Stochastic Cramer–Rao bound for direction estimation in unknown noise fields

The stochastic Cramér–Rao bound (CRB) plays an important role in array processing because several advanced high-resolution direction-of-arrival (DOA) estimation methods are known to achieve this bound asymptotically. In the paper, the stochastic CRB on the DOA estimation accuracy is studied in the general case of an arbitrary unknown noise field parameterised by a vector of unknowns. Explicit closed-form expressions for the CRB are derived and its properties are examined theoretically and by practically relevant numerical examples.