On the Stability of the Least-Mean Fourth (LMF) Algorithm

Vítor H. Nascimento, José Carlos M. Bermudez

DOI: 10.14209/sbrt.2004.100

Evento: XXI Simpósio Brasileiro de Telecomunicações (SBrT2004)

Keywords:

Abstract

We show that the least-mean fourth (LMF) adaptive algorithm is not mean-square stable when the regressor input is not strictly bounded (as happens, for example, if the input has a Gaussian distribution). This happens no matter how small the step-size is made. We prove this result for a slight modification of the Gaussian distribution in a length M = 1 filter (in order to simplify our arguments), and provide several examples of divergence when the regressor is Gaussian. Our results provide tools for filter designers to better understand what can happen when the LMF algorithm is used, and in which situations it might not be a good idea to use this algorithm.

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