# Far-field multi-beam pattern synthesis for phased array antennas using Lorentz reciprocity theorem

## TL;DR

This paper introduces a new method for designing multi-beam antenna arrays using a physics-based algorithm, achieving precise beam control and uniform signal strength.

## Contribution

A novel algorithm combining Lorentz reciprocity and particle swarm optimization for efficient multi-beam synthesis in phased arrays.

## Key findings

- The method achieves gain variations below 0.1 dB across multiple beams.
- Beam synthesis is completed within 8 seconds computationally.
- Precise beam steering is maintained at target angles with uniform gain.

## Abstract

In this paper, by combining the Lorentz reciprocity theorem with the particle swarm algorithm, the array beam synthesis method based on wireless power transmission efficiency is successfully applied to the automated beam synthesis process. The improved particle swarm algorithm can achieve automatic gain balancing among multiple beams. This method explicitly combines the radiation pattern of the array element to construct the scattering parameter matrix, providing a new approach in addition to simulation software calculation and experimental measurement, and improving the conventional method of maximum power transmission efficiency. For experimental validation, a 2.45 GHz phased array antenna with a dual-layer feed structure is designed and fabricated. The proposed algorithm successfully synthesizes 2D spatially scanned beams, as well as balanced-gain dual-beam and quad-beam patterns, with measured gain variations below 0.1 dB and computational optimization completed within 8 seconds. Experimental results demonstrate precise beam steering at target angles while maintaining exceptional gain uniformity across all beams. The solution’s pattern-dependent framework ensures universal applicability to diverse array configurations requiring multi-beam synthesis with scanning capability and gain equalization, offering a robust tool for next-generation communication and radar systems.