Iterative decision feedback equalization using a variable step-size hyperbolic secant adaptive filter algorithm for under-ice acoustic communication

Small man-portable unmanned underwater vehicles enhance exploration in under-ice environments while reducing deployment costs. Single-input single-output underwater acoustic communication systems are advantageous for these unmanned underwater vehicles due to their low power consumption, compact design, and user-friendliness. However, the lack of diversity gain in single-input single-output systems presents challenges in complex oceanic environments. Although under-ice underwater acoustic channels typically exhibit stability, impulsive noise severely degrades signal quality. Conventional Gaussian noise-based underwater acoustic communication equalizers may experience performance degradation even under moderate signal-to-noise ratio. To address the challenges of sparse multipath underwater acoustic channels and impulsive noise, this paper proposed an iterative decision feedback equalizer (DFE) based on a variable step-size sparse hyperbolic secant adaptive filtering (AF) algorithm. The key to this DFE is to make filter coefficient updates insensitive to outliers, while also introducing correntropy-induced metric to AF algorithm with norm constraints, and then optimizing trade-off between convergence speed and stability by a variable step-size method. Furthermore, the performance of the DFE is further improved by iterative fine-tuning of filter coefficients. Numerical simulations and under-ice experiments validate the superiority of the proposed equalization scheme, achieving approximately 2 dB improvement over alternative AF algorithm-based DFEs at a 1000 m communication distance.