A new approach for analyzing the limiting behavior of the normalized LMS algorithm under weak assumptions
A new approach for analyzing the limiting behavior of the normalized LMS algorithm under weak assumptions
复制标题
DOI：
10.1016/j.sigpro.2009.04.040
复制
发表时间：
2009-11
期刊：
影响因子：
--
通讯作者：
E. Eweda
中科院分区：
文献类型：
--
作者：
E. Eweda
本文提出了一种新的和简单的方法来分析的限制行为的归一化LMS算法在弱假设。对连续回归量之间的依赖性、回归量元素之间的依赖性、自适应滤波器的长度或滤波器输入和噪声的分布类型没有限制。该分析适用于在0和2之间的范围内的算法步长的所有值。分析进行了使用一个新的性能指标，根据时间演变的分量的回归向量的方向的权重偏差向量。该分量被称为有效权重偏差，因为它是在自适应滤波器的输出处对过量估计误差有贡献的唯一分量。本文推导了均方有效加权偏差、平均绝对超额估计误差和均方超额估计误差的长期平均值的上界。文中的分析结果得到了仿真的支持。
This paper presents a new and simple approach to analyzing the limiting behavior of the normalized LMS algorithm under weak assumptions. No restrictions are made on the dependence between successive regressors, the dependence among the regressor elements, the length of the adaptive filter, or the distribution types of the filter input and the noise. The analysis holds for all values of the algorithm step-size in the range between 0 and 2. The analysis is carried out using a new performance measure, based on the time evolution of the component of the weight deviation vector in the direction of the regressor. This component is termed as the effective weight deviation since it is the only component that contributes to the excess estimation error at the output of the adaptive filter. The paper derives upper bounds for the long-term averages of the mean-square effective weight deviation, mean absolute excess estimation error, and of the mean-square excess estimation error. The analytical results of the paper are supported by simulations.