Widely linear kernel-based adaptive filters

Widely linear estimation for complex-valued signal processing is growing in popularity, especially in the cases where the involved signals exhibit non-circular characteristics. In this paper, the extended Wirtinger´s calculus in complex Reproducing Kernel Hilbert Spaces (RKHS), presented in [1], is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of widely linear filters, which, to our knowledge, haven´t been considered before. Our results indicate that, in contrast to many cases where the gains from adopting widely linear estimation filters, instead of ordinary linear filters, are rudimentary, for the case of kernel-based widely linear filters significant performance improvements can be obtained.