Design Guidelines Using Groove Gap-Waveguide Technology for Realizing a Millimeter-Wave 4×4 Butler Beamforming Matrix for Space Multiplexing

This paper presents a practical design guideline for implementing a 4×4 Butler Beamforming Matrix (BBM) using Groove Gap-Waveguide (GGW) technology to enable multi-beam functionality. The proposed BBM consists of 3-dB hybrid directional couplers, crossovers, phase shifters, and phase compensators. A GGW-inspired unit-cell is optimized to provide a wide stopband spanning 22-40GHz. This unit-cell is employed to realize the BBM's structural components, ensuring broadband operation across 30-40GHz and achieving the required phase shifts for multi-beam capability. By integrating these components according to the proposed architecture, a compact and efficient 4×4 BBM suitable for antenna arrays in space multiplexing systems is realized. This design approach can be extended to other beamforming networks such as Nolen and larger-scale Butler matrices. Key advantages include a straightforward design process, wideband operation, low-loss, low-profile, ease of fabrication, and cost-effectiveness, making it well-suited for applications in satellite communications, space multiplexing, and radar tracking systems at millimeter-wave frequencies.