A note on the Cramer-Rao bound for 2-D direction finding based on 2-D array

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