A nonlinear channel equalization using an algebraic approach and the Affine Projection Algorithm

In this paper, the problem of nonlinear equalization is addressed. We use an algebraic approach which allows us to define the existence conditions of a left inverse, for a nonlinear system and therefore the equalization conditions. These existence conditions need the computation of the rank of some jacobian matrices. This approach is applied to a Volterra filter, which represents a nonlinear system. We will show also that these equalizability conditions depend to the coefficients of the nonlinear system and input values therefore we can verify for any channel with assumed known coefficients if this system is ideally equalizable or not. The appropriate algorithm that we have used to test the performance of the equalization is the APA (Affine Projection Algorithm). The choice of APA is justified by the use of a colored excitation signal as an input signal due to the nonlinear channel characteristics.