Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

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 O(K²n_t²) and O(Kn_t) for the MRF and the FG with GAI approaches, respectively, where K and n_t 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 Kn_t. From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Kn_t. 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 M-QAM symbol detection.