Dynamic Independent Component Extraction with Blending Mixing Vector: Lower Bound on Mean Interference-to-Signal Ratio

TL;DR

This paper introduces a new dynamic source extraction model, CvxCSV, which improves interference suppression and requires weaker conditions for source identifiability compared to previous models.

Contribution

The paper proposes CvxCSV, a reduced-parameter model for dynamic BSE, and derives a lower bound on ISR showing its advantages over existing models.

Findings

CvxCSV achieves lower mean ISR than previous models.

CvxCSV requires weaker conditions for source identifiability.

The derived lower bound guides the design of more effective BSE algorithms.

Abstract

This paper deals with dynamic Blind Source Extraction (BSE) from where the mixing parameters characterizing the position of a source of interest (SOI) are allowed to vary over time. We present a new source extraction model called CvxCSV which is a parameter-reduced modification of the recent Constant Separation Vector (CSV) mixing model. In CvxCSV, the mixing vector evolves as a convex combination of its initial and final values. We derive a lower bound on the achievable mean interference-to-signal ratio (ISR) based on the Cram\'er-Rao theory. The bound reveals advantageous properties of CvxCSV compared with CSV and compared with a sequential BSE based on independent component extraction (ICE). In particular, the achievable ISR by CvxCSV is lower than that by the previous approaches. Moreover, the model requires significantly weaker conditions for identifiability, even when the SOI is Gaussian.