Angular resolution limit for array processing: Estimation and information theory approaches

In this paper, we study the behavior of the angular resolution limit (ARL) for two closely spaced sources in the context of array processing. Particularly, we derive new closed-form expressions of the ARL, denoted by δ, for three methods: the first one, which is the main contribution of this work, is based on the Stein´s lemma which links the Chernoff´s distance and a given/fixed probability of error, P_e, associated to the binary hypothesis test: H₀: δ = 0 versus H₁: δ = 0. The two other methods are based on the well-known Lee and Smith´s criteria using the Cramér-Rao Bound (CRB). We show that the proposed ARL based on the Stein´s lemma and the one based on the Smith´s criterion have a similar behavior and they are proportional by a factor which depends only on P_fa and P_d and not on the model parameters (number of snapshots, sensor, sources, ....). Another conclusion is that for orthogonal signals and/or for a large number of snapshots, it is possible to give an unified closed-form expression of the ARL for the three approaches.