Gibbs Sampling-based Sparse Estimation Method over Underwater Acoustic Channels

The estimation of sparse underwater acoustic (UWA) channels can be regarded as an inference problem involving hidden variables within the Bayesian framework. While the classical sparse Bayesian learning (SBL), derived through the expectation maximization (EM) algorithm, has been widely employed for UWA channel estimation, it still differs from the real posterior expectation of channels. In this paper, we propose an approach that combines variational inference (VI) and Markov chain Monte Carlo (MCMC) methods to provide a more accurate posterior estimation. Specifically, the SBL is first re-derived with VI, allowing us to replace the posterior distribution of the hidden variables with a variational distribution. Then, we determine the full conditional probability distribution for each variable in the variational distribution and then iteratively perform random Gibbs sampling in MCMC to converge the Markov chain. The results of simulation and experiment indicate that our estimation method achieves lower mean square error and bit error rate compared to the classic SBL approach. Additionally, it demonstrates an acceptable convergence speed.