Mean-square-deviation analysis of probabilistic LMS algorithm

• Published in: Digital signal processing Vol. 92; pp. 26 - 35
• Main Authors: Huang, Fuyi, Zhang, Jiashu, Zhang, Sheng
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2019
• Subjects: Adaptive filter; Least-mean-square; Mean-square-deviation; Performance analysis; Probabilistic model; Variable step-size; Mean-square-deviation; Probabilistic model; Adaptive filter; Performance analysis; Least-mean-square; Variable step-size
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1016/j.dsp.2019.05.003

A stochastic analysis of the probabilistic least-mean-square (Prob-LMS) algorithm would be a useful guideline for designing the adaptive filter. However, no analytical expressions for the stochastic analysis of the Prob-LMS algorithm have been reported in the literature. Hence, this paper analyzes the mean-deviation and mean-square-deviation (MSD) behavior of the Prob-LMS algorithm for the general case of an unknown Gauss-Markov channel. Analytical expressions are derived for the transient and steady-state MSD of the Prob-LMS algorithm. Monte Carlo simulations for fixed and time varying channels show excellent agreement between the simulated and theoretical MSD for a wide range of parameters such as SNR, filter length and input signal statistics. Monte Carlo MSD simulation results are presented for the Prob-LMS algorithm which compare favorably to several well-known VSS algorithms.