Off-Eccentricity in a Multi-Ring Planar Array—Improving the Cramér–Rao Bound for Azimuth-Elevation Direction Finding

This paper proposes an off-centric variation of the concentric circular array, which constitutes the most general planar array grid that offers azimuthal rotational symmetry for direction finding (with the “azimuth” defined on the circular plane). This off-centric variation improves direction-finding precision without adding more sensors and without enlarging the aperture size. These advantages are predicated on an astonishing insight uncovered in this paper that off-centering the rings’ origins will lower (i.e., improve) the overall array’s direction-finding Cramér-Rao bounds, which are analytically derived in this paper in mathematically closed forms.