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

TL;DR

This work tackles the fixed-step-size limitation and impulsive-noise vulnerability of FxNLMS-based active noise control by deriving an MSD-based analysis and introducing switched-step-size FxNLMS (SSS-FxNLMS). A robust variant, R-SSS-FxNLMS, further integrates a correntropy-inspired scaling $g[e_m]$ (MCC) to suppress impulsive disturbances, with an AD-enhanced version for colored noise. Theoretical MSD recursions guide per-iteration step-size selection, yielding fast convergence and lower steady-state error, validated across Gaussian, $\alpha$-stable, factory, and hammering noises. The results demonstrate improved ANC performance with imperfect secondary-path estimates and in non-Gaussian environments, highlighting practical applicability and robustness improvements over existing FxNLMS, VSS, and CC schemes, as well as potential extensions to dynamic step-size strategies.

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.

Figures (22)

• Figure 1: Diagram of a single-channel feedforward ANC system.
• Figure 2: ANR curves of the SSS-FxNLMS algorithm versus different $\rho$.
• Figure 3: ANR curves of the SSS-FxNLMS algorithm and standard FxNLMS algorithm with four fixed step-sizes in Gaussian white noise.
• Figure 4: The switching process of step-sizes in the SSS-FxNLMS algorithm.
• Figure 5: ANR curves of different algorithms in Gaussian white noise.