Blind identification of LTI-ZMNL-LTI nonlinear channel models

Abstract

A simple method is proposed for blind identification of discrete-time nonlinear models consisting of two linear time invariant (LTI) subsystems separated by a polynomial-type zero memory nonlinearity (ZMNL) of order N (the LTI-ZMNL-LTI model). The linear subsystems are allowed to be of nonminimum phase (NMP), though the first LTI can be completely identified only if it is of minimum phase. With a circularly symmetric Gaussian input, the linear subsystems can be identified using simple cepstral operations on a single 2-D slice of the N+1 th-order polyspectrum of the output signal. The linear subsystem of an LTI-ZMNL model can be identified using only a 1-D moment or polyspectral slice if it is of minimum phase. The ZMNL coefficients are not identified and need not be known. The order N of the nonlinearity can, in principle, be estimated from the output signal. The methods are analytically simple, computationally efficient, and possess noise suppression characteristics. Computer simulations are presented to support the theory.