Design of Extended Nolen Matrix With Enhanced Beam Controllability and Widened Spatial Coverage

In this brief, novel extended lower order Nolen matrices to achieve enhanced beam controllability and wider spatial coverage are presented. The extended Nolen matrices are composed of standard lower order (3×3/4×4) Nolen matrices cascaded with phase shifters controlled by single-pole multi-throw (SPMT) switches. The proposed extended 3×3 and 4×4 Nolen matrices are theoretically capable of achieving spatial coverage with 3M and 4M beams, respectively, using a concise structure and reducing design complexity. As an example, a switchable 6-beamforming network (6-BFN) based on the extended 3×3 Nolen matrix and a switchable 8-BFN based on the extended 4×4 Nolen matrix are fabricated and measured. As demonstrated, the proposed beam-switching systems exhibit the potential for enhanced beam controllability and widened spatial coverage.