On the convergence of Volterra filter equalizers using a pth-order inverse approach

The pth-order inverse method is one of important approaches to Volterra equalization. However, when a pth-order Volterra equalizer instead of an exact Volterra equalizer is connected in cascade before (after) a nonlinear system, the existence of Volterra filter equalization and the approximation output error bound of the resulting system have yet to be reported. In this paper, the concept of local l/sup 2/ stability for a Volterra system is introduced, and the algorithmic formulae of a pth-order inverse equalizer via a multidimension z-transform are presented. The output error signal and the approximation output error bound of the resulting system are investigated as well. It is shown that the approximation output error tends to zero as p tends to infinity for a finite range of input amplitude values. Finally some simulation results are presented and discussed.