Stochastic Cramér-Rao Bound Analysis for DOA Estimation in Spherical Harmonics Domain

Cramér-Rao bound (CRB) has been formulated in earlier work for linear, planar and 3-D array configurations. The formulations developed in prior work, make use of the standard spatial data model. In this paper, the existence of CRB for the spherical harmonics data model is first verified. Subsequently, an expression for stochastic CRB is derived for direction of arrival (DOA) estimation in spherical harmonics domain. The stochastic CRBs for azimuth and elevation are plotted at various signal to noise ratios (SNRs) and snapshots. It is noted that a lower bound on the CRB is attained at high SNR. A similar observation is made when larger number of snapshots are used.