Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs |
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Authors: | Neil J. Bershad,José C.M. Bermudez[Author vitae] |
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Affiliation: | a1621 Santiago Drive, Newport Beach, CA, United States;bDepartment of Electrical Engineering, Federal University of Santa Catarina, Florianopolis, SC 88040-900, Brazil |
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Abstract: | Normalized forms of adaptive algorithms are usually sought in order to obtain convergence properties independent of the input signal power. Such is the case of the well-known Normalized LMS (NLMS) algorithm. The Least-Mean Fourth (LMF) adaptive algorithm has been shown to outperform LMS in different situations. However, the LMF stability is dependent on both the signal power and on the adaptive weights initialization. This paper studies the behavior of two normalized forms of the LMF algorithm for Gaussian inputs. Contrary to what could be expected, the mean-square stability of both normalized algorithms is shown to be dependent upon the input signal power. Thus, the usefulness of the NLMF algorithm is open to question. |
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Keywords: | Adaptive filters Analysis Normalized Least-Mean Fourth Stochastic algorithms |
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