On the existence of nonlinear equalizer

We consider the problem of the existence of nonlinear equalizer for a nonlinear channel. We use the module theoretical approach developed by Fliess, in which the rank of nonlinear channel 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. This approach will impose some conditions on the transmitted signal which allow us to have an ideal equalization. Finally, a simulation result is given to illustrate the presented approach.