The stochastic CRB for array processing: a textbook derivation

The stochastic Cramer-Rao bound (CRB) for direction estimation in array processing applications was indirectly derived some ten years ago as the (asymptotic) covariance matrix of the maximum likelihood (ML) estimator. Attempts to obtain the stochastic CRB directly via the CRB theory fell short of providing a simple derivation and consequently, no direct derivation of this useful performance bound was available in the open literature. we correct this situation by providing a textbook-like direct derivation of the stochastic CRB.