Abstract
The kernel methods are founded on the robust mathematical framework of reproducing kernel Hilbert spaces (RKHS), this space offers an important framework for the construction of nonlinear adaptive filters. In this paper, we present a comparative study between the kernel method in Hilbert space with a reproducing kernel, and linear adaptive algorithms, which are, least mean square (LMS), normalized least mean square (NLMS) and recursive least square (RLS) algorithms. The simulation results of the system are presented, which are simulated using MATLAB. These results show that the kernel algorithm has a good precision measured in terms of mean square error (MSE) compared to the linear adaptive algorithms, this by adopting the very fast fading channels called Broadband Radio Access Network (BRAN).KeywordsBRAN channelsIdentificationPositive definite kernelsHammerstein systemRKHSLMSNLMSRLS
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