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arxiv: 2605.09895 · v1 · submitted 2026-05-11 · 📡 eess.SP

Recognition: 2 theorem links

· Lean Theorem

Efficient Airy Beam Training for Quasi-LoS Terahertz Near-Field Communications

Chong Han, Wenqi Zhao

Pith reviewed 2026-05-12 04:14 UTC · model grok-4.3

classification 📡 eess.SP
keywords Airy beamsTHz communicationsnear-fieldbeam trainingcodebook designquasi-LoSspectral efficiency
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The pith

Polar codebook designs cut Airy beam training overhead by over half for THz near-field links

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

The paper shows that deriving bounds on Airy beam generation with finite antenna apertures lets designers prune invalid codewords, then build a two-stage non-uniform polar codebook that probes bending direction and samples in polar space. This approach delivers higher spectral efficiency than earlier hierarchical methods while cutting pilot overhead substantially, which matters for maintaining high data rates in 6G terahertz systems where large apertures make near-field propagation and partial obstructions common. A simpler fast-scanning one-dimensional codebook further slashes overhead for low-latency needs at a small efficiency cost.

Core claim

By establishing theoretical bounds of Airy beam generation under finite apertures to prune physically invalid codewords, a two-stage Non-Uniform Polar Codebook (NUPC) is presented that uses a probing mechanism to resolve bending direction and a polar-domain spatial sampling strategy; simulations show NUPC raises average spectral efficiency by 13.4 bit/s/Hz and lowers training overhead by 54.2 percent versus the hierarchical focusing-Airy codebook, while the Fast-Scanning 1D Codebook (FS1C) reduces overhead by 92.9 percent with only a 0.3 bit/s/Hz spectral efficiency drop.

What carries the argument

The two-stage Non-Uniform Polar Codebook (NUPC) that resolves Airy beam bending direction via probing and generates valid beams through polar-domain sampling after pruning invalid codewords with finite-aperture bounds.

If this is right

  • NUPC raises average spectral efficiency by 13.4 bit/s/Hz over the hierarchical focusing-Airy codebook.
  • Training overhead falls 54.2 percent with NUPC while preserving performance.
  • FS1C reduces overhead by 92.9 percent with only a 0.3 bit/s/Hz spectral efficiency reduction.
  • Both designs address the need for low training overhead in large-aperture THz systems with quasi-LoS conditions.

Where Pith is reading between the lines

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

  • The bounding and pruning step could extend to training other curved or self-accelerating beams in near-field settings.
  • Lower overhead might allow more frequent retraining as users or obstacles move in practical deployments.
  • The polar sampling strategy suggests similar efficiency gains are possible in other large-array beam management problems beyond Airy beams.

Load-bearing premise

The simulation channel models and finite-aperture Airy beam generation bounds accurately capture real quasi-LoS propagation and hardware constraints.

What would settle it

A hardware testbed experiment that measures actual training overhead and spectral efficiency in a terahertz setup with partial obstructions using the proposed codebooks versus the prior hierarchical method.

Figures

Figures reproduced from arXiv: 2605.09895 by Chong Han, Wenqi Zhao.

Figure 1
Figure 1. Figure 1: Airy beam boundary (B > 0). tercept Xint(z) increases monotonically with z. Thus, the most stringent aperture constraint is imposed at the maximum propagation distance, i.e., z = zr. To guarantee physical realizability, the intercept must satisfy |Xint(zr)| ≤ Dt/2. By defining the geometric ratios u = xs zb − xr zr , v = 1 zb − 1 zr , and X = u/v, the intercept at the receiver can be rewritten as Xint(zr) … view at source ↗
Figure 2
Figure 2. Figure 2: Non-unified polar codebook. cannot follow the predefined trajectory, resulting in target misalignment. By symmetry, for the case B < 0, the tangent intercept is constrained by the lower edge of the aperture, i.e., Xint(zr) ≥ −Dt/2. This yields the symmetric lower feasible boundary: xs,min(zb) = − 5Dt 12  1 − zb zr  + xr zb zr . (14) IV. NON-UNIFORM POLAR CODEBOOK DESIGN In this section, we propose a non-… view at source ↗
Figure 3
Figure 3. Figure 3: Fast-scanning 1D codebook. configured. To ensure the waypoint avoids aperture truncation while maximizing the power, x (i) r should be strictly bounded. According to (13), the boundary constraint translates to x (i) bound = zr z (i) b x (i) s − 5Dt 12 zr z (i) b − 1 ! . (17) Considering the physical boundaries of the Rx array, the optimal target point is selected as x (i) r = max  Dr 2 , min  xc, x (i) b… view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison of various Airy beam codebooks under a quasi-LoS scenario with a 65.8% blockage ratio. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SE versus height of blockage. D = 3 m, zb = 1.5 m [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SE versus overhead. FS1C provides a highly efficient alternative. It outperforms HFAC in the low-to-moderate blockage regime and maintains near-optimal SE with only a marginal gap of 0.6 bit/s/Hz compared to NUPC. Although the SE of FS1C falls below HFAC at extreme blockage heights due to the simplified 1D search space, it requires significantly fewer pilots. To evaluate the overall robustness, [PITH_FULL… view at source ↗
read the original abstract

With the enlargement of antenna apertures in 6G Terahertz (THz) communications, the Rayleigh distance expands significantly, rendering near-field propagation a dominant scenario in THz links. Beyond conventional Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) conditions, quasi-LoS scenarios with partial obstructions have emerged as a critical challenge. Airy beams offer a promising solution to circumvent obstacles due to their unique curving trajectory. However, existing Airy beam training methods typically rely on parameter-based sampling or exhaustive search, leading to significant pilot overhead and low training efficiency. In this paper, an efficient Airy beam training framework is proposed to address this research gap. First, the theoretical bounds of Airy beam generation under finite apertures to prune physically invalid codewords are derived. Based on this, a two-stage Non-Uniform Polar Codebook (NUPC) design is presented, utilizing a probing mechanism to resolve the bending direction and a polar-domain spatial sampling strategy to generate Airy beams. To address ultra-low latency requirements, a Fast-Scanning 1D Codebook (FS1C) is further developed that sweeps the entire LoS region with minimal codewords. Simulation results demonstrate that NUPC achieves a higher average spectral efficiency (SE) by 13.4 bit/s/Hz while reducing training overhead by 54.2% compared to the state-of-the-art hierarchical focusing-Airy codebook (HFAC). Furthermore, FS1C reduces overhead by 92.9% with only a marginal 0.3 bit/s/Hz reduction compared with HFAC.

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 proposes an efficient Airy beam training framework for quasi-LoS THz near-field communications with large apertures. It first derives theoretical bounds on Airy beam generation under finite apertures to prune invalid codewords. Building on this, it introduces a two-stage Non-Uniform Polar Codebook (NUPC) that uses a probing mechanism to determine bending direction followed by polar-domain spatial sampling, plus a Fast-Scanning 1D Codebook (FS1C) that sweeps the LoS region with minimal codewords. Monte-Carlo simulations report that NUPC improves average spectral efficiency by 13.4 bit/s/Hz while cutting training overhead by 54.2% relative to the hierarchical focusing-Airy codebook (HFAC), and that FS1C reduces overhead by 92.9% at the cost of only 0.3 bit/s/Hz SE loss.

Significance. If the underlying channel and beam models prove accurate, the reported overhead reductions with preserved or improved SE would be practically relevant for low-latency THz links operating in the near-field regime with partial obstructions. The finite-aperture bounds constitute a reusable theoretical contribution that could inform other curved-beam designs.

major comments (2)
  1. [Simulation Results] Simulation Results section: The headline claims (13.4 bit/s/Hz SE gain and 54.2% overhead reduction for NUPC; 92.9% overhead reduction for FS1C) are obtained exclusively from Monte-Carlo runs that invoke the derived finite-aperture Airy bounds and the two-stage polar sampling procedure. No hardware measurements, no comparison against measured THz traces with real partial blockages, and no sensitivity sweeps over obstacle permittivity, geometry, or surface roughness are reported; consequently the numerical margins remain conditional on the fidelity of the synthetic quasi-LoS model.
  2. [Section III] Section III (Proposed Codebook Designs), Eq. (finite-aperture bound): The pruning of physically invalid codewords rests on the derived bounds, yet the manuscript does not quantify how sensitive the final SE and overhead figures are to small violations of those bounds (e.g., aperture truncation errors or phase quantization).
minor comments (2)
  1. [Section III] Notation for the two-stage probing mechanism and polar sampling radii is introduced without an accompanying table that maps symbols to physical quantities; this slows reading of the algorithmic description.
  2. [Figures] Figure captions for the beam-pattern plots do not state the carrier frequency, aperture size, or obstacle parameters used, making direct reproduction of the curves difficult.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Simulation Results] Simulation Results section: The headline claims (13.4 bit/s/Hz SE gain and 54.2% overhead reduction for NUPC; 92.9% overhead reduction for FS1C) are obtained exclusively from Monte-Carlo runs that invoke the derived finite-aperture Airy bounds and the two-stage polar sampling procedure. No hardware measurements, no comparison against measured THz traces with real partial blockages, and no sensitivity sweeps over obstacle permittivity, geometry, or surface roughness are reported; consequently the numerical margins remain conditional on the fidelity of the synthetic quasi-LoS model.

    Authors: We acknowledge that the reported performance gains are derived from Monte-Carlo simulations based on the theoretical models developed in the paper. In THz near-field beam training research, simulation-driven evaluation using established quasi-LoS channel models with partial obstructions is the prevailing methodology, given the practical challenges of realizing large-aperture hardware testbeds for Airy beams. The underlying propagation model follows standard THz literature. To directly address the concern about sensitivity, we will add new simulation results in the revised manuscript that include sweeps over obstacle permittivity, geometry, and surface roughness, thereby demonstrating the robustness of the SE and overhead improvements under model variations. revision: partial

  2. Referee: [Section III] Section III (Proposed Codebook Designs), Eq. (finite-aperture bound): The pruning of physically invalid codewords rests on the derived bounds, yet the manuscript does not quantify how sensitive the final SE and overhead figures are to small violations of those bounds (e.g., aperture truncation errors or phase quantization).

    Authors: We agree that explicitly quantifying the sensitivity of the final metrics to small violations of the finite-aperture bounds would improve the rigor of the pruning strategy. In the revised manuscript, we will incorporate additional analysis and figures that introduce controlled perturbations, including small aperture truncation errors and phase quantization, and report their effects on spectral efficiency and training overhead. revision: yes

standing simulated objections not resolved
  • Hardware measurements and direct comparisons against measured THz traces with real partial blockages, as these require specialized experimental facilities beyond the scope of the current theoretical and simulation-based study.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives theoretical bounds on finite-aperture Airy beam generation to prune invalid codewords, then constructs NUPC (two-stage polar sampling with probing) and FS1C designs from those bounds, and reports simulation performance metrics. These steps do not reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the SE gains and overhead reductions are obtained from Monte-Carlo evaluation of the new codebooks against HFAC, using independent channel models. The chain is self-contained with no tautological reductions visible.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claims rest on the validity of derived theoretical bounds for finite-aperture Airy beams and on the assumption that the simulated quasi-LoS channels represent practical conditions; no explicit free parameters, axioms, or invented entities are identifiable from the abstract alone.

pith-pipeline@v0.9.0 · 5589 in / 1142 out tokens · 44866 ms · 2026-05-12T04:14:21.293985+00:00 · methodology

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Reference graph

Works this paper leans on

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