A theory of the FXLMS algorithm based on statistical-mechanical method
A theory of the FXLMS algorithm based on statistical-mechanical method
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DOI：
10.1109/ispa.2013.6703818
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发表时间：
2013-09
期刊：
影响因子：
--
通讯作者：
S. Miyoshi;Y. Kajikawa
中科院分区：
文献类型：
--
作者：
S. Miyoshi;Y. Kajikawa
我们分析了FXLMS算法的学习曲线，使用的是一种机械的方法。主路径的元素和自适应滤波器的元素之间的互相关和自适应滤波器的元素的自相关被视为宏观变量。在抽头延迟线较长的条件下，我们得到了描述宏观变量动力学行为的联立微分方程。我们解析求解方程，以获得相关性，并最终计算均方误差。该理论引入了输入信号的相关函数，不仅可以处理白色信号，而且可以处理非白色信号。所得理论与计算机模拟结果定量吻合。
We analyze the learning curves of the FXLMS algorithm using a statistical-mechanical method. Cross-correlations between the element of a primary path and that of an adaptive filter and autocorrelations of the elements of the adaptive filter are treated as macroscopic variables. We obtain simultaneous differential equations that describe the dynamical behaviors of the macroscopic variables under the conditions in which the tapped-delay line is long. We analytically solve the equations to obtain the correlations and finally compute the mean-square error. Introducing the correlation function of the input signal, the theory can treat not only the white but also the nonwhite signal. The obtained theory quantitatively agrees with the results of computer simulations.