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Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures

Liu, Chun-Lin and Vaidyanathan, P. P. (2020) Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures. Signal Processing, 171 . Art. No. 107517. ISSN 0165-1684.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Liu, Chun-Lin0000-0003-3135-9684
Vaidyanathan, P. P.0000-0003-3003-7042
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.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-18-1-2390
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 UniversityUNSPECIFIED
Subject Keywords:Sparse arrays; Difference coarrays; Essentialness; Fragility; Numerical algorithms
Record Number:CaltechAUTHORS:20200131-154057752
Persistent URL:
Official Citation:Chun-Lin Liu, P.P. Vaidyanathan, Novel algorithms for analyzing the robustness of difference coarrays to sensor failures, Signal Processing, Volume 171, 2020, 107517, ISSN 0165-1684, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101044
Deposited By: Tony Diaz
Deposited On:31 Jan 2020 23:51
Last Modified:01 May 2020 18:26

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