Closed-form expression of the Weiss-Weinstein bound for 3D source localization: The conditional case

In array processing, lower bounds are used as a benchmark to evaluate the ultimate performance of estimators. Among these bounds, the Weiss-Weinstein bound (WWB) is known as the tightest bound of Weiss-Weinstein family, and is able to predict the threshold effect of estimator's mean square error (MSE) at low signal-to-noise ratio (SNR) and/or at low number of snapshots. In this paper, we derive a closed-form expression of the WWB for 3D source localization using an arbitrary planar antenna array in the case of a deterministic known signal. The presented results are shown to be useful for system design such as array geometry optimization.