By L. Morales
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In the next section, the steady-state performances for complex and real adaptive filters are derived, which are summarized in Theorem 1 based on separation principle and Theorem 2 for white Gaussian regressor, respectively. In section 3, based on Theorem 1 and Theorem 2, the steady-state performances for the real and complex least-mean p-power norm (LMP) algorithm, LMMN algorithm and their normalized algorithms, are investigated, respectively. Simulation results are given in Section 4, and conclusions are drawn in Section 5.
2009.  N. R. Yousef and A. H. Sayed, “Fixed-point steady-state analysis of adaptive filters,” Int. J. Contr. Signal Processing, vol. 17, pp. 237-258, 2003.  B. Lin, R. He, X. Wang and B. Wang, “The excess mean square error analyses for Bussgang algorithm,” IEEE Signal Processing Letters, vol. 15, pp. 793-796, 2008.  A. Goupil and J. Palicot, “A geometrical derivation of the excess mean square error for Bussgang algorithms in a noiseless environment”, ELSEVIER Signal Processing, vol.
2 Random signals In many real life situations, observations are made over a period of time and they are influenced by random effects, not just at a single instant but throughout the entire interval of time or sequence of times. In a “rough” sense, a random process is a phenomenon that varies to some degree unpredictably as time goes on. If we observed an entire time-sequence of the process on several different occasions, under presumably “identical” conditions, the resulting observation sequences, in general, would be different.
Adaptive Filtering by L. Morales