Efficiency of subspace-based estimators

This paper addresses subspace-based 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 associated with the general linear model y
t
= A(Θ)x
t
+ n
t
where the signals x
t
are complex circular or noncircular and dependent or independent. Using closed-form expressions of AMV bounds based on estimates of different orthogonal projectors, we prove that these AMV bounds attain the stochastic Cramer-Rao bound (CRB) in the case of independent circular or noncircular Gaussian signals.