Statistical analysis of multichannel FxLMS algorithm for narrowband active noise control

This paper analyzes the statistical performance of a multichannel narrowband active noise control (NANC) system based on the filtered-x least mean square (FxLMS) algorithm. The difference equations for the mean and mean square transient convergence behavior of the multichannel NANC system are derived. Steady-state expressions for weight-errors and mean square errors are then developed in closed forms. Stability boundaries for the multichannel FxLMS algorithm in the mean and mean square sense are also derived. When considering the mean square convergence, the coupling between the cross secondary paths and different frequencies is considered skillfully by matrixing and vectorization operations. Ex-tensive simulations verify the accuracy of the theoretical analysis. Our findings deepen the understanding of the transient and steady-state behaviors of the multichannel NANC system and provide guidance for algorithm design, facilitate its improvement, and assist in parameter selection. (c) 2022 Elsevier B.V. All rights reserved.