Robust Filtered-x LMS Algorithm Based on Adjustable Softsign Framework for Active Impulsive Noise Control

For active control of impulsive noise, the conventional filtered-x least mean square (FxLMS) algorithm has poor noise reduction performance. To address this issue, this paper designs a robust cost function by embedding the cost function of the FxLMS algorithm into the framework of the adjustable Softsign function, thereby designing a robust Softsign-FxLMS (SFxLMS) algorithm for ANC systems. Furthermore, the parameter λ of the SFxLMS algorithm significantly influences its robustness and convergence speed. Therefore, a variable λ-parameter SFxLMS (VSFxLMS) algorithm is designed to improve the performance of the ANC system. Simulation studies indicate that the proposed SFxLMS algorithm and VSFxLMS algorithm exhibit stronger robustness, faster convergence rates, and better tracking performance compared to several robust FxLMS algorithms. Moreover, the symmetric properties of the proposed Softsign function contribute to balanced error suppression in both positive and negative directions, enhancing the robustness and stability of the ANC system under asymmetric impulsive noise conditions.