Computationally efficient version of the affine projection algorithm for multichannel active noise control

A computationally efficient version of the affine projection (AP) algorithm avoiding matrix inversions is presented and developed for multichannel active noise control (ANC) systems. A comparative study of the classical multichannel filtered-x LMS (MFXLMS), the multichannel filtered-x affine projection (MFXAP) and its computationally efficient version, named here in after new multichannel filtered-x affine projection (NMFXAP) algorithm, is carried out. Those aforementioned algorithms have been simulated in a multichannel ANC system for local control. Simulations using real data have been carried out. The computational complexity of the algorithms is evaluated for different number of transducers. Although the proposed NMFXAP algorithm exhibits a slightly higher computational complexity than the MFXLMS, it keeps the convergence properties of the AP algorithms thus providing faster convergence speed than the MFXLMS. On the other hand, the NMFXAP shows a remarkable decrease of the number of operations per iteration compared to the MFXAP. This fact is due to a recursion used to calculate matrix inversions needed in the updating of the adaptive filter coefficients of the MFXAP algorithm. The proposed algorithm is specially suitable for real time multichannel ANC applications running on a Digital Signal Processing (DSP) card.