Robust Sparse Underwater Acoustic Channel Estimation Using a Bidirectional Proportionate Recursive Maximum Correntropy Criterion Algorithm

Aiming at the problem that sparse channel estimation in underwater acoustic communication is susceptible to complex multipath propagation, non-Gaussian impulsive noise, and channel time variations, this paper proposes a bidirectional proportionate recursive maximum correntropy criterion algorithm, referred to as Bi-PRMCC. By introducing a bidirectional filtering structure into the proportionate recursive maximum correntropy criterion (PRMCC) framework, the proposed algorithm jointly exploits the information from forward and backward data sequences, thereby improving the estimation accuracy and block-based channel variation tracking capability for sparse underwater acoustic channels. Meanwhile, the maximum correntropy criterion enhances the robustness of the algorithm against non-Gaussian impulsive noise and outlier error samples, while the proportionate update mechanism improves its identification capability for dominant taps in sparse channels. To verify the effectiveness of the proposed algorithm, short-range sparse underwater acoustic channels and long-range complex multipath underwater acoustic channels are constructed based on the Bellhop ray-tracing model. Simulation experiments are then conducted under three typical non-Gaussian noise environments, namely Cauchy noise, α-stable distribution noise, and Middleton noise. The experimental results show that, compared with recursive least squares (RLS), bidirectional recursive least squares (Bi-RLS), proportionate recursive least squares (PRLS), recursive maximum correntropy criterion (RMCC), and PRMCC, Bi-PRMCC achieves a lower steady-state normalized mean square deviation (NMSD) under different non-Gaussian noise conditions, indicating stronger robustness against impulsive noise. Under different signal-to-noise ratio conditions, the proposed algorithm still maintains superior steady-state estimation performance. In addition, in the channel abrupt-change tracking experiment, Bi-PRMCC can rapidly reconverge after channel variations occur, demonstrating favorable reconvergence capability under abrupt channel variations. The ablation study further verifies the stable performance gain brought by the bidirectional structure to PRMCC. Overall, the proposed Bi-PRMCC algorithm exhibits high estimation accuracy, robustness, and reconvergence capability under complex non-Gaussian noise and abrupt channel variation conditions.