Fractional-order hyperbolic tangent adaptive algorithm for vehicular acoustic echo cancellation

In vehicle environments, echo cancellation is often severely compromised by non-Gaussian impulsive noise, challenging the capabilities of conventional adaptive filtering techniques. To address this issue, this paper proposes a fractional-order hyperbolic tangent adaptive filtering (FoHTAF) algorithm, which advances existing hyperbolic tangent cost function-based methods from two key perspectives: enhancing noise adaptability through a more flexible nonlinear function and systematically formulating a fractional-order gradient strategy using principles of fractional calculus, leveraging the fractional chain rule to modulate the adaptation process. Moreover, theoretical analysis is provided, establishing steady-state mean-square deviation and convergence bounds. The analytical findings are corroborated through numerical simulations, demonstrating close alignment with theoretical predictions. Double-talk echo cancellation experiments are conducted. Time-frequency domain evaluations consistently verify the superior robustness and effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noise.