Abstract-In this paper we consider the design of planar arrays that optimize direction-of-arrival (DOA) estimation performance. We assume that the single source DOA is a random variable with a known prior probability distribution and the sensors of the array are constrained to lie in a region with an arbitrary boundary. The Cramér-Rao Bound (CRB) and the Fisher Information Matrix (FIM) for single source DOA constitute the basis of the optimality criteria. We relate the design criteria to a Bayesian CRB criterion and to array beamwidth; we also derive closed-form expressions for the design criteria when the DOA prior is uniform on a sector of angles. We show that optimal arrays have elements on the constraint boundary, thus providing a reduced dimension iterative solution procedure. Finally, we present example designs.Index Terms-array design, planar arrays, direction of arrival estimation, Cramér-Rao bound

Abstract-We consider the effect of unknown signal propagation velocity on direction-of-arrival (DOA) estimation performance using an array of sensors. For general arrays, the DOA estimation variance, as measured by the Cramér-Rao bound (CRB), degrades when the propagation velocity is unknown. In this letter, we show that for both two-and three-dimensional arrays, the CRB on the DOA angle is independent of whether or not the propagation velocity is known if and only if the sensor locations satisfy the isotropy conditions given in earlier work. The results hold for both narrowband and wideband signals.