On the Angular Resolution Limit for Array Processing in the Presence of Modeling Errors

In this correspondence, we study the impact of modeling errors on the angular resolution limit (ARL) for two closely spaced sources in the context of array processing. Particularly, we follow two methods based on the well-known Lee and Smith´s criteria using the Cramér-Rao lower bound (CRB) to derive closed-form expressions of the ARL with respect to (w.r.t.) the error variance. We show that, as the signal-to-noise ratio increases, the ARL does not fall into zero (contrary to the classical case without modeling errors) and converge to a fixed limit depending on the method for which we give a closed-form expression. One can see that at high SNR, the ARL in the Lee and Smith sense are linear as a function of the error variance. We also investigate the influence of the array geometry on the ARL based on the Lee´s and Smith´s criteria.