A general class of nonlinear normalized adaptive filtering algorithms (Q2723868)

The paper generalizes the normalized least mean squares algorithm (NLMS) to the nonlinear case. The motivation is the necessity of providing the LMS algorithm with a suitable time-varying step-size; this is particularly important in the nonlinear case where stability problems are particularly stringent. An auxiliary dimensionless fixed step-size is introduced in the general algorithm with stability region independent of the signal statistics. The general algorithm is applied to two specific filter structures: Volterra filters and the recently developed class of Myriad filters. Simulations show that the proposed algorithms have in general faster convergence than their LMS-type counterparts.