Stochastic Cramer-Rao bound for direction estimation of non-circular signals in unknown noise fields

This paper gives explicit closed-form expressions of the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for non-circular Gaussian sources in the case of an arbitrary unknown noise field parameterized by a vector of unknowns from the Slepian-Bangs formula. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai (1990), Weiss and Friedlander (1993), Ottersten et al. (1992), and Gershman et al. (2002). Some properties of these CRB are proved, then these bounds are numerically compared with the conventional CRB under the circular complex Gaussian distribution for different unknown noise field models.