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

TL;DR

This paper offers a comprehensive tutorial on continuous-aperture array systems, emphasizing electromagnetic principles, modeling, and capacity analysis, to guide future wireless system design.

Contribution

It introduces a physics-consistent continuous-aperture framework, bridging electromagnetic theory with information theory for advanced wireless array analysis.

Findings

CAPA systems are modeled as continuous electromagnetic fields governed by Maxwell's equations.

Tools like wavenumber-domain methods and compressive sensing help reduce infinite-dimensional problems.

The paper discusses capacity limits and degrees of freedom in CAPA 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.