Abstract-In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are ( 2 2 ) and ( ) for the MRF and the FG with GAI approaches, respectively, where and denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large . From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing . Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of -QAM symbol detection.Index Terms-Factor graphs, graphical models, large dimensions, low-complexity detection, Markov random fields, multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels, pairwise interaction, severe delay spreads.

Abstract-In this paper, we are concerned with low-complexity detection in large multiple-input multiple-output (MIMO) systems with tens of transmit/receive antennas. Our new contributions in this paper are two-fold. First, we propose a lowcomplexity algorithm for large-MIMO detection based on a layered low-complexity local neighborhood search. Second, we obtain a lower bound on the maximum-likelihood (ML) bit error performance using the local neighborhood search. The advantages of the proposed ML lower bound are i) it is easily obtained for MIMO systems with large number of antennas because of the inherent low complexity of the search algorithm, ii) it is tight at moderate-to-high SNRs, and iii) it can be tightened at low SNRs by increasing the number of symbols in the neighborhood definition. Interestingly, the proposed detection algorithm based on the layered local search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher-order QAM. For e.g., in a 32 × 32 V-BLAST MIMO system, the proposed detection algorithm performs close to within 1.7 dB of the proposed ML lower bound at 10 −3 BER for 16-QAM (128 bps/Hz), and close to within 4.5 dB of the bound for 64-QAM (192 bps/Hz).

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Abstract-Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 × 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10 −3 uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme. Keywords -Non-orthogonal STBCs, large dimensions, low-complexity near-ML decoding, tabu search, high spectral efficiencies.I. INTRODUCTION MIMO systems that employ non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) for arbitrary number of transmit antennas, N t , are attractive because they can simultaneously provide both full-rate (i.e., N t complex symbols per channel use, which is same as in V-BLAST) as well as full transmit diversity [1], [2]. The 2 × 2 Golden code is a well known non-orthogonal STBC from CDA for 2 transmit antennas [3]. High spectral efficiencies of the order of tens of bps/Hz can be achieved using large non-orthogonal STBCs. For e.g., a 16 × 16 STBC from CDA has 256 complex symbols in it with 512 real dimensions; with 16-QAM and rate-3/4 turbo code, this system offers a high spectral efficiency of 48 bps/Hz. Decoding of non-orthogonal STBCs with such large dimensions, however, has been a challenge. Sphere decoder and its low-complexity variants are prohibitively complex for decoding such STBCs with hundreds of dimensions. Recently, we proposed a low-complexity near-ML achieving algorithm to decode large non-orthogonal STBCs from CDA; this algorithm, which is based on bitflipping approach, is termed as likelihood ascent search (LAS) algorithm [4]- [6]. In this paper, we present a reactive tabu search (RTS) based approach to near-ML decoding of nonorthogonal STBCs with large dimensions.