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A New Variable-Regularized Transform-Domain NLMS Algorithm with Automatic Step-Size Selection for Adaptive System Identification/ Filtering

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Abstract

A new variable-regularized (VR) switch-mode noise-constrained (SNC) transform-domain normalized least mean squares (VR-SNC-TDNLMS) algorithm for adaptive system identification and filtering is proposed. It exploits prior knowledge of the additive noise variance and results in a generalized VR-TDNLMS algorithm with a variable step-size (VSS) for improving convergence speed. It also reduces estimation variance, sensitivity to input signal level and eigenvalue spread by means of variable-regularization and decorrelation transformation. To select the variable step-size online, the convergence behavior of the proposed algorithm is analyzed. From the mean convergence analysis, the maximum step-size (MSS) for convergence is first determined. The theoretical results suggest that improved performance can be obtained if the MSS is employed initially while the NC adaptation is adopted near convergence to reduce steady- state misadjustment. Therefore, a switch-mode scheme which employs a MSS mode together with a NC mode is incorporated to further improve its convergence speed. The mean square convergence behavior is also studied by means of a Lyapunov stability-based method to characterize its convergence condition and steady-state misadjustment. Based on the theoretical results, a new automatic threshold selection method for mode switching is developed. General recommendations for choosing other algorithmic parameters are also proposed to facilitate its online and practical usage. The proposed method is expected to find a wide range of applications in areas related to instrumentation and measurement involving low-complexity and recursive linear estimation. In particular, its potential application and effectiveness in system identification problems and several acoustic applications are demonstrated by computer simulations.

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Notes

  1. Though the concept of using two or more step-sizes for adaptation is simple intuitively, it is somewhat difficult to be fully utilized in practice as the switching threshold between the operating modes is difficult to be determined.

  2. The measurement noise may result from quantization errors, modeling errors, etc. and is usually assumed to be white Gaussian distributed. In many practical situations, some prior knowledge on noise variances is also available.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, Hong Kong

    S. C. Chan & Y. J. Chu

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  1. S. C. Chan
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  2. Y. J. Chu
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Corresponding author

Correspondence to S. C. Chan.

Additional information

A preliminary version of the SNC-TDNLMS algorithm was presented in IEEE ISCAS’2011 [1]. An improved version using a maximum step-size mode and variable regularization is proposed in the paper. Moreover, a detailed performance analysis using Lyapunov function for step size selection is presented.

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Chan, S.C., Chu, Y.J. A New Variable-Regularized Transform-Domain NLMS Algorithm with Automatic Step-Size Selection for Adaptive System Identification/ Filtering. J Sign Process Syst 84, 181–196 (2016). https://doi.org/10.1007/s11265-015-1036-y

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  • DOI: https://doi.org/10.1007/s11265-015-1036-y

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