On the Complexity of Electromagnetic Far-Field Modeling

2026-01-09

arXiv.org

AI Summary

This study addresses the need for efficient modeling of complex electromagnetic far-field behavior in modern wireless systems, where precise control and reflection of electromagnetic waves are critical. Building upon Maxwell’s equations and integrating frequency-domain bandwidth modeling with finite-rank operator approximation theory, the work rigorously establishes—for the first time—that the far-field response of general antenna architectures possesses intrinsic finite complexity. It further demonstrates that the approximation error decays super-exponentially with increasing operator rank. These findings provide a foundational finite-parameter representation theory for antenna far fields, offering a rigorous theoretical basis for high-fidelity, computationally efficient digital electromagnetic simulations.

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• Cognitive Modeling & Cognitive Systems: Analogy
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Sampling/Simulation-based Search

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Abstract

Modern wireless systems are envisioned to employ antenna architectures that not only transmit and receive electromagnetic (EM) waves, but also intentionally reflect and possibly transform incident EM waves. In this paper, we propose a mathematically rigorous framework grounded in Maxwell's equations for analyzing the complexity of EM far-field modeling of general antenna architectures. We show that-under physically meaningful assumptions-such antenna architectures exhibit limited complexity, i.e., can be modeled by finite-rank operators using finitely many parameters. Furthermore, we construct a sequence of finite-rank operators whose approximation error decays super-exponentially once the operator rank exceeds an effective bandwidth associated with the antenna architecture and the analysis frequency. These results constitute a fundamental prerequisite for the efficient and accurate modeling of general antenna architectures on digital computing platforms.

Problem

• electromagnetic far-field
• antenna architectures
• modeling complexity
• Maxwell's equations
• finite-rank operators

Innovation

• electromagnetic far-field modeling
• finite-rank operators
• Maxwell's equations
• antenna complexity
• super-exponential approximation