Angular statistical resolution limit of two closely-spaced point targets: A GLRT-based study

The study of statistical resolution limit (SRL) of two closely spaced targets has attracted considerable interests in the last decade. Two definitions for SRL have been proposed: One is based on the Cramér-Rao bound (CRB) and the other is based on a decision-based process. In this paper, we focus on the latter one. Different from the existing study, which assumes that the center parameter of interests (POIs) is known a priori, we use a more general model where all the POIs are unknown. We exploit the first-order Taylor expansion of the signals to get an approximate linear model with respect to the tested parameter, namely, the separation of directions of arrival of two sources. Then, we apply the general likelihood rate test to get a closed-form expression of SRL. We consider both the cases with known and unknown noise variance. Moreover, we analyze the impact of some parameters (including the resolution rate, the false-alarm rate, and the waveforms) on the SRL. For comparison, we also derive the CRB-based SRL, which is essentially different with our decision-based counterpart. Numerical simulation results demonstrate the validity of our theoretical results.