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arxiv: 2604.18040 · v1 · submitted 2026-04-20 · 📡 eess.SP

User Mobility Demands Near-Field Communications in Terahertz Band Wireless Networks Beyond 6G

Peng Zhang , Vitaly Petrov , Arjun Singh , Emil Bj\"ornson , Josep Miquel Jornet This is my paper

Pith reviewed 2026-05-10 04:33 UTC · model grok-4.3

classification 📡 eess.SP
keywords terahertznear-field communicationsfar-fielduser mobilitywireless networksbandwidth limitsFraunhofer distance6G
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The pith

Mobile THz links cannot support tens of GHz bandwidth while staying in the far field without unrealistic user equipment transmit power.

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

The paper develops a feasibility framework that enforces both the Fraunhofer distance for far-field operation and a target SNR at the worst-case distance. It derives closed-form upper bounds on the largest bandwidth that remains compatible with far-field conditions for both stationary and mobile users. Stationary links can meet these constraints with realizable antenna apertures, but mobility scenarios involving rotation and displacement make the bounds impractically tight. The resulting limits show that practical mobile THz access requires near-field-aware designs rather than far-field-only operation.

Core claim

We develop a proof-by-contradiction feasibility framework that jointly enforces (i) a far-field requirement based on the Fraunhofer distance and (ii) a reliability requirement specified by a target SNR at the worst-case link distance. We derive closed-form upper bounds on the far-field-feasible bandwidth for stationary and mobile links. We further incorporate practical misalignment through several UE rotation and mobility scenarios. Numerical results show that stationary THz links can remain far-field-only with physically realizable apertures while supporting extremely large bandwidths, whereas practical mobile THz systems cannot.

What carries the argument

Proof-by-contradiction feasibility framework that combines the Fraunhofer far-field boundary with a worst-case SNR reliability constraint to produce closed-form bandwidth upper bounds.

If this is right

  • Stationary THz links can achieve extremely large bandwidths while remaining far-field only with physically realizable apertures.
  • Mobile THz systems cannot reach tens-of-GHz bandwidth targets under far-field constraints without unrealistically high UE transmit power.
  • Far-field-only operation remains feasible at sub-6 GHz and to a significant extent at mmWave for moderate bandwidths.
  • Near-field-aware designs become essential for mobile THz access to maintain broadband rates and coverage.

Where Pith is reading between the lines

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

  • THz system architectures will need spherical-wave channel models and adaptive beam focusing rather than planar-wave assumptions when serving moving users.
  • Cross-band resource allocation may shift: lower frequencies handle mobility while THz bands target high-rate static or slowly moving links.
  • Antenna array size and placement choices at both base station and UE will be constrained by mobility-induced misalignment tolerances.

Load-bearing premise

The Fraunhofer distance is treated as the definitive and sufficient boundary separating near-field from far-field behavior, and the chosen UE rotation and mobility traces are assumed to represent the dominant misalignment effects in real deployments.

What would settle it

Deploy a mobile THz link with measured UE movement and rotation, record the maximum bandwidth that meets the target SNR at the Fraunhofer distance, and check whether that bandwidth exceeds the paper's closed-form upper bound at the modeled transmit power.

Figures

Figures reproduced from arXiv: 2604.18040 by Arjun Singh, Emil Bj\"ornson, Josep Miquel Jornet, Peng Zhang, Vitaly Petrov.

Figure 1
Figure 1. Figure 1: Non-stationary THz link operating exclusively in the far field. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Baseline aligned scenario, where the UE is fixed. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Scenario 1: UE rotated by a single angle [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scenario 2: UE rotated by two angles, θUE around the x-axis and ϕUE around the z-axis. Using D1 = LD2 and dmax = M dmin with M = dmax/dmin, (47) becomes LD2 2 ≥ λπM dmin G0|f(θUE, ϕUE)| r NFkT B Pt 10 SNRth,dB 20 . (48) Combining (44) and (48) and eliminating D2 2 in the same manner as in Scenarios 0 and 1, we obtain an upper bound on the bandwidth of a mobile THz system with two UE rotation angles as B (m… view at source ↗
Figure 6
Figure 6. Figure 6: Scenario 4: The UE maintains its array orthogonal to the instanta [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The maximum achievable bandwidth for the far-field stationary THz link and the corresponding antenna sizes. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Maximum achievable bandwidth under UE rotation and mobility. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Maximum achievable bandwidth under direction variation and mobility. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Required UE transmit power Pt as a function of the target maximum bandwidth B for (a) sub-6 GHz, (b) mmWave, and (c) THz bands under different UE rotation and direction variation conditions. The four-tuple (θUE, ϕUE, θrel, ϕrel) specifies the UE rotation and direction variation angles. existing mobile THz hardware systems can deliver [46]. The minimal level of Pt,dBm also grows rapidly with bandwidth. At … view at source ↗
read the original abstract

Near-field propagation is often unavoidable at terahertz (THz) frequencies due to the large apertures needed for sufficient array gain, yet near-field operation complicates practical system design, especially under user mobility. This paper asks whether a mobile THz link can remain broadband, achieve the desired high rates and coverage, while operating exclusively in the radiative far field. To answer this question, we develop a proof-by-contradiction feasibility framework that jointly enforces (i) a far-field requirement based on the Fraunhofer distance and (ii) a reliability requirement specified by a target SNR at the worst-case link distance. We derive closed-form upper bounds on the far-field-feasible bandwidth for stationary and mobile links. We further incorporate practical misalignment through several UE rotation and mobility scenarios. Numerical results show that stationary THz links can remain far-field-only with physically realizable apertures while supporting extremely large bandwidths, whereas practical mobile THz systems cannot. In practically relevant mobile THz access settings, the far-field-feasible bandwidth becomes a severe limiting factor: achieving tens-of-GHz targets would require unrealistically high UE transmit power. A cross-band comparison further shows that far-field-only operation is largely attainable at sub-6~GHz and, to a significant extent, at mmWave for moderate bandwidths, while near-field-aware designs become essential for mobile THz access.

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 paper develops a proof-by-contradiction feasibility framework that jointly enforces far-field operation (via the Fraunhofer distance) and a target SNR at worst-case distance to derive closed-form upper bounds on far-field-feasible bandwidth for stationary and mobile THz links. It incorporates UE rotation and mobility scenarios for misalignment, shows that stationary links can support large bandwidths with realizable apertures while mobile links cannot without unrealistically high UE power, and contrasts this with sub-6 GHz and mmWave bands.

Significance. If the closed-form bounds and numerical results hold under the stated assumptions, the work provides a clear quantitative argument that mobility-induced misalignment makes exclusive far-field operation impractical for high-bandwidth THz access, thereby motivating near-field-aware designs for beyond-6G THz networks. The cross-band comparison and explicit incorporation of rotation/mobility scenarios are useful for system-level planning.

major comments (2)
  1. [Section on far-field requirement and proof-by-contradiction framework (likely §III)] The central feasibility conclusion rests on the Fraunhofer distance (2D²/λ) as the sole far-field boundary. This conventional phase-error threshold (≈π/8) is used to enforce the contradiction in the proof framework, but the paper does not provide a sensitivity analysis showing how the derived bandwidth upper bounds change under a stricter criterion (e.g., phase error <π/16 or curvature-based metric) that may be more appropriate for large THz arrays under UE rotation. Because the effective aperture projection varies with mobility, the instantaneous boundary is not fixed; this modeling choice directly affects the claimed need for high UE transmit power in mobile scenarios.
  2. [Derivation of closed-form bounds and numerical results section] The closed-form upper bounds on bandwidth (derived from the joint far-field and SNR constraints) are presented for several UE mobility/rotation scenarios, yet the manuscript does not report the explicit dependence of these bounds on the time-varying effective aperture or instantaneous Fraunhofer distance. Without this, it is unclear whether the numerical results for mobile cases fully capture the variability or rely on worst-case static projections.
minor comments (2)
  1. [System model] Notation for the worst-case link distance and target SNR should be introduced with explicit symbols in the system model before being used in the bound derivations.
  2. [Numerical results] Figure captions for the numerical results should state the exact parameter values (e.g., carrier frequency, array size, target SNR) used in each curve to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment point-by-point below, providing clarifications on our modeling choices and indicating the revisions we will implement to strengthen the analysis.

read point-by-point responses

  1. Referee: [Section on far-field requirement and proof-by-contradiction framework (likely §III)] The central feasibility conclusion rests on the Fraunhofer distance (2D²/λ) as the sole far-field boundary. This conventional phase-error threshold (≈π/8) is used to enforce the contradiction in the proof framework, but the paper does not provide a sensitivity analysis showing how the derived bandwidth upper bounds change under a stricter criterion (e.g., phase error <π/16 or curvature-based metric) that may be more appropriate for large THz arrays under UE rotation. Because the effective aperture projection varies with mobility, the instantaneous boundary is not fixed; this modeling choice directly affects the claimed need for high UE transmit power in mobile scenarios.

    Authors: We acknowledge that the specific far-field boundary criterion influences the quantitative results. The Fraunhofer distance with the conventional π/8 phase-error threshold is the standard definition used throughout the wireless literature for planar arrays and is appropriate for the proof-by-contradiction framework. To address the concern directly, we will add a sensitivity analysis in the revised manuscript (new subsection in §III and corresponding numerical results) that evaluates stricter phase-error thresholds (e.g., π/16) and discusses curvature-based alternatives. We will also explicitly incorporate the effect of UE rotation on the time-varying projected aperture when computing the instantaneous boundary. These additions will demonstrate that, while the precise bandwidth values shift, the core conclusion—that mobile THz links cannot sustain high bandwidths under far-field-only operation without unrealistically high UE power—remains robust. revision: yes

  2. Referee: [Derivation of closed-form bounds and numerical results section] The closed-form upper bounds on bandwidth (derived from the joint far-field and SNR constraints) are presented for several UE mobility/rotation scenarios, yet the manuscript does not report the explicit dependence of these bounds on the time-varying effective aperture or instantaneous Fraunhofer distance. Without this, it is unclear whether the numerical results for mobile cases fully capture the variability or rely on worst-case static projections.

    Authors: The closed-form bounds are obtained by jointly enforcing the far-field condition (via the Fraunhofer distance) and the target SNR at the worst-case distance and misalignment for each mobility/rotation scenario, using the corresponding effective aperture projection. The numerical results then evaluate these scenario-specific bounds. We agree that explicitly reporting the dependence on the time-varying aperture would improve transparency. In the revision we will augment the derivation section with analytical expressions that show the bandwidth upper bound as an explicit function of the instantaneous effective aperture and Fraunhofer distance. We will also add plots illustrating the bound’s variation along representative mobility trajectories, while retaining the worst-case projections for the feasibility conclusions. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses external Fraunhofer distance and target SNR as independent inputs to closed-form bounds

full rationale

The paper's core framework is a proof-by-contradiction that takes the conventional Fraunhofer distance (2D²/λ) and a user-specified target SNR at worst-case distance as given inputs, then derives closed-form upper bounds on far-field-feasible bandwidth for stationary and mobile cases. These inputs are standard external definitions and scenario parameters, not fitted quantities or self-referential outputs. No self-citations are load-bearing for the central claim, no parameters are fitted then renamed as predictions, and no ansatz or uniqueness theorem is smuggled via prior author work. The numerical results and cross-band comparisons follow directly from the stated constraints without reduction to the inputs by construction. This is a standard non-circular feasibility analysis.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard electromagnetic propagation axioms and user-specified performance targets rather than new fitted parameters or invented physical entities.

free parameters (2)
  • target SNR
    User-specified reliability requirement that defines the worst-case link distance constraint.
  • UE transmit power
    Parameter varied in numerical results to illustrate power requirements for mobile cases.
axioms (2)
  • domain assumption Far-field operation requires link distance greater than Fraunhofer distance
    Standard antenna theory definition invoked to enforce the far-field requirement in the feasibility framework.
  • domain assumption Worst-case link distance governs the reliability requirement
    Used to set the SNR target that bounds feasible bandwidth.

pith-pipeline@v0.9.0 · 5553 in / 1386 out tokens · 46529 ms · 2026-05-10T04:33:22.922810+00:00 · methodology

discussion (0)

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Reference graph

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