Leaky LMS algorithm: MSE analysis for Gaussian data

• Published in: IEEE transactions on signal processing Vol. 45; no. 4; pp. 927 - 934
• Main Authors: Mayyas, K., Aboulnasr, T.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.1997; Institute of Electrical and Electronics Engineers
• Subjects: Adaptive algorithm; Algorithm design and analysis; Applied sciences; Convergence; Data analysis; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Interference; Least squares approximation; Performance analysis; Signal and communications theory; Signal processing algorithms; Signal, noise; Steady-state; Telecommunications and information theory; Telephony; Statistical method; Adaptive algorithm; Least squares method; Gaussian signal; Signal estimation; Signal processing; Performance analysis; Mean square error
• ISSN: 1053-587X
• DOI: 10.1109/78.564181

Despite the widespread usage of the leaky LMS algorithm, there has been no detailed study of its performance. This paper presents an analytical treatment of the mean-square error (MSE) performance for the leaky LMS adaptive algorithm for Gaussian input data. The common independence assumption regarding W(n) and X(n) is also used. Exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady-state excess MSE are developed. Rigorous conditions for MSE convergence are also established. Analytical results are compared with simulation and are shown to agree well.