Sparse Mixed Norm Adaptive Filtering Technique
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Sparse Mixed Norm Adaptive Filtering Technique Nafiseh Maleki1 · Masoumeh Azghani1 Received: 7 August 2019 / Revised: 16 April 2020 / Accepted: 17 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we would suggest a sparse adaptive filtering technique which is robust against Gaussian and non-Gaussian noises. To this goal, a linear combination of the least mean square and the least mean fourth loss functions has been considered as the fidelity term. Moreover, in order to promote the sparsity property of the underlying vector, we have added different sparsity-inducing penalty terms. To optimize the resultant cost function, the quasi-Newton scheme has been adopted which accelerates the convergence of the algorithm. The convergence of the proposed method has been proved analytically. Furthermore, the efficiency of the suggested scheme has been evaluated through extensive simulation scenarios which confirm the superiority of the proposed algorithm over the other state-of-the-art schemes. Keywords Adaptive filtering · Sparsity · Sparse adaptive filter
1 Introduction The adaptive filters have found various applications in different fields ranging from digital signal processing to wireless communications and control systems [27–29]. Adaptive filters are most commonly used in the dynamic environments where the system parameters are changing. Some of the widely used applications of the adaptive filters are system identification [13,26], channel estimation [19], adaptive feedback cancellation [15], and noise cancellation [14]. The system noise is usually considered as Gaussian. However, there are various applications where non-Gaussian noises come into play. For instance, in different systems such as spectroscopy, neuroimaging, sensors and power systems, the involving noise is non-Gaussian. The impulsive noise and uniform noise are the examples of the non-Gaussian noise. The impulsive noise is due to malfunctioning of the signal capturing sensors, analog-to-digital converter errors,
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Masoumeh Azghani [email protected] Laboratory of Wireless Communications and Signal Processing (WCSP), Faculty of Electrical Engineering, Sahand University of Technology, Tabriz, Iran
Circuits, Systems, and Signal Processing
erroneous memory locations in hardware, or transmission errors. The motivation of this paper is to devise an adaptive filtering technique to handle both the Gaussian and non-Gaussian noises. The proposed method can be exploited in various applications such as channel estimation, echo cancellation, noise removal, source separation, and system identification where both Gaussian and non-Gaussian noises are present. A wide range of the algorithms have been designed based on the assumption that the environmental noise is Gaussian. Therefore, the mean square error criterion, which has shown to be proper for the Gaussian noise, has been adopted as the cost function [23]. However, there are also a limited number of adaptive filtering algorithms developed based on non-me
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