Mean square analysis of a fast filtered-x affine projection algorithm

This paper provides an analysis of the steady-state behavior of the filtered-x affine projection algorithm (FXAP). This efficient affine projection (AP) algorithm for active noise control (ANC) applications is based on the filtered-x scheme, unlike most AP algorithms based on the more computationally demanding modified filtered-x scheme. This study depends on energy conservation arguments and does not require an specific signal distribution. The theoretical expressions derived for the mean square error (MSE) allowed to accurately predict the steady-state performance of the FXAP for meaningful practical cases. Simulation results of a single-channel ANC system validate the analysis and the theoretical expressions derived.