CramÉr-rao Bound for DOA Estimators under the Partial Relaxation Framework

Abstract

In this paper, the Cramér-Rao Bound for the Direction-ofArrival parameter under the partial relaxation framework is derived. We introduce a non-redundant parameterization of the signal model corresponding to the partial relaxation framework, in which the array structure in part of the steering matrix is neglected while the rank of the relaxed steering matrix is maintained. We prove that the stochastic Cramér-Rao Bound for the Direction-of-Arrival parameter under the partial relaxation signal model is lower-bounded by that of the conventional stochastic Cramér-Rao Bound. Furthermore, we prove that the partial relaxation estimator for the Weighted Subspace Fitting criterion asymptotically achieves the conventional Cramér-Rao Bound in the case of uncorrelated source signals.