Theoretical convergence analysis of complex Gaussian kernel LMS algorithm  

作　　者：Wei Gao Jianguo Huang Jing Han Qunfei Zhang 

机构地区：[1]School of Marine Science and Technology,Northwestern Polytechnical University

出　　处：《Journal of Systems Engineering and Electronics》2016年第1期39-50,共12页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China(61001153;61271415;61401499;61531015);the Fundamental Research Funds for the Central Universities(3102014JCQ01010;3102014ZD0041);the Opening Research Foundation of State Key Laboratory of Underwater Information Processing and Control(9140C231002130C23085)

摘　　要：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 algonthms 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.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 algonthms 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.

关 键 词：nonlinear adaptive filtering complex Gaussian kernel convergence analysis non-circular data kernel least mean square（KLMS）. 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]