An alternate view of nonlinear adaptive filters

Nonlinear adaptive filters have been developed mostly using polynomial models such as truncated Volterra series, Weiner and Hammerstein models and utilizing linear adaptive algorithms such as NLMS, RLS, APA. Recently, there have been Kernel methods introduced to transform nonlinear adaptive filtering problems to a linear space where these well-known linear adaptive filter algorithms can also be used. Some of the key issues to be resolved when using recently popularized Kernel adaptive filters include (i) need to accommodate complex data (ii) need to select a proper kernel function (iii) need for regularization and (iv) need for curtailing the growth of the filter structure. In this paper, we compare performance of some of our recently-developed nonlinear adaptive algorithms based on Volterra, Wiener and Hammerstein models. We have applied these algorithms to real applications with good results. We also present a complex Kernel APA algorithm for nonlinear channel equalization. We study the concept of "surprise" as a statistical criterion for kernel adaptive filters and its use in a sparsification scheme to curtail the growth of the adaptive filter.