Fast Affine Projection Algorithms for Filtered-x Multichannel Active Noise Control

In recent years, affine projection algorithms have been proposed for adaptive system applications as an efficient alternative to the slow convergence speed of least mean square (LMS)-type algorithms. Whereas much attention has been focused on the development of efficient versions of affine projection algorithms for echo cancellation applications, the similar adaptive problem presented by active noise control (ANC) systems has not been studied so deeply. This paper is focused on the necessity to reduce even more the computational complexity of affine projection algorithms for real-time ANC applications. We present some alternative efficient versions of existing affine projection algorithms that do not significantly degrade performance in practice. Furthermore, while in the ANC context the commonly used affine projection algorithm is based on the modified filtered-x structure, an efficient affine projection algorithm based on the (nonmodified) conventional filtered-x structure, as well as efficient methods to reduce its computational burden, are discussed throughout this paper. Although the modified filtered-x scheme exhibits better convergence speed than the conventional filtered-x structure and allows recovery of all the signals needed in the affine projection algorithm for ANC, the conventional filtered-x scheme provides a significant computational saving, avoiding the additional filtering needed by the modified filtered-x structure. In this paper, it is shown that the proposed efficient versions of affine projection algorithms based on the conventional filtered-x structure show good performance, comparable to the performance exhibited by the efficient approaches of modified filtered-x affine projection algorithms, and also achieve meaningful computational savings. Experimental results are presented to validate the use of the algorithms introduced in the paper for practical applications.