一种变步长LMS自适应滤波算法及分析

A Variable Step Size LMS Adaptive Filtering Algorithm and Its Analysis

本文对变步长自适应滤波算法进行了讨论 ,建立了步长因子 μ与误差信号e(n)之间另一种新的非线性函数关系 .该函数比已有的Sigmoid函数简单 ,且在误差e(n)接近零处具有缓慢变化的特性 ,克服了Sigmoid函数在自适应稳态阶段步长调整过程中的不足 .由此函数本文得出了另一种新的变步长自适应滤波算法 ,并且分析了参数α ,β的取值原则及对算法收敛性能的影响 .该算法有较好的收敛性能且计算量少 .计算机仿真结果与理论分析相一致 。

This paper discusses about some algorithms of variable step size LMS adaptive fi ltering and establishes another new non-linear functional relationship between ~{&L~} and ~{*+~}e(n)~{*+~}.The functional relationship is not only simpler than Sigmoid fun ctional relationship,but also has the property of slight change ~{*+~}e(n)~{*+~} near to zero.Therefore it is superior to Sigmoid functional relationship in the process of step size change of adaptive steady state.On the basis of the functional rel ationship,The author presents the new algorithm of variable step size LMS adapti ve filtering and analyses the algorithm with various ~{&A~} and ~{&B~}.the algorithm has less computational complexity than the former algorithms,besides good convergen ce properties.Computer simulation results confirms the theoretical analysis and shows the algorithm performance is better than that of former algorithms.