Title: A robust non-parametric VSS-NLMS algorithm based on the error autocorrelation

Authors: José Gil Fausto Zipf

Addresses: Department of Electrical Engineering, FURB – Universidade Regional de Blumenau, Rua São Paulo, 3250, 89030-000, Blumenau, SC, Brazil

Abstract: Variable step-size least-mean-square (VSSLMS) algorithms have huge practical importance, since they exhibit a better performance as compared with those using fixed step size, allowing to obtain, simultaneously, both higher convergence speed and smaller error misadjustment. However, the performance of most VSSLMS adaptive filters is strongly affected by measurement noise. Furthermore, different levels of noise require different adjustments of the algorithm parameters, which can be a hard task, especially when changes in noise power occur during the adaptive filter operation. This paper introduces a new non-parametric VSS normalised LMS (VSS-NLMS) algorithm based on the error autocorrelation. Such an algorithm requires neither parameter adjustment nor prior knowledge of the measurement noise variance. The strategy used here enhances the algorithm immunity to noise power fluctuation. In addition, a stochastic analysis of the proposed algorithm is presented. Numerical simulation results confirm the effectiveness of the proposed approach.

Keywords: system identification; least-mean-squares algorithm; adaptive filters; error autocorrelation; variable step-size algorithms; adaptive algorithms; noise cancellation; telecommunications; channel equalisation; echo cancellation.

DOI: 10.1504/IJMIC.2025.150862

International Journal of Modelling, Identification and Control, 2025 Vol.46 No.2, pp.111 - 123

Received: 03 Jun 2024
Accepted: 27 Aug 2025
Published online: 24 Dec 2025 *

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