Switched Step-Size-Based Filtered-x NLMS Algorithm for Active Noise Control

While the filtered-x normalized least mean square (FxNLMS) algorithm is widely applied due to its simple structure and easy implementation for active noise control system, it faces two critical limitations: the fixed step-size causes a trade-off between convergence rate and steady-state residual error, and its performance deteriorates significantly in impulsive noise environments. To address the step-size constraint issue, we propose the switched step-size FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the mean-square deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different step-sizes, the optimal step-size for each iteration is selected. Furthermore, to enhance the algorithm’s robustness in impulsive noise scenarios, we integrate a robust strategy into the SSS-FxNLMS algorithm, resulting in a robust variant of it. The effectiveness and superiority of the proposed algorithms has been confirmed through computer simulations in different noise scenarios.