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Conditions for Identifiability in Sparse Spatial Spectrum Sensing

Pal, Piya and Vaidyanathan, P. P. (2013) Conditions for Identifiability in Sparse Spatial Spectrum Sensing. In: 21st European Signal Processing Conference (EUSIPCO). Vol.3. IEEE , Piscataway, NJ, pp. 1832-1836. ISBN 9781479936878. https://resolver.caltech.edu/CaltechAUTHORS:20141021-071826078

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Abstract

Spatial Spectrum estimation is a key technique used in a wide variety of problems arising in signal processing and communication, particularly those employing multiple antennas. In many scenarios such as direction finding using antenna arrays, it is crucial to estimate which directions in space contribute to active sources (indicated by a non zero power). It has been recently shown that if the sources from different directions are statistically uncorrelated, it is possible to identify as many as O(M2) active sources using only M physical antennas. A sparse representation for the spatial spectrum was further exploited to reconstruct the spectrum using convex optimization techniques. In this paper, we consider the situation when there is non zero cross correlation between the sources impinging from different directions. We investigate if, fundamentally, it still possible to identify more sources than the number of physical sensors and what role the cross correlation terms play. Recovery guarantees are developed to ensure uniqueness of the sparse representation for spectrum sensing. They are further extended to establish conditions under which a greedy heuristic, namely the Orthogonal Matching Pursuit algorithm will successfully recover the sparse spectrum. It is shown that in both cases, it is possible to recover support of larger size provided the correlation terms are small compared to the power of the impinging signals.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6811756PublisherArticle
ORCID:
AuthorORCID
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2013 IEEE. Work supported in parts by the ONR grant N00014-11-1-0676, and the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0676
CaltechUNSPECIFIED
Subject Keywords:Sparse Spectrum Estimation, Correlated Sources, Khatri-Rao Product, Kruskal Rank Orthogonal Matching Pursuit.
Record Number:CaltechAUTHORS:20141021-071826078
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141021-071826078
Official Citation:Pal, P.; Vaidyanathan, P.P., "Conditions for identifiability in sparse spatial spectrum sensing," Signal Processing Conference (EUSIPCO), 2013 Proceedings of the 21st European , vol. 3, no., pp.1832-1836, 9-13 Sept. 2013
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50590
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Oct 2014 15:27
Last Modified:09 Mar 2020 13:19

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