Fast Efficient Coefficient Update for Filtered-X Affine Projection Algorithms

An efficient version of the affine projection (AP) algorithm, which is called FXAP-AC throughout the paper, is presented. This algorithm uses the filtered-x structure instead of the modified structure which is required for the implementation of the AP algorithm when the desired signal is not available, for instance in Active Noise Control (ANC) applications. The conventional AP algorithm for ANC, which is based on the modified structure (MFXAP), provides good performance. However the filtered-x structure is advisable for practical cases since it achieves a meaningful computational saving avoiding the additional filtering needed by the modified structure without significantly affect the performance in practice. This fact is specially important in multichannel applications where the computational resources are limited. Furthermore, different low-cost strategies already proposed in the conventional AP algorithm such as the fast error vector calculation or the efficient computation of coefficient update can be applied to the FXAP. Throughout this paper, the efficient computation of coefficient update is developed for the FXAP (resulting in the FXAP-AC). This strategy can be meaningfully combined with others previously reported to achieve very fast and robust FXAP algorithms. Experimental results validate the use of the proposed algorithm for practical applications.