Mean Square Convergence of Reproducing Kernel for Channel Identification: Application to Bran D Channel Impulse Response

Abstract

Nowadays, in the field of nonlinear system identification, the function approximation builds on the theory of reproducing kernel Hilbert spaces (RKHS) is of high importance in kernel-based regression methods. In this paper, we are focused on the finite impulse response identification problem for single-input single-output (SISO) nonlinear systems, whose outputs are detected by binary value sensors. In the one hand, we have used kernel adaptive filtering methods, such as, kernel least mean square (KLMS) and kernel normalized least mean square (KNLMS) to identify the practical frequency selective fading channel called Broadband Radio Access Network (BRAN). In the other hand, the mean square convergence is also investigated to indicate the robustness of the kernel normalized LMS algorithm. Monte Carlo simulation results in noisy environment and for various data length, shows that the kernel-normalized LMS algorithm can provide superior accuracy as opposed to the kernel-based LMS algorithm.