Steady-state performance of multichannel affine projection algorithms for active noise control

In the field of adaptive filtering, it is well known that affine projection (AP) algorithms lead to a good tradeoff between convergence speed and computational load. For multichannel sound control, some computationally efficient AP (fast AP) algorithms have been recently proposed. This paper analyzes the steady-state mean square error of two efficient affine projection algorithms (representative of the different approaches) for multichannel active noise control (ANC) applications based on a different filtering-x scheme: the modified filtered-x affine projection (MFXAP) algorithm (with the modified filtered-x structure embedded) and the filtered-x affine projection (FXAP) algorithm (based on the conventional filtered-x structure). This study depends on energy conservation arguments and does not require a specific signal distribution. The theoretical models derived allow to accurately predict the steady-state performance of the algorithms considered. Simulation results obtained in practical single-channel and multichannel ANC systems validate the analysis and the derived expressions.