Digital Signal Processing with Kernel Methods

9Adaptive Kernel Learning for Signal Processing

9.1 Introduction

Adaptive filtering is a central topic in signal processing. An adaptive filter is a filter structure provided with an adaptive algorithm that tunes the transfer function, typically driven by an error signal. Adaptive filters are widely applied in nonstationary environments because they can adapt their transfer function to match the changing parameters of the system that generates the incoming data (Hayes 1996 ; Widrow et al. 1975). They have become ubiquitous in current DSP, mainly due to the increase in computational power and the need to process streamed data. Adaptive filters are now routinely used in all communication applications for channel equalization, array beamforming, or echo cancellation, to cite just a few, and in other areas of signal processing, such as image processing or medical equipment.

By applying linear adaptive filtering principles in the kernel feature space, powerful nonlinear adaptive filtering algorithms can be obtained. This chapter introduces the wide topic of adaptive signal processing, and it explores the emerging field of kernel adaptive filtering (KAF). Its orientation is different from the preceding ones, as adaptive processing can be used in a variety of scenarios. Attention is paid to kernel LMS and RLS algorithms, to previous taxonomies of adaptive kernel methods, and to emergent kernel methods for online and recursive KAF. MATLAB code snippets are included as well to illustrate ...