Simplest Nontrivial Maxwellian Random Field Models for Stochastic LoS MIMO Using the Dyadic Green's Function

2026-06-07

AI Summary

Existing empirical fading models struggle to rigorously adhere to the physical laws governing electromagnetic wave propagation and thus fail to accurately characterize stochastic line-of-sight (LoS) MIMO channels. This work proposes a full-wave modeling framework based on the stochastic dyadic Green’s function (SDGF), establishing for the first time a minimal yet nontrivial random field model that strictly satisfies Maxwell’s equations while preserving the vector nature and dispersion relation of electromagnetic fields, encompassing both propagating and evanescent modes. By employing Gaussian wavenumber and stochastic plane wave (SPW) formulations, the approach elucidates the physical mechanism underlying the enhancement of channel capacity and degrees of freedom beyond deterministic benchmarks in two-dimensional continuous MIMO systems, and demonstrates that the simplified Gaussian model can effectively reproduce the key performance characteristics of the SPW model.

Abstract

This letter introduces a novel, full-wave, physics-compliant stochastic dyadic Green's function (SDGF) framework for modeling electromagnetic (EM) multiple-input-multiple-output (MIMO) channels under wavenumber uncertainty. Unlike conventional phenomenological fading models, the proposed approach provides what appear to be the simplest exact random field models of electromagnetic line-of-sight (LoS) propagation that are also exact solutions of Maxwell's equations. Hence, we dub them Maxwellian random field theoretic models. These physically consistent stochastic models, including an analytically tractable wavenumber Gaussian model and a more general stochastic plane wave (SPW) model, serve as fundamental baseline models for stochastic LoS channel characterization. By preserving the vectorial structure of Maxwell's equations and the dispersion relation, the framework naturally incorporates both propagating and evanescent modes. Our analysis of ergodic capacity and degrees of freedom (DoF) reveals that the key results of the complex SPW model can be reproduced by the simpler Gaussian model with limited variance. Furthermore, we provide examples using 2D continuous MIMO systems, illustrating how the model's Maxwell-consistent stochasticity explains observed increases in channel capacity and DoF over the deterministic MIMO capacity baseline. These idealized Maxwellian random field theoretic models offer a physically grounded reference point for understanding fundamental limits in stochastic LoS propagation environments.

Problem

• Maxwellian random field
• stochastic LoS MIMO
• dyadic Green's function
• wavenumber uncertainty
• electromagnetic channel modeling

Innovation

• Maxwellian random field
• stochastic dyadic Green's function
• LoS MIMO
• wavenumber uncertainty
• ergodic capacity