Derivation of an analytical expression of the Gaussian model Statistical Resolution Limit

Statistical Resolution Limit (SRL), defined as the minimal separation to resolve two closely spaced signals, is one of the important tools to evaluate a given system performance. Based on S.T. Smith´s formulation of the SRL, this paper provides a methodology to compute an approximate analytical expression of the resolution limit in the Gaussian model case. As an application, we consider the particular case of two sources located in the near field and consider the resolution limit in terms of minimum angular separation. Discussion and numerical illustrations are then given to get more insights on the proposed derivation and to validate our theoretical results.