Equalization Algorithms for MIMO Communication Systems Based on Factor Graphs

Abstract

In this paper, we consider a bit-interleaved coded spatial multiplexing MIMO communication system over a frequency-selective MIMO channel. We present a factor-graphbased derivation of two different equalization algorithms. To this end, we propose a cycle-free factor graph representation of the equalizer, to which we apply the sum-product algorithm (SPA). By using different message representations in the SPA, the resulting equalization algorithms correspond to the optimal MAP equalizer and the low-complexity LMMSE equalizer, respectively. Both algorithms are soft-input soft-output equalization algorithms and can be used in turbo processing. We demonstrate that after 3 iterations the BER performance of the LMMSE equalizer is similar to that of the MAP equalizer.

A Low-Complexity Graph-Based LMMSE Receiver for MIMO ISI Channels With $M$ -QAM Modulation

“…Also, the complexity of the lately studied LMMSE equalizer in [18] which was proposed to implement using a different factor graph structure from ours is O(N N 3 t L 3 ) which is still greater than the complexity of the structure in this study. Moreover, although the result of the LMMSE estimation in [18] is the same as our graph output on Gaussian domain, it results in an error floor for large SNR values due to their LLR exchange algorithm between Gaussian and binary domains. Overall, our proposed LMMSE solution is a practical receiver for high data rate applications with its lower complexity than those presented in the literature and its close performance to matched filter bound to be presented in the subsequent section.…”

“…We conduct our simulations under quasi-static Rayleigh fading channels with independent ISI taps, i.e., each tap is constant over one block and change independently from block to block. The ISI channel between each transmit-receive antenna pair has identical, equal power delay profile similar to the studies in [4], [16], [18], i.e., all L taps have equal power which is normalized so that the total power of channel response is unity…”

“…2, are identical to each other. On the other hand, messages in [10], [18] piece-wisely defined on three different regions, which further complicates implementation. Hence, in this study, a graph structure is constructed using state space representation.…”

“…One can easily show the equivalency for the transient states following the same steps. In the following steps, (Σ, µ) denotes the messages in [18] with the corresponding indices.…”

Hybrid MCMC and LMMSE Detector for MIMO Frequency-Selective Channels

“…In our approach, we follow the lead in [2], [3] and [4] and use the factor graph (FG) model to graphically represent the factorization of the joint probability distribution of the transmitted symbols, which improves the visualization of the problem. Marginal distributions can be calculated on a FG using the sum-product algorithm (SPA) [2], also known as message-passing.…”