A General Approach for Synthesizing Multibeam Antenna Arrays Employing Generalized Joined Coupler Matrix

Abstract

Despite the rapidly increasing interest in analog multibeam antennas, there has been a lack of systematic theoretical approaches to synthesizing circuit-type multiple beamforming networks, such as the Blass matrix and the Nolen matrix. To address the issue, this article presents a new concept, the generalized joined coupler (GJC) matrix, which encapsulates both the Blass matrix and the Nolen matrix, as well as their variants, and presents a novel theoretical framework for generating individually and independently controllable multiple beams using the GJC matrix. A GJC matrix has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N $ </tex-math></inline-formula> columns to feed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N $ </tex-math></inline-formula> antenna elements and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M $ </tex-math></inline-formula> rows to feed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M $ </tex-math></inline-formula> beams, and the direction of each individual beam can be controlled by tuning the phase shifters in the associated row of the GJC matrix. In this article, a matrix theory is developed, and an optimization algorithm is proposed to provide a mathematical tool for synthesizing such matrices and, consequently, the multiple beams. Using a particle swarm optimization algorithm, numerical results demonstrate that multibeams with independent control of individual beam directions and sidelobes can, indeed, be synthesized in a systematic manner. Specifically, two GJC matrix variants, the Blass-like matrix and the Nolen-like matrix, are investigated.