Selection of the convergence step of the Fx-LMS algorithm

• Published in: Signal processing 2023-10, Vol.211, p.109118, Article 109118
• Main Authors: Ferrer, Miguel, de Diego, Maria, García-Mollá, Víctor M., Gonzalez, Alberto
• Format: Article
• Language: English
• Subjects: Active noise control; Adaptive filtering; Convergence analysis; Filtered-x LMS
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2023.109118

•The convergence parameter of FxLMS is determined by a fast method.•It is based on energy estimation of the filtered reference signal in sub-bands.•The method requires low computational cost.•The convergence parameter can be calculated for any filtered reference signal.•It guarantees stability and fast convergence in practical cases. 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.