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Although the sparse kernel adaptive filtering algorithms have been proposed to address the problem of redundant dictionary in non-stationary environments, there is few attempt of analyzing their stochastic convergence behaviors. In this paper, we briefly review the zero-attracting kernel least-mean-square (ZA-KLMS) algorithm with $\ell _{1}$ -norm regularization from the perspective of nonlinear sparse system. Then, the theoretical transient convergence performance of ZA-KLMS algorithm using Gaussian kernel function with pre-tuned dictionary is analyzed in the mean and mean-square senses. The simulation results illustrate the accuracy of derived analytical models by the excellent consistency between the Monte Carlo simulations and the theoretical predictions, and the ZA-KLMS algorithm has better convergence performance than the KLMS algorithm for nonlinear sparse systems in stationary environment.

Transient Performance Analysis of Zero-Attracting Gaussian Kernel LMS Algorithm With Pre-Tuned Dictionary