An ESPRIT-like method for quadratic phase coupling estimation

Abstract

Two algorithms are proposed for estimating the quadratically coupled frequency pairs (QC pairs) in a signal consisting of complex sinusoids in white noise. Three matrices are constructed from the complex third-order cumulants of the noisy signal, the second and third being time shifted versions of the first. The list of coupled frequencies is obtained from the rank reducing numbers of the matrix pencil formed from the first matrix and either of the latter two. The first algorithm then pairs these components by relating quadratic coupling to the intersection of generalized eigenspaces corresponding to two of these frequencies. The coupling strengths are also obtained in terms of generalized eigenvectors in this intersection space. The second algorithm constructs a two-parameter matrix pencil using all the three matrices. The rank reducing pairs of this pencil on the unit circle yield the QC pairs and the associated generalized eigenvectors: the coupling strengths.