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On Active Impulsive Noise Control (AINC) Systems

Developing a Filtered-Reference Adaptive Algorithm Using a Convex-Combined Normalized Step-Size Approach

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Abstract

This paper develops an efficient adaptive filtering algorithm for active impulsive noise control (AINC) systems. For AINC systems, the filtered-x least mean square (FxLMS) algorithm fails to converge due to the impulsive nature of the noise source. In previous work, the step-size of the FxLMS algorithm was normalized using the power estimate of the error as well as the reference signals, resulting in the improved normalized step-size FxLMS (INSS-FxLMS) algorithm. The INSS-FxLMS algorithm exhibits a robust performance for AINC systems; however, it uses a preselected fixed step-size. Therefore, the INSS-FxLMS algorithm results in a compromise between convergence speed and noise reduction. The proposed algorithm employs a convex-combined step-size (CCSS) within the framework of the INSS-FxLMS algorithm. While normalization takes care of the impulsive nature of noise, the CCSS solves the above-mentioned trade-off issue. Essentially, the CCSS selects a large (small) value of the step-size in the transient (steady) state of the AINC system. It is demonstrated by extensive computer simulations that the proposed algorithm outperforms the existing counterparts for a variety of case studies in AINC systems.

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Notes

  1. A few ad hoc modifications have been employed for the FxLMK algorithm [27]. These include using the \({\text {sgn}}(\cdot )\) operator with both e(n) and \({\mathbf {x}}_f(n)\) and performing normalization with respect to e(n) in update equation (7).

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Acknowledgements

We thank the anonymous reviewers for their critical evaluation and insightful comments, which have greatly helped in improving the manuscript. This research was partially supported by the Faculty Development Competitive Research Grants Program of Nazarbayev University under Grant Number 110119FD4525.

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  1. Department of Electrical and Computer Engineering, School of Engineering and Digital Sciences, Nazarbayev University, 53 Kabanbay Batyr Avenue, Nur-Sultan, Kazakhstan

    Muhammad Tahir Akhtar

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Akhtar, M.T. On Active Impulsive Noise Control (AINC) Systems. Circuits Syst Signal Process 39, 4354–4377 (2020). https://doi.org/10.1007/s00034-020-01368-z

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