Stochastic Electromagnetic Dyadic Correlation Green's Functions for Wireless Communications --- Part I: Theory and Concepts

We provide a comprehensive framework for analyzing stochastic electromagnetic (EM) correlation phenomena in multiple-antenna systems. The proposed theory derives the stochastic cross-correlation between two generic base-station antennas in a multiple-input-multiple-output (MIMO) system using reciprocity theory. Unlike classical far-field incident-field models, the formulation is grounded in random EM sources, modeled through randomized current distributions over a rigorously defined probability space, and naturally accommodates both near-field (NF) and far-field (FF) excitations. The resulting expression is written in terms of a generalized stochastic correlation Green’s function (CGF), which links source statistics to receive-antenna correlation. User equipment antennas and scattering clusters are represented by randomized infinitesimal dipole models, and convergence of the IDM-CGF approximation to the continuous correlation is established in the L2 sense. The CGF is further decomposed to reveal the physical mechanisms of NF and FF correlation, while electromagnetic mutual coupling is incorporated through a nine-term current decomposition. The framework provides a physics-driven foundation for correlation analysis and design optimization in dense and NF-dominated wireless systems.