Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms

Abstract

We present a new necessary and sufficient condition for essential uniqueness of the decomposition of a third-order tensor in rank-$(L_r,L_r,1)$ terms. We derive a new deterministic technique for blind signal separation that relies on this decomposition. The method assumes that the signals can be modeled as linear combinations of exponentials or, more generally, as exponential polynomials. The results are illustrated by means of numerical experiments.