Estimation of Measurement-Noise Variance for Variable-Step-Size NLMS Filters

Least-mean-square (LMS) filters are a well-studied processing technique that adapts iteratively to an unknown process. It has been proven that the parameters of the LMS filter converge to the optimum (Wiener) solution. Unfortunately, this is only possible if the adaptation steps are infinitely small. Small steps, however, result in slow convergence. The challenge is to vary the step size such that they are large, when the LMS filter coefficients are far from their optimal values and to lower the step size, when the adaptive system is approaching the optimum. State-of-the-art approaches to variable-step-size determination take estimates of the measurement noise into account for optimal performance. This paper proposes a new technique for the estimation of the measurement-noise variance, which also can deal with sudden changes of the unknown system. Based on investigations with a broad range of experimental conditions in terms of test signals and different measurement-noise levels, it is shown that the proposed estimation technique is robust to changes of the unknown system and outperforms other methods.