Statistical analysis of the FXLMS algorithm about the steady-state solution

Abstract

This paper presents a statistical analysis of the filtered-x LMS algorithm about the steady-state solution. Analytical models are derived for the mean weight-error vector and the mean square error behaviors which are simpler than existing models. The simpler models allow the determination of new convergence and steady-state results that should prove useful for design purposes. Simulation results display excellent agreement between theoretical predictions and Monte Carlo simulation results. Examples show that the new theory can be used to predict both transient and steady-state behaviors of the FXLMS algorithm in active control of sound and vibration.