A Comparison of MCMC and AMP Symbol Detectors for Single-Carrier Underwater Acoustic Communications

Markov chain Monte Carlo (MCMC) and approximate message passing (AMP), as two typical approximate Bayesian inference approaches, have been extensively investigated in symbol detection for underwater acoustic (UWA) communications. Both types of symbol detectors have shown advantages over classical linear minimum mean squared error (LMMSE) symbol detector. However, it is unclear which detector shall be preferred from a point view of practical use. Motivated by this fact, we make a comparison between MCMC and AMP symbol detectors in terms of performance and complexity. Without loss of generality, a single-carrier UWA communication system is considered. Analytical results show MCMC-type detectors have higher complexity than AMP-type detectors. As to performance, experimental results indicate a standard MCMC detector using Gibbs sampler is inferior to a vector AMP (VAMP) detector. However, in light of the matrix splitting technique in form of successive over-relaxation (SOR), an SOR-MCMC detector with proper relaxation parameter can be comparable to the VAMP detector.