Optimum Ambiguity-Free Directional and Omnidirectional Planar Antenna Arrays for DOA Estimation

This paper studies the antenna array geometry impact on both direction of arrival (DOA) estimation accuracy and array rank ambiguity. Some restrictions are imposed on the array geometry that guarantee first-order ambiguity-free arrays and, at the same time, reduce the cost of a global systematic optimization. The subsequently derived Cramer-Rao bound (CRB) on the DOA estimates shows to be attractive for numerical evaluation. Depending on whether the DOA estimation accuracy is desired to be uniform in all possible directions or is to be enhanced in a given aperture around some privileged direction, two optimization problems are formulated and solved by exhaustive search to compute the optimal array geometries. The obtained optimal arrays significantly outperform their circular counterparts and tend to have a form close to the V shape. We study in details V-shaped arrays and derive asymptotic performance measures that apply for large sized arrays where exhaustive search is unaffordable.