Electromagnetic Signal and Information Theory: A Continuous-Aperture Array Perspective

2026-05-12

AI Summary

Conventional discrete array models struggle to accurately characterize the channel and signal properties of large-scale, high-density, high-frequency reconfigurable electromagnetic aperture systems. This work proposes a continuous-space modeling paradigm that unifies the representation of channels, signals, and beamformers as continuous fields and operators governed by Maxwell’s equations, thereby effecting a fundamental shift from discrete to continuous formulations. By integrating electromagnetics with information theory and leveraging wavenumber-domain analysis, functional analysis, and compressive sensing, the study reveals the intrinsic degrees of freedom and capacity limits of continuous apertures and develops finite-dimensional equivalent methods capable of handling infinite-dimensional problems. These contributions establish a theoretical foundation, provide essential analytical tools, and outline practical hardware implementation pathways for future wireless systems.

Abstract

Emerging wireless systems are evolving toward larger, denser, higher-frequency, and more reconfigurable apertures, which motivates the study of continuous-aperture arrays (CAPAs). Unlike conventional spatially discrete arrays (SPDAs), CAPAs are more naturally modeled as spatially continuous electromagnetic apertures and therefore call for a fundamental shift in both signal processing and information-theoretic analysis. In particular, the underlying channels, signals, and beamformers are no longer finite-dimensional vectors and matrices, but continuous fields and operators governed by Maxwell's equations. This paper provides a tutorial overview of CAPA systems from the perspective of electromagnetic signal and information theory (ESIT), with an emphasis on the transition from discrete array models to physics-consistent continuous-aperture formulations. We review the electromagnetic foundations of CAPAs, practical hardware implementations, line-of-sight and multipath channel modeling, continuous-space beamforming and channel estimation, and the fundamental degrees of freedom and capacity limits of CAPA systems. We also highlight how tools such as wavenumber-domain methods, functional analysis, and compressive sensing can transform challenging infinite-dimensional problems into tractable finite-dimensional ones while preserving the essential physical structure of the channel. Overall, this tutorial aims to clarify the key principles, analytical tools, and open challenges that shape CAPA-enabled wireless communications.

Problem

• continuous-aperture arrays
• electromagnetic signal theory
• information theory
• Maxwell's equations
• infinite-dimensional systems

Innovation

• continuous-aperture arrays
• electromagnetic signal and information theory
• infinite-dimensional channel modeling
• wavenumber-domain methods
• physics-consistent beamforming