Impulsive noise can greatly affect the performance of underwater acoustic (UA) orthogonal frequency-division multiplexing (OFDM) systems. In this paper, by utilizing the sparsity of the UA channel impulse response and impulsive noise, we first propose a novel sparse Bayesian learning (SBL) based expectation maximization (EM) algorithm for joint channel estimation and impulsive noise mitigation in UA OFDM systems. Secondly, considering that the UA channel and impulsive noise are fast time-varying, we develop a new approach which combines the SBL with the forward-backward Kalman filtering to track the UA channel and impulsive noise. To further improve the system performance, we utilize the information available on data subcarriers for joint time-varying channel estimation and data detection, based on the SBL algorithm and the Kalman filter. The performance of our proposed algorithms is verified through both numerical simulations and by data collected during a UA communication experiment conducted in the estuary of the Swan River, Perth, Australia. The results demonstrate that compared with existing approaches, the proposed algorithms achieve a better system bit-error-rate and frame-error-rate performance.

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