Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions, its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications. This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics. Then the theoretical convergence behavior of the complex Gaussian kernel least mean square (LMS) algorithm is studied by using the fixed dictionary strategy. The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algorithms using non-circular complex data. The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error (MSE) performance among of complex kernel LMS (KLMS) methods according to the specified kernel bandwidth and the length of dictionary.