The Extended Feature LMS Algorithm: Exploiting Hidden Sparsity for Systems with Unknown Spectrum

• Published in: Circuits, systems, and signal processing Vol. 40; no. 1; pp. 174 - 192
• Main Authors: Yazdanpanah, Hamed, Apolinário, José A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2021; Springer Nature B.V
• Subjects: Algorithms; Circuits and Systems; Convergence; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Signal,Image and Speech Processing; Sparsity; Steady state; Adaptive filtering; LMS algorithm; Sparsity; Feature; Computational complexity; norm
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-020-01461-3

The feature least-mean-square (F-LMS) algorithm has already been introduced to exploit hidden sparsity in lowpass and highpass systems. In this paper, by proposing the extended F-LMS (EF-LMS) algorithm, we boosted the F-LMS algorithm to exploit hidden sparsity in more general systems, those which are neither lowpass nor highpass. To this end, by means of the so-called feature matrix, we reveal the hidden sparsity in coefficients and utilize the l 1 -norm to exploit the exposed sparsity. As a result, the EF-LMS algorithm will improve the convergence rate and the steady-state mean-squared error (MSE) as compared to the traditional least-mean-square algorithm. Moreover, in this work, we analyze the convergence behavior of the coefficient vector and the steady-state MSE performance of the EF-LMS algorithm. Through synthetic and real-world experiments, it has been seen that the EF-LMS algorithm can improve the convergence rate and the steady-state MSE whenever the hidden sparsity is revealed.