Computationally Efficient ESPRIT-Like Algorithm for Estimating Quadratic Phase Coupling

An eigen-subspace algorithm is proposed for estimating the quadratically-phase-coupled (QPC) frequency pairs in a random harmonic signal corrupted by white noise. A single-parameter matrix-pencil is formed from third order cumulant matrices. The rank reducing numbers of the matrix pencil directly yield the quadratically-phase-coupled frequency pairs. The corresponding generalized eigenvectors are used to determine the coupling strengths. The determination of these rank reducing numbers and generalized eigenvectors is shown to be equivalent to obtaining the eigenvalues and eigenvectors of a single matrix. The algorithm presented here is a considerable improvement over ESPRlT-like algorithm developed. The original algorithm involved a search overhead of complexity O(q²) where q is the number of distinct QPC pairs. The algorithm presented here eliminates any kind of search, which renders it feasible for practical implementations