Selection of the convergence step of the Fx-LMS algorithme

The choice of a suitable convergence step that allows the fast convergence of the filtered-x LMS algorithm in practical scenarios is usually carried out by trial and error, since the theoretical developments provide only indicative values. The particularity of the filtered-x structure, which adds a delay between the output of the adaptive filter and the error signal and colors the reference signal, increases the inaccuracy of the theoretical models. Furthermore, the use of band-limited reference signals is beyond the scope of most theoretical studies, which focus on the cases of full-band reference signals, making it difficult to extrapolate these models to band-limited signals. In this paper, we propose a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases. It can be used regardless of the type of the reference signal, the system delays, and the nature of the filter required in the filtered-x structure. Numerical simulations are performed to validate the effectiveness of the proposed approach. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

Choosing a suitable convergence step for the filtered-x LMS algorithm is usually done through trial and error, as theoretical developments provide only indicative values. The filtered-x structure, which introduces delay and colors the reference signal, increases the inaccuracy of theoretical models. Most theoretical studies focus on full-band reference signals, making it difficult to extrapolate these models to band-limited signals. This paper proposes a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases, regardless of the reference signal, system delays, and the filter required in the filtered-x structure. Numerical simulations validate the effectiveness of the proposed approach.