On the steady‐state performance of bias‐compensated LMS algorithm

• Published in: Electronics letters Vol. 57; no. 2; pp. 85 - 88
• Main Authors: Pimenta, Rodrigo, Resende, Leonardo, Petraglia, Mariane R., Haddad, Diego B.
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.01.2021; Wiley
• Subjects: Adaptive algorithms; Adaptive filters; Algorithms; Bias; Energy; Expected values; Filtering methods in signal processing; Hypotheses; Interpolation and function approximation (numerical analysis); Noise; Reference signals; Signal processing; Signal processing theory; Simulation
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/ell2.12044

Adaptive filtering algorithms are widespread today owing to their flexibility and simplicity. Due to environments in which they are normally immersed, their robustness against noise has been a topic of interest. Traditionally, in the literature it is assumed that noise is mainly active in the reference signal. Since this hypothesis is often violated in practice, recently some papers have advanced strategies to compensate the bias introduced by noisy excitation data. The contributions of this paper are twofold. The first one establishes that, in some conditions, the bias‐compensated least mean square algorithm implements an optimum estimator, in the sense that it presents the smallest variance of the set of unbiased estimators. Since the asymptotic mean‐square performance of this algorithm has not yet been investigated in detail, the second contribution adopts an energy conservation relationship to derive its theoretical steady‐state mean squared distortion. The final result is presented in a closed form, is consistent with simulations and is able to provide important guidelines to the designer.