Blind Demixing and Deconvolution with Noisy Data: Near-optimal Rate

Conference: WSA 2017 - 21th International ITG Workshop on Smart Antennas
03/15/2017 - 03/17/2017 at Berlin, Deutschland

Proceedings: WSA 2017

Pages: 5Language: englishTyp: PDF

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Authors:
Stoeger, Dominik; Krahmer, Felix (Zentrum Mathematik, Technische Universität München, 85748 Garching (Munich) , Germany)
Jung, Peter (Communications and Information Theory Group, Technische Universität Berlin, 10587 Berlin, Germany)

Abstract:
We consider simultaneous blind deconvolution of r source signals from its 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. is applied 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 this significantly improves over recent results.