Stochastic behavior analysis of the Gaussian Kernel Least Mean Square algorithm

Like its linear counterpart, the Kernel Least Mean Square (KLMS) algorithm is also becoming popular in nonlinear adaptive filtering due to its simplicity and robustness. The "kernelization" of the linear adaptive filters modifies the statistics of the input signals, which now depends on the parameters of the used kernel. A Gaussian KLMS has two design parameters; the step size and the kernel bandwidth. Thus, new analytical models are required to predict the kernel-based algorithm behavior as a function of the design parameters. This pa per studies the stochastic behavior of the Gaussian KLMS algorithm for white Gaussian input signals. The resulting model accurately predicts the algorithm behavior and can be used for choosing the algorithm parameters in order to achieve a prescribed performance.