A Bayesian Receiver for Semiblind Equalization in Sparse Underwater Acoustic Channels Using Bernoulli Priors

Underwater acoustic channels are characterized by sparse channel structures, where very few significantly strong non-zero taps exist out of long delay spreads. Though some existing works typically have attempted to take advantage of the sparsity of multipath channels, substantial performance improvement remains elusive. In this work, we develop an iterative Markov chain Monte Carlo (MCMC) algorithm based on Gibbs sampling designed for sparse channels. We decompose the sparse channel response into components of sparsity pattern and sparse coefficient, and incorporate the sparse structure of channels in Bernoulli prior probability distribution for sparsity pattern. We derive the posterior distributions of both sparsity pattern and sparse coefficient components, thereby sampling of sparse channels could be obtained. Furthermore, our proposed algorithm is also generalizable to time-varying underwater acoustic channels. Numerical results are provided to demonstrate performance of our proposed algorithm.