基于对数函数的新变步长LMS算法

New Variable Step Size LMS Algorithm Based on Logarithmic Function

针对固定步长最小均方(LMS,least mean square)算法以及变步长LMS算法在收敛速度与稳态误差性能方面的不足,本文提出了一种新的基于对数函数改进的LMS算法.由于该算法中不涉及指数的运算,使得算法的计算量大大下降,收敛速度更快.仿真结果表明,对数函数改进的LMS算法比基于反正切函数改进的LMS算法具有近似相同的稳态误差性能,然而本文算法收敛更快,速度平均提高1.5倍.并且比基于双曲正切函数改进的LMS算法中的稳态误差平均降低0.5倍,同时收敛速度平均提高1.0倍.

Aiming at the inadequate function of the convergence speed and the steady-state error that exist in the fixed and variable step LMS algorithm,a new improved LMS algorithm based on logarithmic function was proposed in this paper.Due to the new improved LMS algorithm does not involve the exponent arithmetic,the computation of this LMS algorithm decreased a lot,and the convergence speed become much faster too.The consequence of this simulation indicate that the new improved LMS algorithm keeps nearly the same steady-state error with the improved algorithm which based on arc-tangent function,but the former has improved the convergence speed,and its speed has increased by an average of 1.5times than the latter.Moreover,the steady-state error of the new improved LMS algorithm has decreased by an average of 0.5times than that of the improved algorithm based on hyperbolic tangent function and its speed has also increased by an average of 1.0times than the latter.