Optimal variable step-size LMS model and algorithm with independence assumption  

作　　者：谷源涛 唐昆 崔慧娟 杜文 

机构地区：[1]State Key Laboratory on Microwave and Digital Communications,Department of Electronics Engineering,Tsinghua University,Beijing 100084,China

出　　处：《Science in China(Series F)》2003年第6期409-419,共11页中国科学（F辑英文版）

基　　金：This work was supported in part by the National Fundamental Research Program(Grant No.G1998030406);the National Natural Science Foundation of China(Grant No.69972020);by the State Key Lab on Microwave and Digital Communications,Department of Electronics Engineering,Tsinghua University.

摘　　要：To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.

关 键 词：LMS OVS-LMS variable step-size optimal step-size theorem. 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]