Practical regularization of the affine projection algorithm

It is well-known that a matrix inversion is required within the affine projection algorithm (APA). Depending on the character of the input signal, this matrix can be very ill-conditioned. Consequently, it needs to be regularized before inversion, i.e., a positive constant is added to the elements of its main diagonal. Also known as the regularization parameter, this constant plays a major role in practice; if it is not chosen properly, the APA may never converge, especially under low signal-to-noise ratio conditions. The contribution of this paper is twofold. First, we provide a formula for choosing an “optimal” regularization parameter, aiming at attenuating the effects of the noise in the adaptive filter estimate. Second, two practical ways for evaluating this parameter are proposed. Simulations performed in the context of acoustic echo cancellation (in different noisy environments) prove the validity of the proposed solutions.