A comparison of antenna placement criteria based on the Cramér–Rao and Barankin bounds for radio interferometer arrays

• Published in: Signal processing Vol. 219; p. 109404
• Main Authors: Wang, Jianhua, Bacharach, Lucien, Larzabal, Pascal, El Korso, Mohammed Nabil
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2024; Elsevier
• Subjects: Antenna placement; Barankin bound; Cramér–Rao bound; Engineering Sciences; Signal and Image processing; Antenna placement; Barankin bound; Cramér–Rao bound; Cramér-Rao bound
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2024.109404

In this paper, we consider the problem of antenna placement for radio interferometer arrays. In this type of applications, signal-to-noise ratios (SNR) are typically low, and possibly lower than a SNR threshold under which the estimation performance of source parameters may degrade significantly. In this regime, the Cramér–Rao bound (CRB), which is often used for array design, is not a tight bound of the MSE. Therefore, we study the use of a Barankin-type bound (BTB) as an alternative array design criterion. We assess and compare the array geometries based on the CRB and the BTB in terms of MSE for a source’s DOA and intensity. We also study how both geometries perform for imaging purposes. Specifically, the obtained results are assessed in terms of uv-plane coverage (completeness of spatial frequency sampling), mainlobe width and sidelobe level of the synthesized beam, as well as image reconstruction performance. Numerical experiments show that the BTB-based design leads to better overall estimation performance over a fairly wide range of SNR and to an enhanced array imaging capability, compared with a CRB-based approach.