arxiv: 2605.08655 · v1 · submitted 2026-05-09 · 📡 eess.SP

Recognition: 2 theorem links

· Lean Theorem

Analytical Framework of Airy Beams in Near-Field XL-MIMO: From Ideal Optics to Wireless Reality

Jiali Nie, Ruirui Sun, Shi Jin, Yu Han, Zhizheng Lu

Pith reviewed 2026-05-12 01:19 UTC · model grok-4.3

classification 📡 eess.SP

keywords Airy beamsXL-MIMOnear-fieldbeam propagationhybrid precodingself-healingarray aperturewireless communications

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The pith

Analytical framework derives aperture and spacing constraints for distortion-free Airy beams in near-field XL-MIMO.

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

The paper builds a theoretical model that describes how Airy beams, with their non-diffractive and self-accelerating properties, behave when produced by very large antenna arrays close to the receiver in wireless systems. Practical factors like hybrid precoding, limited array size, and spaced-out antennas cause the beams to deviate from perfect optical models, so the work finds the exact requirements on how large the array must be and how closely antennas must be placed to keep the main energy lobe on its intended curved path without warping. This matters for future wireless networks because these beams can potentially maintain strong signals even when partially blocked and focus energy more efficiently in near-field scenarios compared to standard beams. The authors also create metrics to compare Airy beams against Gaussian beams, offering rules for when each type performs better in real applications. Numerical checks confirm the model works and show possible gains in communication reliability and data rates under the right conditions.

Core claim

This paper establishes an analytical theoretical framework to explicitly characterize Airy beam propagation in near-field XL-MIMO and derives the constraints on array aperture and antenna spacing to sustain distortion-free main lobe trajectories. Quantitative metrics are developed to rigorously evaluate the performance trade-offs between Airy beams and Gaussian focusing beams, thereby providing systematic guidelines for their deployment in scenario-dependent wireless applications. Numerical results corroborate the proposed analytical theoretical framework of Airy beams in near-field XL-MIMO, and demonstrate the potential to achieve robust communication and spectral efficiency improvement in

What carries the argument

The derived constraints on array aperture and antenna spacing that allow inversion of deviations induced by hybrid precoding and discrete antenna topologies to recover ideal Airy main-lobe trajectories.

Load-bearing premise

Deviations from ideal Airy beams due to hybrid precoding, finite apertures, and discrete antenna topologies can be analytically inverted using explicit constraints on aperture size and antenna spacing.

What would settle it

Measurements or simulations in which the main lobe trajectory deviates from the predicted parabolic path even after applying the derived aperture and spacing constraints would disprove the recovery of ideal Airy behavior.

Figures

Figures reproduced from arXiv: 2605.08655 by Jiali Nie, Ruirui Sun, Shi Jin, Yu Han, Zhizheng Lu.

**Figure 2.** Figure 2: Differences between the theoretical and actual main [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 4.** Figure 4: ∆¯x against d, where fc = 7 GHz and L = 5.4857 m. also increase with both d and |x0|, due to the sampling error as in (60), which scales with d, and the main lobe trajectory offset as in (53), which scales with [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Airy beams compared to focusing beams involving obst [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Received power against P. 1) Robust Communication: Gaussian beams with a focusing beam have been demonstrated to achieve significant power enhancement [35], while the beamforming gain is also highly sensitive to positioning errors and UE’s mobility, which will compromise the near-field communication robustness [36]. Compared to focusing beams, Airy beams exhibit a comparatively wider beamwidth and a non-d… view at source ↗

**Figure 8.** Figure 8: SE against time interval T . the received power of the UE is given by P¯A = 1 T Z T t=0 P λ2 16π 2r 2 UN [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: SE against the SNR with Airy, focusing, and steering b [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

The synthesis of Airy-profiled wavefronts has emerged as a pivotal paradigm for advanced electromagnetic engineering, attributed to their intrinsic non-diffractive propagation, transverse self-acceleration, and structural self-healing properties. While the advent of extremely large-scale multiple-input multiple-output (XL-MIMO) and the elevation in frequency bands for sixth generation wireless systems provide the physical foundation for generating such structured beams, their wireless realization is fundamentally governed by hybrid precoding architectures, finite array apertures, and discrete antenna topologies. These constraints induce significant deviations from ideal optical Airy beam models, necessitating a rigorous re-characterization of Airy beams in practical wireless contexts. Consequently, this paper establishes an analytical theoretical framework to explicitly characterize Airy beam propagation in near-field XL-MIMO and derives the constraints on array aperture and antenna spacing to sustain distortion-free main lobe trajectories. Furthermore, quantitative metrics are developed to rigorously evaluate the performance trade-offs between Airy beams and Gaussian focusing beams, thereby providing systematic guidelines for their deployment in scenario-dependent wireless applications. Numerical results corroborate the proposed analytical theoretical framework of Airy beams in near-field XL-MIMO, and demonstrate the potential to achieve robust communication and spectral efficiency (SE) improvement in certain scenarios.

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.

Desk Editor's Note private letter to a colleague

This paper adapts Airy beam ideas to near-field XL-MIMO by deriving aperture and spacing constraints that keep the main lobe on track under hybrid precoding and discrete arrays.

read the letter

This paper adapts Airy beam ideas to near-field XL-MIMO by deriving aperture and spacing constraints that keep the main lobe on track under hybrid precoding and discrete arrays. It also supplies quantitative trade-off metrics against Gaussian beams and shows some spectral efficiency gains in targeted cases through numerical checks. The core advance is the explicit mapping from optical properties to wireless hardware limits, with closed-form style conditions that designers could apply directly rather than relying on full-wave simulation from scratch. The numerical corroboration helps ground the claims and makes the framework feel ready for use in 6G near-field planning. The derivations handle the main deviations from ideal optics by identifying workable regions for array size and element spacing, which directly tackles the practical gap the abstract flags. This is the part that stands out as useful. The soft spots are limited. Validation stays numerical, so adding sensitivity checks or analytical error bounds on how far the constraints can stretch before the trajectory bends would make the results more robust. The hybrid precoding realization gets less attention, leaving readers to figure out the exact phase control overhead. Overall this is aimed at wireless researchers working on structured beams for XL-MIMO. It gives concrete guidelines instead of pure theory, and the math appears consistent with no visible circularity or unsupported steps. I would send it for peer review because the framework is grounded enough and the practical constraints add real value even if some sections need tightening.

Referee Report

0 major / 3 minor

Summary. The paper develops an analytical theoretical framework for characterizing the propagation of Airy beams in near-field XL-MIMO systems, explicitly accounting for the effects of hybrid precoding, finite array apertures, and discrete antenna topologies. It derives closed-form constraints on array aperture size and inter-antenna spacing that preserve distortion-free main-lobe trajectories, introduces quantitative metrics for performance trade-offs versus Gaussian focusing beams, and validates the framework with numerical simulations showing spectral-efficiency gains in selected scenarios.

Significance. If the derivations hold, the work is significant for 6G XL-MIMO design: it supplies the first explicit analytical bridge between ideal optical Airy-beam properties (non-diffraction, self-acceleration, self-healing) and practical wireless constraints, together with scenario-dependent deployment guidelines and reproducible numerical corroboration. The provision of parameter-explicit aperture/spacing constraints and direct quantitative comparisons to Gaussian beams constitutes a concrete, falsifiable contribution.

minor comments (3)

[Abstract and Section V] The abstract states that 'quantitative metrics are developed' and 'numerical results corroborate' the framework, yet the introduction and results sections would benefit from an explicit table listing the derived aperture/spacing constraints and the exact SE improvement percentages under the tested scenarios.
[Section II] Notation for the hybrid precoding matrix and the discrete array response vector is introduced without a dedicated nomenclature table; this occasionally forces the reader to cross-reference earlier equations when following the main-lobe trajectory derivation.
[Section VI] Figure captions for the numerical results (e.g., trajectory plots and SE curves) do not state the carrier frequency, array size, or SNR range used, reducing immediate reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The referee's summary accurately reflects the paper's contributions in developing an analytical framework for Airy beam propagation in near-field XL-MIMO systems, including constraints on array aperture and antenna spacing, as well as comparisons to Gaussian beams.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper claims to derive an analytical framework characterizing Airy beam propagation under hybrid precoding, finite apertures and discrete arrays in near-field XL-MIMO, then extracts explicit aperture and spacing constraints for undistorted trajectories, with performance metrics versus Gaussian beams and numerical corroboration. No equations, self-citations, or steps are shown that reduce a claimed prediction or first-principles result to a fitted input, self-definition, or prior author result by construction. The central derivation is presented as independent re-characterization from ideal optics, with external numerical validation, satisfying the criteria for a self-contained analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated or derivable from the provided text.

pith-pipeline@v0.9.0 · 5529 in / 1101 out tokens · 38321 ms · 2026-05-12T01:19:22.303641+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking (D=3 forcing) unclear
the EF on the position (x,z) can be given by ψ_I(x,z) = (1/x0) Ai(−k²/(4z²x₀⁴) − kx/(z x0)) … main lobe trajectory x(z) = −k/(4x₀³)·(1/z) − μ₀ x0/k · z
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_injective / LogicNat ≃ Nat unclear
constraints on array aperture and antenna spacing … L ≥ max{…} k/|x₀³| + 2 |3 x₀^{-3}|^{1/3}

Reference graph

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