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...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.展开更多
为了解决LMS(least mean square)算法中收敛速度和稳态误差之间的矛盾,基于独立假设,以最小均方误差为准则,提出并证明最优步长定理,说明最优步长和均方误差之间存在一一映射的关系;以此构造最优变步长LMS(optimal variable step-sizeLM...为了解决LMS(least mean square)算法中收敛速度和稳态误差之间的矛盾,基于独立假设,以最小均方误差为准则,提出并证明最优步长定理,说明最优步长和均方误差之间存在一一映射的关系;以此构造最优变步长LMS(optimal variable step-sizeLMS,OVS-LMS)模型,确定了变步长LMS算法收敛速度的理论极限;讨论了最优初始相对步长的选取方法和未知系统跳变时最优步长的计算。根据导出的两个最优步长迭代式,提出OVS-LMS算法,仿真结果表明,该算法和OVS-LMS模型的学习曲线基本一致,证明该算法是独立假设条件下的最优变步长LMS算法。展开更多
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.
文摘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.
文摘为了解决LMS(least mean square)算法中收敛速度和稳态误差之间的矛盾,基于独立假设,以最小均方误差为准则,提出并证明最优步长定理,说明最优步长和均方误差之间存在一一映射的关系;以此构造最优变步长LMS(optimal variable step-sizeLMS,OVS-LMS)模型,确定了变步长LMS算法收敛速度的理论极限;讨论了最优初始相对步长的选取方法和未知系统跳变时最优步长的计算。根据导出的两个最优步长迭代式,提出OVS-LMS算法,仿真结果表明,该算法和OVS-LMS模型的学习曲线基本一致,证明该算法是独立假设条件下的最优变步长LMS算法。
