Nonefficiency of stochastic beamforming bearing estimates at high SNR and finite number of samples

It is well known that the stochastic maximum-likelihood (SML) method yields Gaussian and efficient estimates when the number of independent identically distributed samples tends to infinity. This letter investigates the behavior of SML bearing estimation for a single source impinging on an antenna array when the SNR tends to infinity for a fixed number of samples. We prove that, rather surprisingly, the bearing estimates are not efficient and are asymptotically distributed according to a Student law. Simulation results confirm theoretical analysis.