A Sliding-Window Kernel RLS Algorithm and its Application to Nonlinear Channel Identification

Steven Van Vaerenbergh, Javier Via and Ignacio Santamaria
Dept. of Communications Engineering, University of Cantabria, Spain
E-mail: {steven,jvia,nacho}@gtas.dicom.unican.es

Abstract:

In this paper we propose a new kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, we combine a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional $L2$-norm regularization (to improve generalization). The proposed kernel RLS algorithm is applied to a nonlinear channel identification problem (specifically, a linear filter followed by a memoryless nonlinearity), which typically appears in satellite communications or digital magnetic recording systems. We show that the proposed algorithm is able to operate in a time-varying environment and tracks abrupt changes in either the linear filter or the nonlinearity.