Broad-Band Nolen Beamforming Matrix Inspired by Groove Gap Waveguide Technology for Multi-Beam Antenna Arrays in mmWave Satellite-Oriented Space Multiplexing Systems

This work presents the design and experimental validation of an integrated single-layer 4 × 4 Nolen beamforming matrix (NBM) implemented in groove gap waveguide (GGW) technology as an enabling front-end for multi-beam satellite gateway systems. The matrix is designed for operation within the 30–40 GHz upper Ka-band region, with optimal impedance matching and beamforming performance centered around 38 GHz, offering low-loss planar routing suitable for compact mmWave front-end architectures. The network combines broadband H-plane directional couplers (3.04, 4.77, and 6.0 dB) with fundamental and delay-compensation phase shifters to equalize amplitudes and maintain progressive phase. A WR-28-compatible input-feeding transition enables practical interfacing without disturbing the internal phase states, and a linear 4×4 slot-array antenna is integrated to demonstrate wide-angle multibeam radiation. In contrast to prior Nolen matrices, including recent GGW implementations, this work introduces a fully single-layer GGW realization with parallel routing and built-in delay compensation, achieving phase error within (±10^◦), near-equalized amplitudes, and simplified fabrication within a compact footprint. In particular, compared to the recent GGW-based Nolen matrices, which employ the multilayer configurations and report only simulation results, the proposed work demonstrates the first experimentally validated single-layer GGW Nolen matrix with integrated feeding transition and radiating array. Measurements confirm return loss better than −15 dB, port-to-port isolation exceeding 15 dB, amplitude imbalance within ±1.2 dB (around 6 dB nominal output), and phase error within ±10^◦ with stable phase progression around 38 GHz.