Efficiency of subspace-based DOA estimators

This paper addresses subspace-based direction of arrival (DOA) estimation and its purpose is to complement previously available theoretical results generally obtained for specific algorithms. We focus on asymptotically (in the number of measurements) minimum variance (AMV) estimators based on estimates of orthogonal projectors obtained from singular value decompositions of sample covariance matrices in the general context of noncircular complex signals. After extending the standard AMV bound to statistics whose first covariance matrix of its asymptotic distribution is singular and deriving explicit expressions of this first covariance matrix associated with several projection-based statistics, we give closed-form expressions of AMV bounds based on estimates of different orthogonal projectors. This enable us to prove that these AMV bounds attain the stochastic Cramer–Rao bound (CRB) in the case of circular or noncircular Gaussian signals.