Cramer-Rao bounds on angle estimation with a two-dimensional array

Cramer-Rao variance bounds are derived for azimuth and elevation estimates made with a planar array. A necessary and sufficient condition on the array geometry which ensures that these estimates uncouple is presented. As examples, a line array which does not satisfy this condition and a planar array which does satisfy this condition are examined. It is impossible to estimate both azimuthal and elevation angles with a line array. The planar array example presents an important special case for which uncoupled estimation is achieved. This basic array configuration of concentric circular subarrays can be used to synthesize arrays which yield uncoupled estimates of azimuth and elevation