On the asymptotic resolvability of far-field stochastic sources

The resolvability of two closely spaced signals is an important performance measure for parametric estimation problems. In this paper, we investigate the minimum signal-to-noise ratio, denoted by SNR_min, required to correctly resolve two closely spaced stochastic sources in the far-field context. As a by-product, we first derive an analytical expression of the stochastic Cramér-Rao bound (CRB) with respect to the separation parameter (i.e., we consider a new parametrization where one source is fixed). Then using the Smith criterion, we derive a closed-form expression of the SNR_min. Our analytical expression reveals some insightful properties that are discussed in detail and, finally, numerical examples are provided to corroborate the proposed theoretical analysis.