# Adaptive Blind Separation of Two Dependent Sources

## TL;DR

This paper explores adaptive blind source separation for two sources that may be dependent, identifying conditions under which separation is feasible and providing simulations to demonstrate successful separation of dependent sources.

## Contribution

It extends blind source separation techniques to dependent sources by analyzing symmetry conditions, broadening the scope beyond independent sources.

## Key findings

- Separation is possible for dependent sources with certain symmetry in their joint pdf.
- Theoretical analysis identifies classes of dependent sources that are separable.
- Simulations confirm the practical effectiveness of the proposed approach.

## Abstract

We consider the problem of adaptive blind separation of two sources from their instantaneous mixtures. We focus on the case where the two sources are not necessarily independent. By analyzing a general form of adaptive algorithms we show that separation is possible not only for independent sources but also for sources that are dependent provided their joint pdf satisfies certain symmetry conditions. A very interesting problem consists in identifying the class of dependent sources that are non-separable, namely, the counterpart of Gaussian sources of the independent case. We corroborate our theoretical analysis with a number of simulations and give examples of dependent sources that can be easily separated.