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arxiv: 2605.02424 · v1 · submitted 2026-05-04 · 📡 eess.SP

On Near-Far-Field Boundaries in Wireless Systems

Alexander Stutz-Tirri , Ahmad Dkhan , Hadi Sarieddeen , Christoph Studer This is my paper

Pith reviewed 2026-05-08 18:32 UTC · model grok-4.3

classification 📡 eess.SP
keywords near-fieldfar-fieldwireless communicationMaxwell's equationsdistance thresholdsIEEE definitionelectromagnetic simulationmulti-antenna systems
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The pith

All single-letter distance thresholds fail to predict the near-to-far-field transition region

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that no simple distance number can tell a wireless system whether it sits in the near-field or far-field regime. It does this by constructing an analysis directly from Maxwell's equations that follows the IEEE definition of where the near-field ends. Readers who design or study multi-antenna communication and sensing systems would care because those fields routinely pick a threshold to decide which propagation model or approximation applies. The authors test both classic and recently proposed single-letter thresholds against analytical calculations and full-wave simulations for single- and multi-antenna arrays. They conclude that every threshold examined leaves a sizable mismatch with the actual region where the field behavior changes.

Core claim

Using a framework grounded in Maxwell's equations and following the IEEE definition of the near-far-field boundary, numerical experiments and full-wave electromagnetic simulations demonstrate that all considered single-letter distance thresholds are insufficient to predict the transition region between the NF and FF regions, while also highlighting several important caveats associated with frequently used NF and FF concepts.

What carries the argument

A framework grounded in Maxwell's equations that analyzes the transition region between the NF and FF following the IEEE definition

If this is right

  • System designers cannot safely use any single distance value to decide which propagation model applies.
  • Multi-antenna arrays require configuration-specific analysis rather than a universal rule to locate the transition region.
  • Full-wave electromagnetic simulation remains necessary when the operating regime must be known accurately.
  • Common definitions of near-field and far-field contain caveats that affect their direct use in system modeling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Standards and design guidelines for near-field communication may need distance-dependent or pattern-dependent criteria instead of fixed thresholds.
  • The transition region width could be studied as a function of array size and carrier frequency to produce practical engineering rules.
  • Real-world over-the-air measurements would be required to confirm whether the simulated mismatch between thresholds and field behavior persists outside idealized models.

Load-bearing premise

The IEEE definition accurately captures the physical NF-FF transition and the numerical experiments and full-wave simulations faithfully represent real electromagnetic behavior.

What would settle it

A full-wave simulation or real measurement in which one of the single-letter thresholds exactly matches the distance at which the field first satisfies the IEEE far-field criteria would falsify the claim of universal insufficiency.

Figures

Figures reproduced from arXiv: 2605.02424 by Ahmad Dkhan, Alexander Stutz-Tirri, Christoph Studer, Hadi Sarieddeen.

Figure 1
Figure 1. Figure 1: Basic concept of our framework: Illustration of the relationship view at source ↗
Figure 2
Figure 2. Figure 2: Sketch of how a result of the proposed framework could look: The view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative sketch of the wavefronts of a parabolic reflector view at source ↗
Figure 4
Figure 4. Figure 4: Setup of the test scenarios used in the experiments. The analyzed antenna (array) lies on the view at source ↗
Figure 5
Figure 5. Figure 5: The framework introduced in Section III-B, when applied to the test scenarios described in Section VI-A, evaluates the near–far-field boundaries listed in Table I. In all antenna array scenarios, the element spacing was set to d = λ/2. The curves for infinitesimal dipole sources are computed from closed-form expressions; those for half-wave dipole and patch antennas are derived from fields obtained via ful… view at source ↗
Figure 6
Figure 6. Figure 6: Approximation error of uniform linear dipole arrays with a total array length of view at source ↗
read the original abstract

Near-field (NF) multi-antenna wireless communication and sensing have attracted growing research interest in recent years. A core question in this area is how to determine whether a wireless system is operating in the NF or far-field (FF) region. In this work, we propose a framework grounded in Maxwell's equations to analyze the transition region between the NF and FF, following the IEEE definition that specifies where the NF ends and the FF begins. Using this framework, we (i) compare a variety of traditional and recently introduced single-letter distance thresholds, often referred to as near-far-field boundaries, and (ii) conduct numerical experiments with both single- and multi-antenna wireless systems and with analytical models as well as full-wave electromagnetic simulations. Our results indicate that all of the considered single-letter distance thresholds are insufficient to predict the transition region between the NF and FF regions. Moreover, we highlight several important caveats associated with frequently (and recently) used NF and FF concepts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a framework grounded in Maxwell's equations to locate the near-field to far-field transition according to the IEEE standard (phase-error, amplitude-variation, and polarization criteria). It analytically and numerically compares a range of single-letter distance thresholds (Fraunhofer, reactive near-field, etc.) for both single- and multi-antenna systems, using closed-form models and full-wave electromagnetic simulations. The central result is that none of the examined single-letter thresholds reliably predict the IEEE-defined transition region; the work also enumerates caveats associated with common NF/FF terminology.

Significance. If the numerical evidence holds, the paper supplies a concrete, electromagnetically grounded demonstration that simple distance-based rules are inadequate for modern NF wireless systems. This directly affects link-budget calculations, beamforming design, and sensing algorithms in 6G and XL-MIMO contexts, where operating distances often straddle the transition zone. The explicit use of the IEEE definition as an external benchmark and the inclusion of full-wave validation are strengths that elevate the work beyond purely analytical comparisons.

major comments (2)
  1. [§4] §4 (Numerical Experiments and Full-Wave Simulations): the manuscript states that full-wave simulations were performed to locate the IEEE transition distances, yet provides no information on the electromagnetic solver, mesh density, absorbing-boundary implementation, frequency sampling, or convergence tolerance. Without these details the quantitative claim that 'all considered single-letter thresholds are insufficient' cannot be independently verified and remains load-bearing for the central conclusion.
  2. [§3.2] §3.2 (Definition of Transition Region): the paper adopts the IEEE criteria but does not specify the exact numerical thresholds applied (e.g., maximum phase error of 22.5°, amplitude ripple of 1 dB, or polarization purity) nor how these are aggregated across observation angles and frequencies when declaring the 'end' of the near-field region. This ambiguity affects the comparison plots and the assertion that every single-letter boundary fails.
minor comments (2)
  1. [Introduction] The abstract and introduction refer to 'recently introduced' single-letter thresholds without providing the corresponding citations or explicit formulas in the main text; readers must consult external references to understand which boundaries were tested.
  2. [Figures 4-7] Figure captions for the simulation results should include the exact antenna geometry, operating frequency, and number of elements so that the plotted transition distances can be reproduced from the text alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation for major revision. We address each major comment below and will revise the manuscript to improve reproducibility and clarity while preserving the central conclusions.

read point-by-point responses

  1. Referee: [§4] §4 (Numerical Experiments and Full-Wave Simulations): the manuscript states that full-wave simulations were performed to locate the IEEE transition distances, yet provides no information on the electromagnetic solver, mesh density, absorbing-boundary implementation, frequency sampling, or convergence tolerance. Without these details the quantitative claim that 'all considered single-letter thresholds are insufficient' cannot be independently verified and remains load-bearing for the central conclusion.

    Authors: We agree that these implementation details are necessary for independent verification of the full-wave results. In the revised manuscript we will add a new subsection (or appendix) that specifies the electromagnetic solver employed, mesh density and convergence criteria, absorbing-boundary implementation, frequency sampling strategy, and any other relevant solver settings used to generate the IEEE transition distances. These additions will allow readers to reproduce the numerical evidence supporting the insufficiency of single-letter thresholds. revision: yes

  2. Referee: [§3.2] §3.2 (Definition of Transition Region): the paper adopts the IEEE criteria but does not specify the exact numerical thresholds applied (e.g., maximum phase error of 22.5°, amplitude ripple of 1 dB, or polarization purity) nor how these are aggregated across observation angles and frequencies when declaring the 'end' of the near-field region. This ambiguity affects the comparison plots and the assertion that every single-letter boundary fails.

    Authors: We acknowledge that the precise numerical thresholds and aggregation procedure should be stated explicitly. In the revised version of §3.2 we will list the exact IEEE-derived thresholds applied (phase-error limit, amplitude-variation limit, and polarization criterion) and describe how the transition distance is determined by aggregating these metrics over the relevant observation angles and frequencies. This clarification will make the comparison plots and the conclusion that no single-letter boundary reliably predicts the transition region fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's framework is explicitly grounded in Maxwell's equations and the external IEEE definition of the NF-FF transition as independent benchmarks. It derives its central claim—that single-letter distance thresholds are insufficient—directly from numerical experiments, analytical models, and full-wave simulations on single- and multi-antenna systems. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input; the comparisons and conclusions follow from applying the stated external criteria to the simulation outputs without self-referential fitting or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Central claim rests on Maxwell's equations as the governing physics and the IEEE definition of the NF-FF boundary; no free parameters or new entities are introduced in the abstract description.

axioms (2)
  • standard math Maxwell's equations govern electromagnetic wave propagation in wireless systems
    Used to ground the framework for analyzing the transition region.
  • domain assumption IEEE definition specifies where the near-field ends and far-field begins
    Followed explicitly for determining the transition region in the analysis.

pith-pipeline@v0.9.0 · 5473 in / 1192 out tokens · 72034 ms · 2026-05-08T18:32:14.356289+00:00 · methodology

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Reference graph

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