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

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.