Study of Switched Step-size Based Filtered-x NLMS Algorithm for Active Noise Cancellation

TL;DR

This paper introduces a switched step-size FxNLMS algorithm for active noise cancellation that dynamically adjusts step-size for better convergence and incorporates robustness against impulsive noise, validated through simulations.

Contribution

It proposes a novel switched step-size strategy for FxNLMS and enhances robustness in impulsive noise environments, improving performance over traditional fixed-step algorithms.

Findings

The proposed algorithm achieves faster convergence.

It maintains lower residual error in steady state.

Robustness is improved in impulsive noise scenarios.

Abstract

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 \mbox{step-size} FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the \mbox{mean-square} deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different \mbox{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.