Title: Blind Demixing and Deconvolution at Near-Optimal Rate,
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.