Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability

TL;DR

This paper extends the theoretical understanding of complex-valued ICA models by establishing conditions for their identifiability, separability, and uniqueness, including properties of complex random vectors and the Darmois-Skitovich theorem.

Contribution

It generalizes real-valued ICA conditions to complex models and introduces new theoretical results for both circular and noncircular complex vectors.

Findings

Conditions for identifiability, separability, and uniqueness are established.

The Darmois-Skitovich theorem is extended to complex-valued models.

Examples illustrate the theoretical concepts.

Abstract

In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA problems to complex-valued models. Relevant properties of complex random vectors are described in order to extend the Darmois-Skitovich theorem for complex-valued models. This theorem is used to construct a proof of a theorem for each of the above ICA model concepts. Both circular and noncircular complex random vectors are covered. Examples clarifying the above concepts are presented.