Affine-Projection-Like Adaptive-Filtering Algorithms Using Gradient-Based Step Size

A new class of affine-projection-like (APL) adaptive-filtering algorithms is proposed. The new algorithms are obtained by eliminating the constraint of forcing the a posteriori error vector to zero in the affine-projection algorithm proposed by Ozeki and Umeda. In this way, direct or indirect inversion of the input signal matrix is not required and, consequently, the amount of computation required per iteration can be reduced. In addition, as demonstrated by extensive simulation results, the proposed algorithms offer reduced steady-state misalignment in system-identification, channel-equalization, and acoustic-echo-cancelation applications. A mean-square-error analysis of the proposed APL algorithms is also carried out and its accuracy is verified by using simulation results in a system-identification application.