On the Complexity of Electromagnetic Far-Field Modeling

TL;DR

This paper develops a rigorous mathematical framework based on Maxwell's equations to analyze the complexity of electromagnetic far-field modeling for advanced antenna architectures, revealing they can be effectively approximated by finite-rank operators with super-exponentially decreasing error.

Contribution

It introduces a novel, mathematically rigorous approach to quantify the modeling complexity of complex antenna architectures using finite-rank operators.

Findings

Antenna architectures exhibit limited complexity under physical assumptions.

Finite-rank operator approximation errors decay super-exponentially beyond a certain rank.

Results enable efficient and accurate digital modeling of complex antennas.

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.