector and hence mayreduce the detection-candidate-list-generation-related complexity interms of the number of PED evaluations by an order of magnitude.As a further beneﬁt, the computational complexity of the extrinsicLLR calculation quantiﬁed in terms of the number of objective functionevaluations as shown in eqn. (12) of [1] was reduced by a factor of about64. The associated memory requirements were also reduced by a factorof 64.# The Institution of Engineering and Technology 200812 November 2007Electronics Letters online no: 20083279doi: 10.1049/el:20083279L. Wang, L. Xu, S. Chen and L. Hanzo (School of ECS, University ofSouthampton, Southampton SO17 1BJ, United Kingdom)E-mail: lw05r@ecs.soton.ac.ukReferences1 Hochwald, B.M., and ten Brink, S.: ‘Achieving near-capacity on amultiple-antenna channel’, IEEE Trans. Commun., 2003, 51,pp. 389–3992 Cui, T., and Tellambura, C.: ‘An efﬁcient generalized sphere decoder forrank-deﬁcient MIMO systems’, IEEE Commun. Lett., 2005, 9,pp. 423–4253 Tuchler, M., Singer, A.C., and Koetter, R.: ‘Minimum mean squarederror equalization using a priori information’, IEEE Trans. Acoust.Speech Signal Process., 2002, 50, pp. 673–683ELECTRONICS LETTERS 10th April 2008 Vol. 44 No. 8

Achieving near-capacity on a multiple-antenna channel’,

An efﬁcient generalized sphere decoder for rank-deﬁcient MIMO systems’,

Minimum mean squared error equalization using a priori information’,

Genetic iterative search-centre-shifting K-best sphere detection for rank-deficient SDM-OFDM systems

Genetic iterative search-centre-shifting K-best sphere detection for rank-deficient SDM-OFDM systems

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