A Random Field Theory of Electromagnetic Information.

Area of Science:

• Electromagnetics
• Information Theory
• Stochastic Processes

Background:

• Electromagnetic information theory (EIT) lacks a general framework for analyzing stochastic structures in complex transmission systems.
• Existing models often struggle with arbitrary random scatterers and mutual coupling.

Purpose of the Study:

• To develop a comprehensive theory for the universal stochastic structure of radiated electromagnetic fields and induced currents.
• To establish a unified framework integrating random fields, electromagnetics, and Green's functions for arbitrary EM information transmission systems.

Main Methods:

• Modeling the EM system as a multiply connected Riemannian manifold using differential geometry.
• Exploiting exact Green's functions (GFs) on manifolds to construct an electromagnetic random field theory (EM-RFT).
• Utilizing the Karhunen-Loève expansion for representing EM random fields and evaluating mutual information.

Main Results:

• A novel EM-RFT is constructed, treating internal system details as a black box via localized GFs.
• It's rigorously shown that EM random fields can be constructed using system GFs driven by external information fields.
• General correlation propagators are introduced, decoupling input fields from medium fluctuations.

Conclusions:

• The developed theory provides a unified framework for characterizing stochastic EM information transmission.
• It enables simulation of arbitrary EM random fields and evaluation of mutual information across spatial domains.
• This approach offers a rigorous foundation for advancing EIT and signal processing in complex EM environments.