Vector approximate message passing based symbol detection for orthogonal frequency division multiplexing underwater acoustic communications over fast-varying channels

In this paper, we propose an approximate Bayesian soft symbol detector (SSD) for multi-input multi-output (MIMO) orthogonal frequency division multiplexing underwater acoustic communications over fast time-varying channels. It is enabled by vector approximate message passing (VAMP) algorithm coupled with expectation-maximization (EM) technique, thus is named the EM-VAMP-SSD. The EM-VAMP-SSD consists of an inner soft slicer and an inner soft estimator (ISE), iteratively exchanging extrinsic information to improve symbol estimation performance. The operation of the ISE requires knowledge about channel and noise power, which are estimated via the orthogonal matching pursuit algorithm and the EM algorithm, respectively. To reduce the complexity of ISE, the frequency-domain MIMO channel is approximated by a block diagonal matrix without sacrificing performance much. The proposed EM-VAMP-SSD has been verified by both numerical and experimental data, showing consistent performance advantage over a conventional linear minimum mean square error SSD.