Physics-Informed Analytical Framework for Design and Optimization of a Dual-Radius Spherical Antenna Array under Mutual Coupling

Developing high-performance antenna arrays for next-generation wireless systems necessitates precise control over radiation characteristics, mutual coupling effects, and spatial configurations. An effective antenna array configuration for examining the spatial characteristics of Electromagnetic (EM) fields is spherical antenna arrays (SAAs). However, the physical properties of the array ultimately determine how well SAA-based signal processing algorithms operate. In particular, the array’s size, the elements’ angular positions, and other variables affect the frequency range over which an SAA offers good spatial information. In contrast to traditional designs, this research explores the design of SAAs that provide a broader frequency range of operation, and elements are dispersed on and away from the surface of a rigid spherical array to achieve this. At first, a general framework for modeling SAAs with elements positioned at different distances from the origin of the array and for calculating optimal filters to decompose the EM wave into spherical harmonic modes is presented. Additionally, an optimization technique is proposed for developing multi-radius SAAs that considers the total number of components and the intended spatial resolution to accomplish an optimally wide frequency range of operation. In addition, a proof-of-concept dual-radius SAA prototype with 64 components is designed based on the optimization results. A comparison between the theoretical predictions and the measurements for the prototype SAA is conducted, and the results obtained are good enough to support the implementation of the proposed framework in practical EM engineering. For instance, this work lays a foundational step toward developing compact, high-gain antenna arrays for emerging applications in 5G/6G communications, satellite systems, and wireless sensor networks.