By L. Morales

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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. [19] 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. [20] 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. 84, pp. 311-315, May, 2004.

Widrow, “The least-mean fourth (LMF) adaptive algorithm and its family,” IEEE Trans. Information Theory, vol. 30, pp. 275-283, 1984. [6] J. A. Chambers, O. Tanrikulu and A. G. Constantinides, “Least mean mixed-norm adaptive filtering,” Electron. , vol. 30, pp. 1574-1575, 1994. [7] O. Tanrikulu and J. A. Chambers, “Convergence and steady-state properties of the leastmean mixed-norm (LMMN) adaptive algorithm,” IEE Proceedings- Vision, Image Signal Processing, vol. 143, pp137-142, 1996. [8] B. Lin, R.

This assumption is referred to as the separation principle in [11]. 4, and using (4), we can rewrite (10) as uE e , e uEq e , e 1Tr Q (11) where u E u u Eg u , 2 2 g u . q e, e f e, e Lemma 1 If e is complex-valued, and e , e and q e , e are defined by (12), then e , e 2 Re ea f e , e , 2 1 f e v , v 2 2 e , e v , v 2 Re f e 1 v , v , v , v 0, (12) 4 2 1 q e , e v , v f e v , v 2 2 Re f v , v f e, e v , v 2 .