A variable step-size affine projection algorithm with a weighted projection matrix

In this paper, we present a forgetting factor scheme for variable step-size affine projection algorithms (APA). The proposed scheme uses a forgetting processed input matrix as the projection matrix of pseudo-inverse to estimate weight deviation. This method introduces time significances into the projection matrix, whereupon the evaluated error has been assigned some time characteristics and accordingly, it is closer to the real error´s behavior than that uses uniform time significances. It is shown that the proposed algorithm is superior in terms of convergence and misadjustment compared to existing algorithms. According to tremendous independent trials with various signals and parameters, the robustness and adaptation stability of the proposed algorithm are also demonstrated. As a special case, a variable step size NLMS algorithm with forgetting factor is also presented in this paper