Blind Demixing and Deconvolution at Near-Optimal Rate

TL;DR

This paper presents a convex optimization approach for blind demixing and deconvolution, enabling near-optimal recovery of multiple source signals and channels in sensor networks with fewer measurements than previous methods.

Contribution

It introduces a convex optimization framework that achieves near-optimal measurement scaling for blind demixing and deconvolution with multiple sources.

Findings

Recovery is robust under noisy conditions.

Measurement requirements scale linearly with the number of sources.

The method outperforms recent approaches in measurement efficiency.

Abstract

We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding using i.i.d. complex Gaussian matrices is used at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in r our result significantly improves over recent works.