Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Abstract

In this paper, we present an extension of linear communication channels identification algorithms to non linear channels using higher order cumulants (HOC). In the one hand, we develop a theoretical analysis of non linear quadratic systems using second and third order cumulants. In the other hand, the relationship linking cumulants and the coefficients of non linear channels presented in the linear case is extended to the general case of the non linear quadratic systems identification. This theoretical development is used to develop three non linear algorithms based on third and fourth order cumulants respectively. Numerical simulation results example show that the proposed methods able to estimate the impulse response parameters
with different precision.