基于双曲正弦函数设计变步长的LMS算法

Design of LMS Algorithm with Variable Step-Size Based on Hyperbolic Sine Function

针对非高斯环境下传统变步长LMS(Variable step-size least mean square,VSS-LMS)算法性能不佳的问题,基于传统的VSS-LMS算法利用双曲正弦函数构建变步长的更新策略,提出一种基于双曲正弦函数的变步长LMS算法。并在理论上分析了新提出VSS-LMS算法的收敛性与算法复杂度,并给出在不同输入信号时对两种特性的线性系统的VSS-LMS算法的辨识结果,且每次仿真中都在不同分布的非高斯噪声下进行。结果表明,提出的算法相比Log-NLMS算法和改进G-SVSLMS算法,新提出的VSS-LMS算法具有更快的收敛速度和较好的稳态特性,且稳态误差趋于理论的SNR。

Aiming at the poor performance of the variable step-size least mean square(VSS-LMS)algorithm in a non-Gaussian environment,this paper proposes a novel VSS-LMS algorithm based on the hyperbolic sine function.Specifically,the hyperbolic sine function was used to design a variable step-size update strategy.Based on this,the convergence and computational complexity of the proposed VSS-LMS algorithm were theoretically analyzed.Further-more,the simulation experiment results of system identification were used to illustrate the principle and efficiency of the proposed VSS-LMS algorithm.The performance of the algorithm was analyzed mathematically and validated ex-perimentally.Simulation results demonstrate that the proposed VSS-LMS is superior to the Log-NLMS and improved the G-SVSLMS algorithm,and the steady-state mean square error tends to the theoretical result SNR.