Published June 2020 | Submitted
Journal Article Open

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

An error occurred while generating the citation.

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

Files

Robustness_Algorithm_SigPro.pdf
Files (467.3 kB)
Name Size Download all
md5:e2df1a50500f257d508fba8a087e28da
467.3 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 19, 2023