Cylindrical Luneburg Lens Antenna Systems for Amplitude-Only Direction-Finding Applications

An approach to design a multibeam Luneburg lens (LL) antenna for correlation-based amplitude-only direction-finding (AODF) systems is presented. The proposed framework expands on the existing literature by prescribing not only the number of detectors and lens radius for some performance but also feed parameters that may be generalized to a wide variety of lens antenna excitations. The approach consists of two main steps. First, beam requirements to achieve low angle-of-arrival (AoA) estimation errors within a prescribed field of view (FoV) are defined using ideal systems consisting of $\cos ^{n}\theta $ beams. Considering the chosen beam model, the requirements may be translated to other multibeam antennas besides LLs. Second, a straightforward semianalytical method is developed to determine the lens radius, and its feed characteristics fulfilling those requirements. Demonstrating the proposed design methodology, an additively manufactured cylindrical LL fed by all-metal Vivaldi elements, operating over the Ka-band, is realized. A good agreement between theory and measurements validates the proposed approach.