Stochastic Cramér–Rao Bound for Noncircular Signals with Application to DOA Estimation

After providing an extension of the Slepian–Bangs formula for general noncircular complex Gaussian distributions, this paper focuses on the stochastic Cramér–Rao bound (CRB) on direction-of-arrival (DOA) estimation accuracy for noncircular sources. We derive an explicit expression of the CRB for DOA parameters alone in the case of noncircular complex Gaussian sources by two different methods. One of them consists of computing the asymptotic covariance matrix of the maximum likelihood (ML) estimator, and the other is obtained directly from our extended Slepian–Bangs formula. Some properties of this CRB are proved, and finally, it is numerically compared with the CRBs under circular complex Gaussian and complex discrete distributions of sources.