Low-Complexity Detection/Equalization 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 {\em message/belief damping}, and 2) use of Factor Graph (FG) based graphical model with {\em Gaussian approximation of interference} (GAI). The per-symbol complexities are $O(K^2n_t^2)$ 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.