A Variable Regularization Method for Affine Projection Algorithm

The affine projection algorithm (APA) is a generalization of the normalized least mean square algorithm. We propose a variable regularization factor for the APA. Instead of the conventional assumption that the a posteriori error is zero, we incorporate the statistical characteristic of the noise into the adaptation process based on a system identification setup. Exact and approximate formulations for the optimal regularization factor are derived. Numerical simulation results show that the proposed algorithm improves the performance of the APA in terms of its convergence rate and steady-state misalignment.