An improved statistical analysis of the least mean fourth (LMF) adaptive algorithm |
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Authors: | Hubscher PI Bermudez JCM |
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Affiliation: | Integration & Tests Lab., Nat. Inst. for Space Res., Sao Jose Dos Campos, Brazil; |
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Abstract: | The paper presents an improved statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior for a stationary Gaussian input. The analysis improves previous results in that higher order moments of the weight error vector are not neglected and that it is not restricted to a specific noise distribution. The analysis is based on the independence theory and assumes reasonably slow learning and a large number of adaptive filter coefficients. A new analytical model is derived, which is able to predict the algorithm behavior accurately, both during transient and in steady-state, for small step sizes and long impulse responses. The new model is valid for any zero-mean symmetric noise density function and for any signal-to-noise ratio (SNR). Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior in several different situations. |
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