[Paper Review] Electromagnetic Signal and Information Theory -- Electromagnetically Consistent Communication Models for the Transmission and Processing of Information

Marco Di Renzo, Marco Donald Migliore|arXiv (Cornell University)|Nov 11, 2023

Advanced Wireless Communication Technologies4 citations

TL;DR

This paper introduces Electromagnetic Signal and Information Theory (ESIT), an interdisciplinary framework unifying electromagnetic theory, signal processing, and information theory to design physically consistent communication systems. It demonstrates that ESIT enables accurate modeling of near-field, line-of-sight channels, reveals the number of effective degrees of freedom (eDoF) in holographic surfaces, and derives optimal waveforms using compact operator theory and prolate spheroidal wave functions, offering a foundation for energy-efficient, wave-domain signal processing in 6G networks.

ABSTRACT

In this paper, we present electromagnetic signal and information theory (ESIT). ESIT is an interdisciplinary scientific discipline, which amalgamates electromagnetic theory, signal processing theory, and information theory. ESIT is aimed at studying and designing physically consistent communication schemes for the transmission and processing of information in communication networks. In simple terms, ESIT can be defined as physics-aware information theory and signal processing for communications. We consider three relevant problems in contemporary communication theory, and we show how they can be tackled under the lenses of ESIT. Specifically, we focus on (i) the theoretical and practical motivations behind antenna designs based on subwavelength radiating elements and interdistances; (ii) the modeling and role played by the electromagnetic mutual coupling, and the appropriateness of multiport network theory for modeling it; and (iii) the analytical tools for unveiling the performance limits and realizing spatial multiplexing in near field, line-of-sight, channels. To exemplify the role played by ESIT and the need for electromagnetic consistency, we consider case studies related to reconfigurable intelligent surfaces and holographic surfaces, and we highlight the inconsistencies of widely utilized communication models, as opposed to communication models that originate from first electromagnetic principles.

Motivation & Objective

• To address the lack of physically consistent communication models in emerging wave-domain technologies like reconfigurable intelligent surfaces (RIS) and holographic surfaces (HoloS).
• To unify electromagnetic theory, signal processing, and information theory into a single framework—ESIT—for designing Maxwellian-compliant communication systems.
• To provide analytical tools for determining the number of effective degrees of freedom (eDoF) and optimal communication waveforms in near-field, line-of-sight channels.
• To expose inconsistencies in conventional communication models and demonstrate the superiority of first-principles electromagnetic modeling.
• To enable the design of energy-efficient, wave-domain signal processing architectures by rigorously modeling mutual coupling and near-field effects.

Proposed method

• Formulates communication channels as compact, self-adjoint integral operators derived from electromagnetic field theory.
• Applies approximation theory and spectral analysis to estimate the number of significant communication modes (NeDoF) via eigenvalue decomposition of the channel operator.
• Uses Kolmogorov’s definition of optimal basis functions to derive optimal waveforms as eigenfunctions of the channel operator, with closed-form solutions in paraxial and symmetric configurations.
• Employs prolate spheroidal wave functions (PSWFs) as optimal basis functions in 2D settings under aligned, parallel HoloS configurations.
• Extends prior results on PSWF-based waveforms to non-ideal, offset-aligned HoloS deployments using numerical eigenproblem solving.
• Validates NeDoF estimates by comparing eigenvalue decay with the threshold of half the largest eigenvalue, confirming robustness even under angular misalignment.

Experimental results

Research questions

• RQ1 How can we accurately model the number of effective communication modes (eDoF) in near-field, line-of-sight channels between holographic surfaces?
• RQ2 What are the optimal communication waveforms for HoloS-based systems, and under what conditions can they be expressed as products of 1D prolate spheroidal wave functions?
• RQ3 How does electromagnetic mutual coupling affect the performance and design of intelligent surface-based communication systems, and how can it be consistently modeled?
• RQ4 In what ways do conventional communication models fail to account for electromagnetic physics, and how can ESIT correct these inconsistencies?
• RQ5 Can integral operator theory be used to derive new, physically consistent signal processing and channel estimation algorithms for wave-domain communications?

Key findings

• The number of effective degrees of freedom (eDoF) in HoloS-aided channels scales with the aperture size and inversely with wavelength and distance, with NeDoF estimated via eigenvalue decay analysis.
• Even with a 30° angular offset between two HoloSs, more than one significant communication mode is supported, indicating robust spatial multiplexing capability.
• Optimal communication waveforms in symmetric, parallel HoloS configurations are the product of two 1D prolate spheroidal wave functions (PSWFs), as derived from Miller’s 2000 work and extended in 2023.
• The NeDoF estimate $ N_2 $, based on the largest eigenvalue and the area of the HoloS, provides a reliable approximation of the number of eigenvalues above half the maximum, validated numerically.
• Electromagnetically consistent models reveal that evanescent waves and near-field effects significantly impact channel capacity and must be included in system design.
• The use of integral operators and spectral theory enables the identification of previously unknown optimal encoding and decoding schemes that are not captured by conventional digital signal processing models.