Abstract
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.
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