By L. Morales
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5. 1. Fig. 6. 1 Steady-State Performance Analyses of Adaptive Filters Fig. 7. 1. Fig. 8. 1. 39 40 Adaptive Filtering Fig. 9. 2. Fig. 10. 1. Steady-State Performance Analyses of Adaptive Filters Fig. 11. 2. Fig. 12. Comparisons of the tracking performance between LMS algorithm and LMP algorithm in Gaussian noise environments and uniformly distributed noise environments. 41 42 Adaptive Filtering 5. Conclusions Based on the Taylor series expansion (TSE) and so-called complex Brandwood-form series expansion (BSE), this paper develops a unified approach for the steady-state mean-squareerror (MSE) and tracking performance analyses of adaptive filters.
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.  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.  D. H. Brandwood, “A complex gradient operator and its application in adaptive array theory,” Proc. Inst. Elect. Eng. F, H, vol.
APPENDIX B. Proof of lemma 2 Consider the real-valued cases. 1) 0. 3) 2 e =2 f e1 v f v f e,2e v ev APPENDIX C. Proof of lemma 3 Let z x jy , where x and y 0 are all real variables, then p 2 z z z z p 2 2 1 2 j x y y 2 x p /2 1 p 2 p x y2 2x j x2 y 2 4 4 p p2 p z x jy z p 2 z 2 2 Likewise, we can obtain operators . 1) 2y p p 2 . Here, we use the Brandword’s derivation p z z z 2 z APPENDIX D.
Adaptive Filtering by L. Morales