Convergence analysis of the conventional filtered-x affine projection algorithm for active noise control

The conventional filtered-x affine projection (CFxAP) algorithm has been proposed for active noise control due to its potential good convergence and moderate computationally cost. Although some work has been done to analyze the convergence performance of the CFxAP algorithm, they usually adopted relatively strong approximations and hence came to inaccurate results especially at the steady-state. In this paper, we propose a new theoretical model for the CFxAP algorithm to address this problem. The recursion of an augmented weight-error vector is constructed, which is adopted for the mean and mean-square performance analysis of the CFxAP algorithm. Both the correlation between the past weight-error vectors and the dependency of weight-error vectors on past noise vectors are fully considered in our theoretical model. In addition, the treatment does not impose any restriction to the signal distributions. Simulation results show that our theoretical results are more accurate than the previous methods.