Analysis of explicit regularization in affine projection algorithms: Robustness and optimal choice

The affine projection algorithms (APA) are a family of adaptive filters with decorrelating properties. In this paper we propose the use of a time-varying explicit regularization factor instead of the classic step size control. We show that APA results stable and has robust performance against disturbances and model uncertainties. This fact is shown by the H
^∞
optimality and error energy bounds we provide. Finally, we find the optimal regularization choice for maximum speed of convergence. We consider first the case under independence assumptions and then with Gaussian hypothesis.