Nonorthogonal Multibeam Network Synthesis Achieving Stein’s Limit and Implementation Based on RGW Technology

This work introduces a novel synthesis method for optimal efficiency multibeam networks. Our design method can create networks able to excite any set of nonorthogonal beams with the optimal power efficiency as dictated by Stein’s limit. To achieve this, we decompose the desired nonorthogonal excitation matrices into two orthogonal and one diagonal excitation matrices with the use of singular value decomposition (SVD). Notably, the orthogonal excitation matrices are implemented as standard Nolen matrices and the diagonal matrix as a set of parallel properly designed transmission lines. To validate our design method, we design a beamforming network for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> planar antenna array. This network operates at 30 GHz and can generate four nonorthogonal beams that can scan in the azimuth and elevation planes. Our design is implemented using ridge gap waveguide (RGW) technology, and its performance is characterized by simulation and measurements. Our beamformer achieves a 30% average power efficiency across its operating band, compared to the maximum theoretical efficiency of 55.5% calculated according to Stein’s limit.