Fundamental resolution limits of closely spaced random signals

Fundamental limitations on estimation accuracy are well known and include a variety of lower bounds including the celebrated Cramér-Rao lower bound. However, similar theoretical limitations on resolution have not yet been presented. The authors exploit results from detection theory for deriving fundamental limitations on resolution. In this correspondence the authors discuss the case of zero mean random Gaussian signals with a general and predefined covariance matrix observed with additive white Gaussian noise. The results are general and are not based on any specific resolution technique and therefore hold for any method and for any probability of successful resolution. The resolution limit is a simple expression of the observation interval, the pre-specified resolution success probability and the second derivative of the covariance matrix. As an example, the authors discuss the bearing resolution of two emitters with closely spaced direction of arrival, impinging on an array of sensors. The theoretical limits are compared with empirical performance of the model order selection criteria known as the Akaike information criterion and the minimum description length.