双曲正切函数的新型变步长LMS算法  

New Variable Step Size LMS Algorithm Based on Hyperbolic Tangent Function

作　　者：李俊毅 邓志祥[1,2] LI Junyi;DENG Zhixiang(Jiangsu Key Laboratory of Power Transmission&Distribution Equipment Technology,Hohai University,Changzhou 213022;School of IoT Engineering,Hohai University,Changzhou 213022)

机构地区：[1]河海大学江苏省输配电装备技术重点实验室,常州213022 [2]河海大学物联网工程学院,常州213022

出　　处：《计算机与数字工程》2024年第8期2272-2278,共7页Computer & Digital Engineering

基　　金：江苏省输配电装备技术重点实验室自主科研课题(编号:2022JSSPD03)资助。

摘　　要：针对自适应最小均方误差(Least Mean Square,LMS)滤波算法迭代步长在算法收敛速度、稳态误差间的折中问题,设计了一种基于双曲正切函数的新型变步长算法,算法以双曲正切函数为基础,建立步长因子μ(n)与误差信号e(n)的非线性函数关系,并引入参数α、β和m,设计了一种新的步长调整公式,使得在算法迭代初始阶段采用较大步长因子,达到更快的收敛速度,在接近收敛时采用较小的步长因子,获得更小的稳态误差。通过仿真分析了不同参数对算法性能的影响,与已有典型变步长算法相比,论文算法具有更快的收敛速度、更小的稳态误差和更优的追踪能力。Aiming at the problem that the convergence rate and steady-state error of the adaptive least mean square(LMS)filtering algorithms with fixed step size cannot be satisfied simultaneously,a new adaptive algorithm with variable step size based on the hyperbolic tangent function is proposed in this paper.A nonlinear functional relationship between the step size factorμ(n)and the error e(n)is constructed.Introducing three parametersα,βand m,a new step size adjustment formula is designed such that faster convergence rate can be achieved with lager step size factor in the initial stage of the iteration and lower steady-state error can be obtained with smaller step size as the algorithm approaches the convergence.The performance of the proposed algorithm with parametersα,βand m is simulated and analyzed.The simulation results show that the algorithm proposed in this paper has faster convergence rate,lower steady-state error and better tracing ability than the other traditional adaptive LMS algorithms.

关 键 词：最小均方算法 双曲正切函数 变步长算法 

分 类 号：TN911.72[电子电信—通信与信息系统]