Regularized Kernel Least Mean Square Algorithm with Multiple-delay Feedback

In the design of adaptive filters, feedback can be utilized to improve the convergence rate and filtering accuracy. This letter introduces a feedback structure with multiple delay to design kernel adaptive filters. A regularized loss function is minimized by using the steepest descent method. The past information of output is therefore reused to update the filter weights in a recurrent fashion, resulting in a novel regularized kernel least mean square algorithm with multiple-delay feedback (RKLMS-MDF). Compared with other kernel adaptive filters with or without feedback, RKLMS-MDF can improve the filtering performance from the respects of the convergence rate and the steady-state mean square error.