Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signals

TL;DR

This paper develops large-sample theoretical results for a non-stationary source separation method based on joint diagonalization, under general assumptions for Gaussian signals, and verifies these results through simulations.

Contribution

It provides the first large-sample theory for NSS-JD, establishing consistency and asymptotic normality under broad conditions.

Findings

Unmixing estimator is consistent and asymptotically normal.

Simulation confirms theoretical convergence and impact of block length.

Method works under general assumptions for Gaussian non-stationary sources.

Abstract

Non-stationary source separation is a well-established branch of blind source separation with many different methods. However, for none of these methods large-sample results are available. To bridge this gap, we develop large-sample theory for NSS-JD, a popular method of non-stationary source separation based on the joint diagonalization of block-wise covariance matrices. We work under an instantaneous linear mixing model for independent Gaussian non-stationary source signals together with a very general set of assumptions: besides boundedness conditions, the only assumptions we make are that the sources exhibit finite dependency and that their variance functions differ sufficiently to be asymptotically separable. The consistency of the unmixing estimator and its convergence to a limiting Gaussian distribution at the standard square root rate are shown to hold under the previous conditions. Simulation experiments are used to verify the theoretical results and to study the impact of block length on the separation.