Array Design for Angle of Arrival Estimation using the Worst-Case Two-Target Cramér-Rao Bound

Journal Article (2025)
Author(s)

Costas A. Kokke (TU Delft - Signal Processing Systems)

M.A. Coutino (TU Delft - Signal Processing Systems, Acoustics and Sonar Department of TNO)

R. Heusdens (Netherlands Defence Academy, TU Delft - Signal Processing Systems)

Geert J.T. Leus (TU Delft - Signal Processing Systems)

Research Group
Signal Processing Systems
DOI related publication
https://doi.org/10.1109/OJSP.2025.3558686
More Info
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Publication Year
2025
Language
English
Research Group
Signal Processing Systems
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. @en
Volume number
6
Pages (from-to)
453-467
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Abstract

Sparse array design is used to help reduce computational, hardware, and power requirements compared to uniform arrays while maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions. To handle the unknown target directions when optimizing the Cramér-Rao bound, we propose to use the worst-case Cramér-Rao bound of two uncorrelated equal power sources with arbitrary angles. This new worst-case two-target Cramér-Rao bound metric has some resemblance to the peak sidelobe level metric which is commonly used in unknown multi-target scenarios. We cast the sensor selection problem for 3-D arrays using the worst-case two-target Cramér-Rao bound as a convex semi-definite program and obtain the binary selection by randomized rounding. We illustrate the proposed method through numerical examples, comparing it to solutions obtained by minimizing the single-target Cramér-Rao bound, minimizing the Cramér-Rao bound for known target angles, the concentric rectangular array and the boundary array. We show that our method selects a combination of edge and center elements, which contrasts with solutions obtained by minimizing the single-target Cramér-Rao bound. The proposed selections also exhibit lower peak sidelobe levels without the need for sidelobe level constraints.

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