Analysis of a subspace-based spatial frequency estimator

In a previous paper we presented a novel method for spatial and temporal frequency estimation assuming that the sources are uncorrelated. The current paper analyzes this method in the case of spatial frequency estimation. In particular an optimal weighting matrix is derived and it is shown that the asymptotic variance of the frequency estimates coincides with the relevant Cramer-Rao lower bound. This means that the estimator is in large samples an efficient subspace-based spatial frequency estimator. The proposed method thus utilizes the a priori knowledge about the signal correlation as opposed to previously known subspace estimators. Moreover, when a uniform linear array is employed, it is possible to implement the estimator in a non-iterative fashion