Channel Identification of Non-linear Systems with Binary-Valued Output Observations Based on Positive Definite Kernels

Laboratory of Innovation in Mathematics, Applications and Information Technologies (LIMATI), Polydisciplinary Faculty, Sultan Moulay Slimane University, Po. Box 592, 23000 Beni Mellal, Morocco

^* Corresponding author: fateh.smi@gmail.com

Abstract

Nowadays, the kernel methods are increasingly developed, they are a significant source of advances, not only in terms of computational cost but also in terms of the obtained efficiencies in solving complex tasks, they are founded on the theory of reproducing kernel Hilbert spaces (RKHS). In this paper, we propose an algorithm for recursive identification of finite impulse response (FIR) nonlinear systems, whose outputs are detected by binary value sensors. This algorithm is based on a nonlinear transformation of the data using a kernel function. This transformation performs a basic change that allows the data to be projected into a new space where the relationships between the variables are linear. To test the accuracy of the proposed algorithm, we have compared it with another algorithm proposed in the literature, for that, we employ the practical frequency selective fading channel, called Broadband Radio Access Network (BRAN). Monte Carlo simulation results, in noisy environment and for various data length, demonstrate that the proposed algorithm can give better precision.