A formulation of the convergence property for the second-order adaptive Volterra filter using NLMS algorithm

In this paper, a formulation of the convergence property of the NLMS method, an updating algorithm for an adaptive Volterra filter, is discussed. To date, much research has been carried out on the convergence property of the updating algorithm in a linear adaptive filter. However, there has been insufficient study of the updating algorithm for the second-order adaptive Volterra filter. In this paper, the convergence property of the E-NLMS method, an updating algorithm in the second-order adaptive Volterra filter, is formulated and the convergence property of the second-order adaptive Volterra filter is theoretically determined. In the formulation of the convergence property we use the first-order recursive filter expression, which is effective for studying various characteristics of the NLMS method in linear adaptive filters. In addition, it is recognized that the nature of the input signal to the diagonal (D) elements of the second-order Volterra system is different from that of the input to the other (ED) components. By means of computer simulation, it is confirmed that the convergence property given by the derived theoretical equation can sufficiently express the actual convergence property. (C) 2002 Wiley Periodicals, Inc.