基于分式函数的新变步长LMS算法

为了解决传统LMS算法在稳态误差和收敛速度之间的矛盾,提出了一种基于分式函数的新型变步长LMS算法(简称VXLMS算法)。因为新型变步长函数不包含指数运算,所以降低了运算量,加快了算法的收敛速度,同时也提高了数据跳变时的跟踪性能。在VXLMS算法收敛的条件下,通过理论推导确定了该变步长函数的参数取值范围,然后通过取不同参数值分析对算法性能的影响,选出最优参数值进行仿真分析。仿真结果表明:相同仿真条件下提出的VXLMS算法相对于VSSLMS算法和SVSLMS算法稳态误差更低、收敛速度更快,即说明提出的小计算量新变步长函数,通过调整步长因子使权向量快速达到最优,进而使VXLMS算法具有更好的收敛性、稳定性以及鲁棒性。

New Variable Step Size LMS Algorithm Based on Fraction Function

In order to solve the contradiction between the steady state error and the convergence speed of the traditional LMS algorithm,a new variable step size LMS algorithm(VXLMS algorithm)based on the fractional function is proposed. Because the new variable step function does not include the exponential operation,it reduces the computational complexity,accelerates the convergence speed of the algorithm,and improves the tracking performance when the data jumps. Under the condition of VXLMS algorithm convergence,the range of parameters of the variable step function is deduced by theoretical derivation. Then,the influence of different parameter values on the performance of the algorithm is selected and the optimal parameter value is selected for simulation analysis. The simulation results show that the VXLMS algorithm proposed in the same simulation condition has a lower steady-state error and a faster convergence rate than the VSSLMS algorithm and the SVSLMS algorithm. That is to say,the small variable step size function is proposed by adjusting the step size factor The VXLMS algorithm has better convergence,stability and robustness.