Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures
- Creators
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Liu, Chun-Lin
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Vaidyanathan, P. P.
Abstract
Sparse arrays have drawn attention because they can identify O(N²) uncorrelated source directions using N physical sensors, whereasuniform linear arrays (ULA) find at most N−1 sources. The main reason is that the difference coarray, defined as the set of differences between sensor locations, has size of O(N²) for some sparse arrays. However, the performance of sparse arrays may degrade significantly under sensor failures. In the literature, the k-essentialness property characterizes the patterns of k sensor failures that change the difference coarray. Based on this concept, the k-essential family, the k-fragility, and the k-essential Sperner family provide insights into the robustness of arrays. This paper proposes novel algorithms for computing these attributes. The first algorithm computes the k-essential Sperner family without enumerating all possible k-essential subarrays. With this information, the second algorithm finds the k-essential family first and the k-fragility next. These algorithms are applicable to any 1-D array. However, for robust array design, fast computation for the k-fragility is preferred. For this reason, a simple expression associated with the k-essential Sperner family is proposed to be a tighter lower bound for the k-fragility than the previous result. Numerical examples validate the proposed algorithms and the presented lower bound.
Additional Information
© 2020 Published by Elsevier B.V. Received 1 May 2019, Revised 12 January 2020, Accepted 30 January 2020, Available online 31 January 2020. This work was supported in part by the ONR grant N00014-18-1-2390, in part by the NSF grant CCF-1712633, in part by the California Institute of Technology, in part by the Ministry of Education, Taiwan, under Grant Numbers NTU-107V0902 and NTU-108V0902, in part by the Ministry of Science and Technology, Taiwan,under Grant Number MOST 108-2218-E-002-043-MY2, and in part by the National Taiwan University.Attached Files
Submitted - Robustness_Algorithm_SigPro.pdf
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Additional details
- Eprint ID
- 101044
- Resolver ID
- CaltechAUTHORS:20200131-154057752
- Office of Naval Research (ONR)
- N00014-18-1-2390
- NSF
- CCF-1712633
- Caltech
- Ministry of Education (Taipei)
- NTU-107V0902
- Ministry of Education (Taipei)
- NTU-108V0902
- Ministry of Science and Technology (Taipei)
- MOST 108-2218-E-002-043-MY2
- National Taiwan University
- Created
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2020-01-31Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field