Optimum ambiguity-free isotropic antenna arrays

Based on the CRB of the 2D-DOA estimation problem, we prove a condition on the sensor coordinates of a planar array to be ambiguity-free and isotropic. A systematic search of such antenna arrays is conducted leading to the identification of all possible ambiguity-free isotropic arrays. In particular, we select the arrays that outperform the popular uniform circular array (UCA). It is shown that these arrays allow to enhance the DOA estimation by as much as 25%, in comparison with UCA. As the number of sensors increases, the best isotropic array tends towards the non-intuitive V-shape.