小波技术对LMS算法的提高与分析

The Improvement and Analysis of Wavelet Transform to LMS Algorithm

变步长LMS(Least Mean Square)算法在同时兼顾快速收敛与降低稳态失调误差的问题上做出了很多改进,但仍有较大的提升空间.本文利用小波技术对变步长LMS算法提出改进.小波技术具有数学"显微镜"功能,步长因子的变化速度可以通过拉伸窗口来实时调整.本文将失调误差与收敛速度之间的比值做为小波窗口调整参数,根据两者之间的相对变化实时调整步长因子的变化速度,可实时准确地调整收敛速度,更好地兼顾快速收敛与降低稳态失调误差问题.仿真证明本文提出的算法比现有技术具有更高的收敛速度和更低的稳态失调误差.

Although Variable Step-Size LMS algorithm has made some perfection in the compromise between the quick convergence and low steady-state misadjustment error, there will be a large space of improvement. The wavelet transforma-tion of LMS algorithm is presented. Because the technology of wavelet has the function of ＂mathematics＇ micro scope＂, the variable speed of step-size is adjusted by pulling the wavelet＇s window. The steady-state misadjustment error to the conver-gence speed ratio is regarded as the window＊ s parameter. So the variable speed of step-size is adjusted timely by the rela-tive variation of the two elements , then the convergence speed is adjusted timely and precisely the compromise between the quick convergence and low steady-state misadjustment error is better solved. The simulations verify that the wavelet transformation of LMS algorithm possesses better convergence speed and lower steady-state misadjustment error.