Steady-State Mean Square Performance of the Multichannel Filtered-X Affine Projection Algorithm

This paper provides a unified analysis of the steady-state behavior of different multichannel filtered-x affine projection algorithms when used in active noise control (ANC) systems. The analysis deals with two different filtering schemes: the modified filtered-x affine projection (MFXAP) algorithm, with the modified filtered-x structure embedded, that has been studied in previous works, and the filtered-x affine projection (CFXAP) algorithm, with the conventional filtered-x structure embedded, that becomes the main contribution of this work. This study is based on energy conservation principles and does not require a specific signal distribution. The derived theoretical models allow to accurately predict the steady-state performance of the considered algorithms for moderate AP orders and low step sizes
$\mu$
. Simulation results obtained in practical ANC systems validate both the analysis and the achieved expressions, showing a relative good match between theory and practice.