On the existence of nonlinear ideal equalizer with application to satellite channels

The purpose of the nonlinear channel equalization boils down to finding the inverse of the transmitter nonlinear channel. The problem of existence of such process, which is not usually simple to handle, is the main focus of this study. We use the module theoretical approach, in which the rank of nonlinear system is clearly defined. We will show that the existence of the nonlinear channel equalizer is related to the computation of the rank of some Jacobian matrices. The credit of this approach is, among others, that it provides an explicit analytical description of subsets of input signal, on which the ideal equalizer lies. Numerical simulations, applied to satellite channel, show the performance of the presented approach.