On the convergence behavior of the LMS and NLMS algorithms

Shows that the NLMS (normalized least-mean-square) algorithm is a potentially faster converging algorithm than the LMS algorithm, when the design of the adaptive filter is based on the usually limited knowledge of its input signal statistics. The author proposes a very simple model for the input signal vectors, which simplifies the analysis of the convergence behavior of the NLMS algorithm. The solutions thus obtained can only lead to a qualitative value. He gives examples to illustrate that even quantitatively, they can be good approximations. Finally, he emphasizes that the convergence of the NLMS algorithm can be speeded up significantly by employing a time-varying stepsize. Within the assumptions of the simple model, it is able to specify a priori the optimal stepsize sequence for the case of a white input signal.