The combination of the kernel trick and the least-mean-square (LMS) algorithm provides an interesting sample by sample update for an adaptive equalizer in reproducing Kernel Hilbert Spaces (RKHS), which is named here the KLMS. This paper shows that in the finite training data case, the KLMS algorithm is well-posed in RKHS without the addition of an extra regularization term to penalize solution norms. In this paper, we propose an algorithm for Kernel equalizers based on LMS algorithm with more simple computation, while the convergence rate will be adjusted based on the algorithm's control step size. The solution can be applied to the equalizers in OFDM satellite systems in order to reduce output errors and capacity of computation. | Novel adaptive equalizers for the nonlinear channel using the Kernel least mean squares algorithm
