Generalized Scattering Matrix Synthesis: Independent Region Decomposition for Hybrid Antenna--Scatterer Systems

This paper presents a unified formulation for synthesizing the generalized scattering matrix (GS-matrix) of hybrid electromagnetic systems comprising arbitrary numbers of antennas and scatterers. The proposed method provides a modular region decomposition framework that enables efficient analysis of electromagnetic interactions between distinct structures, under the relaxed geometric condition that the constituents are separable by a plane. By leveraging the addition theorem of vector spherical wavefunctions (VSWFs), a compact matrix representation is derived to assemble the GS- and S-matrices of individual components into the overall system response. This formulation generalizes and extends prior methods developed for either multiple scattering or antenna array analysis, and is particularly suited to configurations where substructures may be repositioned or reused. Numerical examples are provided to validate the accuracy and versatility of the method, including scenarios involving tightly spaced components and rotational variations in substructure layout.