Linear system blind identification based on fourth order spectral analysis

Abstract

This paper describes algorithms for blind identification of linear time invariant systems. The measured data are the system complex-valued output fourth order statistics. The originality of the contribution is in the development of methods in the frequency domain applied to complex signals instead of techniques in the time domain for processing real data proposed by other authors. Frequency domain analysis is of interest because the validity of the model and the accuracy of the higher order spectrum estimates are directly checked in this domain. The algorithms are extensions of methods applied earlier for the analysis of third order spectra. The first method is recursive and applies when the measurements are accurate. The second minimizes a quadratic criterion. It requires a prior phase unwrapping. Methods performing third order spectra phase unwrapping are extended to fourth order spectra. The validity of the algorithms is checked with simulations.