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Correlation Subspaces: Generalizations and Connection to Difference Coarrays

Liu, Chun-Lin and Vaidyanathan, P. P. (2017) Correlation Subspaces: Generalizations and Connection to Difference Coarrays. IEEE Transactions on Signal Processing, 65 (19). pp. 5006-5020. ISSN 1053-587X. doi:10.1109/TSP.2017.2721915.

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Direction-of-arrival (DOA) estimation finds applications in many areas of science and engineering. In these applications, sparse arrays such as minimum redundancy arrays, nested arrays, and coprime arrays can be exploited to resolve uncorrelated sources using physical sensors. Recently, it has been shown that correlation subspaces, which reveal the structure of the covariance matrix, help to improve some existing DOA estimators. However, the bases, the dimension, and other theoretical properties of correlation subspaces remain to be investigated. This paper proposes generalized correlation subspaces in one and multiple dimensions. This leads to new insights into correlation subspaces and DOA estimation with prior knowledge. First, it is shown that the bases and the dimension of correlation subspaces are fundamentally related to difference coarrays, which were previously found to be important in the study of sparse arrays. Furthermore, generalized correlation subspaces can handle certain forms of prior knowledge about source directions. These results allow one to derive a broad class of DOA estimators with improved performance. It is demonstrated through examples that using sparse arrays and generalized correlation subspaces, DOA estimators with source priors exhibit better estimation performance than those without priors, in extreme cases like low SNR and limited snapshots.

Item Type:Article
Related URLs:
URLURL TypeDescription
Liu, Chun-Lin0000-0003-3135-9684
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2017 IEEE. Manuscript received February 23, 2017; revised June 12, 2017; accepted June 13, 2017. Date of publication June 29, 2017; date of current version July 24, 2017. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Fabiola Colone. This work was supported in part by the ONR under Grant N00014-15-1-2118, in part by the California Institute of Technology, and in part by the Taiwan/Caltech Ministry of Education Fellowship.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-15-1-2118
Ministry of Education (Taipei)UNSPECIFIED
Subject Keywords:DOA estimation, sparse arrays, difference coarrays, generalized correlation subspaces, discrete prolate spheroidal sequences
Issue or Number:19
Record Number:CaltechAUTHORS:20170705-151126529
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Official Citation:C. L. Liu and P. P. Vaidyanathan, "Correlation Subspaces: Generalizations and Connection to Difference Coarrays," in IEEE Transactions on Signal Processing, vol. 65, no. 19, pp. 5006-5020, Oct.1, 1 2017. doi: 10.1109/TSP.2017.2721915
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78774
Deposited By: Kristin Buxton
Deposited On:06 Jul 2017 21:36
Last Modified:15 Nov 2021 17:43

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