Performance bounds of direction finding and its applications for multiple-input multiple-output radar

In this study, the authors derive an explicit expression for Cramer-Rao lower bound (CRLB) on direction parameters with the antenna locations of a single point target in the far-field scenario for multiple-input multiple-output (MIMO) radar, firstly. Since there are two unknown nuisance parameters (target radar cross section and interference-plus-noise strength), the authors use the concentrated CRLB to simplify the analytical computation. Then, the authors derive two sets of necessary and sufficient geometrical constraints for direction estimation with both bistatic and monostatic MIMO radars. Then, the authors consider the bounds on the asymptotic normalised mean-square angular error (ANMSAE), which are useful measures in three-dimensional bearing estimation problems. The authors derive the expressions for ANMSAE in both bistatic and monostatic MIMO radars, and discuss them in terms of the antenna locations. The authors then show that the uncoupled geometrical conditions are also sufficient to ensure that ANMSAE is independent of azimuth. Finally, the authors extend those conditions to obtain two sets of geometry constraints for bistatic and monostatic MIMO radars, respectively, such as some kinds of symmetry on the geometry, that ensure the optimal performance is isotropic, that is, the ANMSAE bounds are independent of all direction parameters. In numerical examples section, the authors give several representative antenna geometries to illustrate the derived antenna geometry strategy.