By L. Morales

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1. Fig. 2. 2. Steady-State Performance Analyses of Adaptive Filters Fig. 3. 1. Fig. 4. 2. 37 38 Adaptive Filtering Fig. 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.

2 If e is complex-valued, the estimation error function f ( e , e ) has two independent variables: e and e . In addition, due to e  e , f ( e , e ) can be replaced by f ( e ) if e is real-valued. Here, we use the  general form f ( e , e ) . 1 2 2 21 Steady-State Performance Analyses of Adaptive Filters ei  di  u i w i , (2) di  u i w o ,i  vi , (3) where u i  1  M  row input (regressor) vector;  step-size; H conjugate and transpose; w i  M  1  weight vector; ei scalar-valued error signal; di scalar-valued noisy measurement; g  u i  scalar variable factor for step-size.

Stearns, Adaptive Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1988. [4] A. I. Sulyman and A. Zerguine, Convergence and steady-state analysis of a variable step-size NLMS algorithm, ELSEVIER Signal Processing, Vol. 83, , pp. 1255-1273, 2003. [5] H. Takekawa. T. Shimamura, and S. A. Jimaa, “An efficient and effective variable step size NLMS algorithm”, 42nd Asilomar conference on signals, systems and computers, CA, USA, October 26-29, 2008. [6] Ling Quin and M. G. Bellanger,” Convergence analysis of a variable step-size normalized adaptive filter algorithm”, Proc.

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