Statistical analysis of narrowband active noise control using a simplified variable step-size FXLMS algorithm

• Published in: Signal Processing Vol. 183; p. 108012
• Main Authors: Ma, Yaping, Xiao, Yegui, Ma, Liying, Khorasani, Khashayar
• Format: Journal Article
• Language: English; Japanese
• Published: Elsevier B.V 01.06.2021; Elsevier BV
• Subjects: Convergent behavior; Mean-squared error (MSE); Narrowband active noise control (NANC); Steady state analysis; Variable step-size FXLMS (VSS-FXLMS) algorithm; Convergent behavior; Narrowband active noise control (NANC); Mean-squared error (MSE); Variable step-size FXLMS (VSS-FXLMS) algorithm; Steady state analysis
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2021.108012

highlights•A simplified variable step-size FXLMS based narrowband ANC system is analyzed.•Difference equations describing the system dynamic behavior are derived.•Closed-form steady-state expressions are provided in mean and mean square senses.•Extensive simulations are conducted to confirm the analytical results.•The analytical findings provide guideline for selecting the user parameters. In this paper, an in-depth statistical analysis is conducted for a typical narrowband active noise control (ANC, NANC) system that is based on a simplified variable step-size (VSS) filtered-x least mean square (SVSS-FXLMS) scheme. Difference equations are derived first that describe the NANC system convergent behavior in both mean and mean square senses. Closed-form steady-state expressions are then derived for the mean residual noise power, the mean and mean squared VSSs as well as the mean squared errors (MSE) of the control filter weights. Extensive simulation results are conducted and provided to demonstrate, illustrate, and confirm validity of the developed analytical results. The obtained insights do significantly enhance our understanding of the dynamic and steady-state properties of the NANC system that is based on our proposed SVSS-FXLMS strategy.