The Augmented Complex Kernel LMS

TL;DR

This paper extends the complex kernel LMS framework by deriving widely-linear estimation filters using an augmented Wirtinger calculus, demonstrating notable performance improvements in kernel-based adaptive filtering.

Contribution

It introduces a novel derivation of complex kernel-based widely-linear filters using an extended Wirtinger calculus, highlighting their advantages over traditional linear filters.

Findings

Kernel-based widely-linear filters show significant performance gains.

The extended Wirtinger calculus facilitates the derivation of complex filters in Hilbert spaces.

Widely-linear filters outperform ordinary linear filters in certain complex data scenarios.

Abstract

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex Reproducing Kernel Hilbert Spaces, developed a suitable Wirtinger-like Calculus for general Hilbert Spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.