LMS和归一化LMS算法收敛门限与步长的确定

DETERMINING OF CONVERGENT THRESHOLD AND STEP-SIZE FOR LMS AND NORMALIZED LMS ALGORITHM

从 LMS算法失调量的准确表达式出发,根据输入信号特征值分布重新研究了 LMS,归一化LMS(Normalized LMS,NLMS)算法收敛的必要条件,推导出 LMS和 NLMS 算法收敛的步长门限,并分析了输入信号特征值分布、滤波器阶数对算法收敛步长门限的影响,推导出满足性能失调下步长的自适应计算公式,减小了应用 LMS,NLMS算法时步长选取的盲目性,与已有的算法相比,具有计算简单、实用、自适应性能强,同时可获得满意失调量的特点,计算机模拟结果表明该方法的正确性。

Based on eigenvalue distributing of input signal, the convergent necessary conditions for LMS and Normalized LMS(NLMS) algorithm are again researched through the accurate analysis of the misadjustment. To avoid blindness for applying LMS and NLMS algorithm, the convergent threshold and the simple adaptive calculating formula for the step-size of them are proposed. The influence of eigenvalue distributing of input signal and order of filter on the threshold of step-size is also analyzed. Compared with an existing algorithm, the characters of lower computational complexity, practicality and stronger adaptive are shown and the satisfied misadjustment is achieved by adopting the presented method for calculating the step-size.