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

2026-01-23

AI Summary

This work addresses the limitations of the conventional filtered-x normalized least mean square (FxNLMS) algorithm, which suffers from a trade-off between convergence speed and steady-state error due to its fixed step size and exhibits significant performance degradation in impulsive noise environments. To overcome these issues, the paper proposes a switching step-size FxNLMS algorithm (SSS-FxNLMS) that dynamically selects the optimal step size at each iteration based on the trend of mean square deviation (MSD) and incorporates a robust mechanism to mitigate the adverse effects of impulsive noise. Implemented within the standard FxNLMS framework, the proposed method effectively balances convergence rate, steady-state error, and robustness against noise. Simulation results demonstrate that the SSS-FxNLMS algorithm consistently outperforms existing approaches across various noise conditions.

Technology Category

• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Semi-Supervised Learning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• active noise cancellation
• FxNLMS algorithm
• step-size trade-off
• impulsive noise
• steady-state error

Innovation

• switched step-size
• FxNLMS
• mean-square deviation
• impulsive noise robustness
• active noise cancellation