An Orthogonal Beamforming Network Synthesis Method Based on Complex Givens Rotation Matrix

This letter studies the possibility of synthesizing an orthogonal beamforming network (BFN) with an arbitrary number of inputs and outputs and beam-shaping functions. The proposed synthesis approach is based on complex Givens rotation matrices and is realized through the optimized program. First, it is derived that a complex Givens rotation matrix can represent a directional coupler with corresponding power ratio and phase difference. Then, this letter presents a computer-aided program to synthesize BFN that combines matrix cascading techniques and optimization algorithms, achieving beam shaping function. For validating the proposed synthesis approach, an example of an orthogonal 2 × 6 BFN with flat-topped radiation patterns for diversity application is presented. The accuracy and efficiency make the proposed synthesis method beneficial in antenna array systems.