Theoretical convergence analysis of FxLMS algorithm

In system identification when a secondary path follows the adaptive filter, the FxLMS algorithm is usually applied for updating the adaptive filter. Although several FxLMS convergence analyses have been conducted in detail, only a few have intended to derive a convergence condition. In fact, available FxLMS convergence conditions are only accurate for simplified cases with pure delay secondary paths or multi-sinusoidal input signals. This paper studies the FxLMS convergence behavior for moving average secondary paths and stochastic input signals. A novel model for predicting the FxLMS convergence behavior is developed. Based on this model, a necessary and sufficient condition for the convergence of the FxLMS is derived. Also, the condition leading to the fastest convergence is proposed. Compared to previously derived convergence conditions, the proposed condition applies to more general secondary paths. Results obtained from this study are found to correspond very well to those obtained from simulation experiments. (C) 2010 Elsevier B.V. All rights reserved.