Temporal Correlation and Message-Passing-Based Sparse Bayesian Learning Channel Estimation for Underwater Acoustic Communications

To mitigate the error propagation of single-carrier time-domain equalization (SC-TDE) with insufficient observation data, this article proposes a low-complexity message-passing-based SC-TDE algorithm. First, the temporal correlation (TC) between subblocks is exploited to improve the performance of conventional message-passing-based sparse Bayesian learning (SBL) when the data are insufficient. The proposed algorithm then models the channel estimation process as a hidden Markov model. It captures the TC property by utilizing a first-order autoregressive model, thus supporting the current subblock with a priori information from the previous subblock. By using belief propagation (BP), the TC and BP-based SBL algorithm (TC-BP-SBL) is derived, which is then approximated to obtain the TC and approximation-message-passing-based SBL (TC-AMP-SBL) with lower computational complexity. Finally, taking advantage of AMP and expectation propagation (EP), a two-layer iterative equalization algorithm is introduced for joint message passing. The inner iteration uses AMP for symbol estimation, and the outer iteration improves the equalization performance by EP based on deterministic approximate variational inference. The proposed algorithm is validated using data collected during the 11th Chinese Arctic Scientific Expedition. The results show that the proposed algorithm can significantly reduce the computational complexity of SC-TDE and effectively mitigate error propagation when the observation data are insufficient.