MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Leveraging Diversity and Sparsity in Blind Deconvolution

Author(s)
Ahmed, Ali; Demanet, Laurent
Thumbnail
Download1610.06098.pdf (1.404Mb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
IEEE This paper considers recovering L-dimensional vectors w, and x1, x2,...,xN from their circular convolutions yn = w * x [subscript n]; n = 1, 2, 3,...,N. The vector w is assumed to be S-sparse in a known basis that is spread out in the Fourier domain, and each input x[subscript n] is a member of a known K-dimensional random subspace. We prove that whenever K + S log[superscript 2]S ≲ L/log[superscript 4](LN), the problem can be solved effectively by using only the nuclear-norm minimization as the convex relaxation, as long as the inputs are sufficiently diverse and obey N ≳ log[superscript 2](LN). By "diverse inputs", we mean that the x[subscript n]'s belong to different, generic subspaces. To our knowledge, this is the first theoretical result on blind deconvolution where the subspace to which w belongs is not fixed, but needs to be determined. We discuss the result in the context of multipath channel estimation in wireless communications. Both the fading coefficients, and the delays in the channel impulse response w are unknown. The encoder codes the K-dimensional message vectors randomly and then transmits coded messages x[subscript n]'s over a fixed channel one after the other. The decoder then discovers all of the messages and the channel response when the number of samples taken for each received message are roughly greater than (K + Slog[superscript 2]S) log[superscript 4](LN), and the number of messages is roughly at least log2(LN).
Date issued
2018-06
URI
http://hdl.handle.net/1721.1/116040
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Ahmed, Ali and Laurent Demanet. “Leveraging Diversity and Sparsity in Blind Deconvolution.” IEEE Transactions on Information Theory (2018) 64, 6: 3975 - 4000 © IEEE
Version: Original manuscript
ISSN
0018-9448
1557-9654

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.