• This work introduces an innovative 3 × 3 beamforming Nolen-matrix feeding network utilizing gap-waveguide technology. • The innovation lies in the matrix’s crossover-free architecture. • The system's performance is experimentally validated over the entire 36–39 GHz band. • The proposed beamformer represents a highly efficient and robust solution for next-generation beamforming arrays and 6G mm-wave satellite communications. This paper presents a compact 3 × 3 beamforming Nolen-matrix feeding network (BNMFN) based on groove gap-waveguide (GGW) technology for Ka-band satellite and space-multiplexing applications. The proposed design eliminates conventional components such as power dividers, crossovers, switches, and terminations by utilizing only directional couplers and phase-shift compensators, thereby reducing size, loss, and complexity. The network employs three 90° couplers (3.14 dB and 4.84 dB) and two-phase shifters (–38° and –63°) to achieve output phase differences of 270°, 30°, and 150° at 38 GHz. Integrated with a GGW-based feeding transition and a three-element slotted antenna array, the system demonstrates multi-beam radiation with gains exceeding 17 dBi over 36–39 GHz. Experimental results validate low loss, wide bandwidth, and accurate phase performance, making the design a promising solution for 6G millimeter-wave satellite communications and IoT connectivity.
Alibakhshikenari et al. (2026) studied this question.