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By L. Morales

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194-195, April, 1962. [25] V. H. Nascimento and J. C. M. Bermudez, “Probability of divergence for the least-mean fourth (LMF) algorithm,” IEEE Trans. Signal Processing, vol. 54, pp. , 2006. [26] J. C. M. Bermudez and V. H. Nascimento, “A mean-square stability analysis of the least mean fourth adaptive algorithm,” IEEE Trans. Signal Processing, vol. 55, pp. , 2007. [27] A. Zerguine, "Convergence and steady-state analysis of the normalized least mean fourth algorithm," Digital Signal Processing, vol.

Meng obtained a general expression for the steady-state MSE for adaptive filters with error 20 Adaptive Filtering nonlinearities [10]. However, this expression is only applicable for the cases with the realvalued data and small step-size. Also using TSE, our previous works have obtained some analytical expressions of the steady-state performance for some adaptive algorithms [8], [17], [19], [28]. Using the Price’s theory, T. Y. Al-Naffouri and A. H. Sayed obtained the steady-state performance as the fixed-point of a nonlinear function in EMSE [11], [18].

1 Fig. 2 Table 2. 3 Tracking ability comparison with LMS algorithm Consider the real-valued cases with g  u i   1 .  p  1   2 p  3 !!  p  1   2   ,  2 p  3 !! p:even , p:odd . (68) in Gaussian noise environments, and LMS 2p  1  min  , LMP 3  min (69) in uniformly distributed noise environments, respectively. Under different parameter p LMS LMP  min (dB) in Gaussian noise (from 2 to 6), Fig. 12 shows two curves for the ratio of  min environments and uniformly distributed noise environments.

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