On the geometry of isotropic arrays

We consider array geometries whose direction-of-arrival (DOA) estimation performance is isotropic. An isotropic array is one whose Cramer-Rao bound (CRB) on the DOA of a single source is uniform for all angles. For both planar arrays and volume arrays we derive necessary and sufficient conditions on array element locations so that the array is isotropic. We also present several designs of isotropic planar and volume arrays. The results apply to both narrowband and wideband scenarios. We analyze the special case where a planar array is used to estimate the DOA of three-dimensional (3-D) source. Finally, we compare isotropic array performance to the best possible array performance.