The mirror-modified filtered-x least mean squares (MMFxLMS ) algorithm is a variation of the FxLMS algorithm with online secondary path modeling that cannot diverge due to secondary path modeling errors. However, problems may occur when the ambient noise is not limited due to insufficient modeling power. This work shows that under a frequency domain analysis without ambient noise, the MMFxLMS algorithm is always stable, and expressions for the maximum residual noise level at any given time are obtained. It is also shown that, under the same context, convergence to the minimum residual noise is guaranteed. Still, convergence can be much slower for high secondary path modeling errors than that of the LMS or MFxLMS algorithms. Simulations confirm these results.

中文翻译：

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低环境噪声的镜面修正滤波x最小均方算法的频域分析

镜像修正滤波 x 最小均方 (MMFxLMS) 算法是 FxLMS 算法的变体，具有在线二级路径建模，不会因二级路径建模错误而发散。然而，当环境噪声由于建模能力不足而不受限制时，可能会出现问题。这项工作表明，在没有环境噪声的频域分析下，MMFxLMS 算法总是稳定的，并且得到了任何给定时间的最大残余噪声水平的表达式。还表明，在相同的上下文下，可以保证收敛到最小残余噪声。尽管如此，与 LMS 或 MFxLMS 算法相比，高次要路径建模误差的收敛速度可能要慢得多。模拟证实了这些结果。