Exact expectation analysis of the deficient-length LMS algorithm

• Published in: Signal processing Vol. 162; pp. 54 - 64
• Main Authors: Lara, Pedro, Tarrataca, Luís D.T.J., Haddad, Diego B.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2019
• Subjects: Adaptive filtering; Deficient-length configuration; Exact expectation analysis; Adaptive filtering; Exact expectation analysis; Deficient-length configuration
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2019.04.009

•We provided further details of the proposed method which aim to clarify the analysis.•The overall context organization of the work has been changed in order to improve readability.•We emphasised what are the main advantages/disadvantages of our method when compared against the classical approach. Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of interest, they by themselves may hamper the modeling accuracy. This paper simultaneously avoids for the first time the employment of two ubiquitous assumptions often adopted in the analysis of the least mean squares (LMS) algorithm. The first of them is the so-called independence assumption, which presumes statistical independence between adaptive coefficients and input data. The second one assumes a sufficient-order configuration, in which the lengths of the unknown plant and the adaptive filter are equal. State equations that characterize both the mean and mean square performance of the deficient-length configuration without using the independence assumption are provided. The devised analysis, encompassing both transient and steady-state regimes, is not restricted neither to white nor to Gaussian input signals and is able to provide a proper step size upper bound that guarantees stability.