An efficient model for the convergence behavior of the fxlms algorithm with gaussian inputs

This paper presents a simple and efficient analytical model for the convergence behavior of the filtered-x LMS (FXLMS) algorithm with Gaussian input data. Deterministic recursions are obtained for the mean weight vector and the mean square error. The new model predicts the algorithm behavior for a wide range of practical applications. This model can be employed either when the adaptive filter lies after the secondary path filter or when their order is reversed in the cascade sequence. Simulation results display excellent agreement with the behavior predicted by the theoretical model for transient and steady-state phases of adaptation. The new simple model should be instrumental in designs systems for active control of sound and vibration.