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

We provide a comprehensive framework for the analysis of stochastic electromagnetic (EM) correlation phenomena in multiple-antenna systems. The proposed theory develops a general derivation of the stochastic cross-correlation between two generic antennas located at the base station (BS) of a multiple-input–multiple-output (MIMO) system. Unlike classical approaches that rely on far-field incident field models, our formalism is grounded in random EM sources—specifically, randomized current distributions modeled as random fields over a rigorously defined probability space. This source-based paradigm naturally accommodates both near-field (NF) and far-field (FF) excitations within a single unified framework. We avoid working with random field theory by relegating all statistical considerations to positions, orientations, and excitations of the user equipment (UE) antennas and scattering clusters while treating the latter as (generally) complex random vectors. An exact EM derivation of the BS correlation coefficient is achieved using reciprocity theory. This yields two complementary decoupling theorems that separate the stochasticity of the environment from the deterministic characteristics of the receive antenna system. The final expression is explicitly written in terms of a new generalized stochastic correlation Green’s function (CGF). Both UE antennas and arbitrary scattering clusters are replaced by a proper randomized infinitesimal dipole model (IDM), and we prove the convergence of the IDM-CGF approximation to the exact continuous correlation in the L^2 -sense under standard regularity conditions. The CGF provides a complete and accurate description of all correlation-type phenomena in generic MIMO systems and internally generates the statistics of the BS illumination field based on NF sources. We provide a detailed decomposition of the CGF into four hierarchical dyadic contributions, revealing a fundamental four-point interaction mechanism where pairs of random source dipoles mediate the correlation between specific current elements on the receive array. This decomposition exposes a clear progression in design flexibility, from isotropic dipole coupling to fully directional, path-mediated interactions. EM mutual coupling between receive antennas is rigorously incorporated through a nine-term decomposition of the antenna currents into isolated self currents, self-current corrections, and cross-antenna induced currents, yielding self-interaction and cross-interaction contributions to the total cross-correlation. We compare the NF and FF correlation structures, identifying six key differences that highlight the richer complexity of the NF regime and its additional design degrees of freedom. The theoretical tools developed here establish a foundation for physics-driven design and optimization of next-generation wireless systems operating in complex, dense, and NF-dominated environments such as massive MIMO, holographic MIMO, and ultra-dense networks.