Blind Multilinear Identification

TL;DR

This paper introduces a novel multilinear technique for blind signal recovery and identification in challenging scenarios with highly correlated sources, enabling applications in antenna processing, CDMA, and spectroscopy.

Contribution

It develops a bounded coherence low-rank multilinear approximation method with theoretical guarantees for unique recovery, extending tensor decomposition theory.

Findings

Enables blind source separation with highly correlated signals

Provides theoretical conditions for uniqueness of solutions

Demonstrates applicability across multiple signal processing domains

Abstract

We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources in antenna array processing, (ii) highly correlated spreading codes in CDMA radio communication, (iii) nearly dependent spectra in fluorescent spectroscopy. This has important implications --- in the case of antenna array processing, it allows for joint localization and extraction of multiple sources from the measurement of a noisy mixture recorded on multiple sensors in an entirely deterministic manner. In the case of CDMA, it allows the possibility of having a number of users larger than the spreading gain. In the case of fluorescent spectroscopy, it allows for detection of nearly identical chemical constituents. The proposed technique involves the solution of a bounded coherence low-rank multilinear approximation problem. We show that bounded coherence allows us to establish existence and uniqueness of the recovered solution. We will provide some statistical motivation for the approximation problem and discuss greedy approximation bounds. To provide the theoretical underpinnings for this technique, we develop a corresponding theory of sparse separable decompositions of functions, including notions of rank and nuclear norm that specialize to the usual ones for matrices and operators but apply to also hypermatrices and tensors.