Blind Deconvolution using Modulated Inputs

DOI10.1109/TSP.2019.2959218arXiv1811.08453MaRDI QIDQ6310015

Author name not available (Why is that?)

Publication date: 20 November 2018

Abstract: This paper considers the blind deconvolution of multiple modulated signals, and an arbitrary filter. Multiple inputs $$ are modulated (pointwise multiplied) with random sign sequences $$, respectively, and the resultant inputs $$ are convolved against an arbitrary input $$ to yield the measurements $$ where $odot$, and $circledast$ denote pointwise multiplication, and circular convolution. Given $$, we want to recover the unknowns $$, and $$. We make a structural assumption that unknown $$ are members of a known $K$-dimensional (not necessarily random) subspace, and prove that the unknowns can be recovered from sufficiently many observations using an alternating gradient descent algorithm whenever the modulated inputs $$ are long enough, i.e, $QgtrsimKN+M$ (to within log factors and signal dispersion/coherence parameters).

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