Regularization of the improved proportionate affine projection algorithm

In sparse adaptive filters, the adaptation gain is “proportionately” redistributed among all the coefficients, emphasizing the large ones in order to speed up their convergence. The improved proportionate affine projection algorithm (IPAPA) is a very attractive choice for echo cancellation, since it combines the good convergence features of the affine projection algorithm (APA) and the gain factors of the improved proportionate normalized least-mean-square (IPNLMS) algorithm. Similar to the APA, a matrix inversion is required within the IPAPA. For practical reasons, the matrix needs to be regularized before inversion, i.e., a positive constant is added to the elements of its main diagonal. In this paper, we propose a formula for choosing the regularization parameter of the IPAPA, aiming at attenuating the effects of the noise in the adaptive filter estimate. Simulation results indicate the validity of this approach in both network and acoustic echo cancellation scenarios.