Spectral efficiency of beamforming-based parameter estimation in the single source case

It is well known that beamforming and Capon spectral or direction estimators are biased and inefficient with respect to the Cramer-Rao bound (CRB). On the other hand, the MUSIC algorithm is known to be asymptotically unbiased and efficient, in the single zero-mean circular Gaussian source case only. In this latter case, we prove in this paper that for constant steering vector modulus, the beamforming and Capon spectral or direction estimators of possible several parameters per source are asymptotically (with respect to the number of snapshots) unbiased and efficient as well, a property previously overlooked. Finally, the theoretical numerical and empirical values of the mean square errors (MSE) of the spectral MUSIC, beamforming and Capon estimators of the direction of arrival (DOA) for a single source impinging on a planar array are compared.