A Note on the Cramer-Rao Bound for 2-D Direction Finding Based on 2-D Array

We present explicit expressions of the Cramer-Rao bound (CRB) for estimating the two-dimensional (2-D) direction of single source based on a 2-D array of identical omnidirectional sensors. The two often used models, random wave model and unknown wave model, are compared. It is shown that the CRB's for the two models have the same dependency on the array structure. A specialization of the CRB for two orthogonal uniform linear arrays (ULA's) is discussed. It is found that the joint CRB's of the direction angles based on the two orthogonal ULA's can be as low as one quarter (for the random wave model with large number of snapshots and low SNR) or one half (for both models with high SNR) of the CRB's based on each ULA.