A Variable Step-Size Partial-Update Normalized Least Mean Square Algorithm for Second-Order Adaptive Volterra Filters
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A Variable Step-Size Partial-Update Normalized Least Mean Square Algorithm for Second-Order Adaptive Volterra Filters Khaled Mayyas1
· Liza Afeef1
Received: 29 March 2019 / Revised: 29 April 2020 / Accepted: 4 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Partial-update (PU) algorithms offer reduced computational complexity to adaptive second-order Volterra filters (SOV) in nonlinear systems while retaining acceptable performance. In this paper, a new selective partial-update technique for the normalized LMS (NLMS) SOV algorithm is proposed, which requires lesser number of comparison operations per iteration than existing methods while providing close performance to the standard M-Max NLMS-SOV algorithm. Convergence properties of the proposed algorithm are enhanced by making the algorithm step-size time varying based on the natural logarithm function. Simulation experiments compare the proposed algorithm with existing PU and variable step-size NLMS-SOV algorithms, which illustrate the advantageous properties of the new algorithm. The proposed algorithm achieves both lower steady-state misalignment and faster convergence speed when compared with the fixed step-size full-update NLMS-SOV algorithm. Simulations also show that comparison operations overhead of the proposed algorithm is reduced significantly compared to that of the standard M-Max NLMS-SOV algorithm. Keywords Adaptive second-order Volterra filters · NLMS algorithm · Partial-update algorithms · Variable step size · Computational complexity
1 Introduction Adaptive second-order Volterra (SOV) filters are used in many adaptive filtering applications due to their ability to combine in their structure linear and nonlinear models,
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Khaled Mayyas [email protected] Liza Afeef [email protected]
1
Department of Electrical Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan
Circuits, Systems, and Signal Processing
and for their capacity to approximate, with reliable accuracy, any fading memory of the nonlinear system [26]. The most popular adaptive algorithm used in updating the filter coefficients of the SOV filters is the NLMS algorithm, which is known for its simplicity, ease of implementation, and attractive stability properties [18]. In many applications, such as active noise control [7, 21, 39], network and acoustic echo cancellation [17], sea clutter cancellation [24, 33], and system equalization [31], adaptive Volterra filters may need a large number of coefficients to model the unknown system with adequate accuracy, resulting in a high computational complexity, and making the adaptive filter implementation impractical. Therefore, partial-update (PU) algorithms [1, 2, 10, 12, 16, 25] were employed in Volterra adaptive filters in an attempt to address the incurred computational complexity of using a large number of coefficients by limiting the number of updated coefficients per iteration [4, 36, 37]. In [4], the M-Max method was directly applied to the NLMS-SOV algorithm by sor
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