Blind identification of nonlinear systems based on higher order cyclic spectra

In this thesis, the blind identifiability of linear subsystems of discrete-time nonlinear models consisting of two finite-memory Linear Time Invariant (LTI) filters separated by a finite-order Zero-Memory Nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI model) is established assuming circular Gaussian and Quadrature Amplitude Modulated (QAM) Non-Gaussian input sequences exhibiting circular-like properties. A range of identification algorithms are proposed. Identification of some general Volterra models is also considered.; It is shown that with circular stationary Gaussian inputs the impulse responses of the two LTI filters of an {dollar}Nsp{lcub}th{rcub}{dollar} order LTI-ZMNL-LTI can be recovered from only a 2-D slice of the {dollar}N+1sp{lcub}th{rcub}{dollar} order polyspectrum of the output. Some simple cepstral domain identification algorithms are proposed. The identifiability of some nonlinear models with stationary Non-Gaussian QAM inputs is also considered.; The blind identifiability of LTI-ZMNL-LTI models using QAM-type cyclostationary inputs is established. Two sets of identification algorithms result, one based on the cross-polyspectra of the Translation Series representors of the output, and the other based on the cyclic polyspectra.; The algorithms proposed in this thesis for nonlinear system identification are blind, and are a new application of the theory of cyclostationarity. The algorithms are analytically simple, suppress several types of noise and interference, do not require the estimation of the ZMNL coefficients, allow the LTI filters to have a Non-Minimum Phase (NMP) response, and are shown by Monte-Carlo simulations to perform effectively.