Study of Barankin bound vs Cramér-Rao bound for interferometric-like array design at low SNR

Abstract

In this paper, we address the antenna array design problem at low signal-to-noise ratio (SNR). The Cramér-Rao bound (CRB) is the most commonly used criterion to solve the array optimization problem due to its computing simplicity and tightness in the asymptotical region. However, there exists a threshold SNR at which the estimation variance significantly deviates from the CRB. In this case, the CRB is no longer a tight bound. To address this issue, we propose the use of the Barankin Bound (BB) on the source location and source intensity in astrometry and photometry problems as an alternative optimization criterion. BB provides a mean square error (MSE)-optimal trade-off mainlobe width and sidelobe level of beampattern. The performance of the obtained array geometries is assessed and compared by evaluating the aforementioned bounds and the mean square error (MSE) on the estimation of source location and intensity. The simulation results illustrate that the BB-based criterion provides a trade-off between increasing the estimation accuracy and reducing the ambiguity.