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arxiv: 2606.00244 · v1 · pith:HWGOP3BZnew · submitted 2026-05-29 · 💻 cs.NI · eess.SP

GNN-based Online Beamforming Design for HAPS-Assisted NTN

Lavanya S S Anjapuli , Animesh Yadav , Halim Yanikomeroglu This is my paper

Pith reviewed 2026-06-28 19:37 UTC · model grok-4.3

classification 💻 cs.NI eess.SP
keywords HAPSNTNbeamformingGNNenergy efficiencycell-edge usersnon-convex optimization
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0 comments X

The pith

A HAPS relay with GNN-optimized beamforming increases 5th-percentile energy efficiency for cell-edge users.

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

The paper aims to show that integrating a high-altitude platform station into terrestrial networks can improve performance for cell-edge users by relaying their data over line-of-sight links. It sets up an energy-efficiency maximization problem for joint beamforming at base stations and the HAPS. Because the problem is non-convex, the authors develop an online graph neural network framework that models the network topology to find solutions. A sympathetic reader would care if this delivers measurable gains precisely where conventional networks perform worst, at the cell edges.

Core claim

Integrating a HAPS into terrestrial networks and using a GNN-based online optimization framework to jointly design beamforming vectors at the BS and HAPS improves network performance by increasing the 5th-percentile energy efficiency for cell-edge users.

What carries the argument

The graph neural network that captures network topology to solve the non-convex joint beamforming problem in an online manner.

If this is right

  • The HAPS provides line-of-sight links that reduce the impact of inter-cell interference and path loss on cell-edge users.
  • Joint beamforming at the terrestrial base stations and HAPS is required to maximize the energy-efficiency objective.
  • Gains appear most clearly in the lower tail of the energy-efficiency distribution rather than in average performance.

Where Pith is reading between the lines

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

  • The online GNN approach may adapt to time-varying user locations or channel conditions without retraining from scratch.
  • Similar graph-based solvers could be tested for beamforming problems that include additional non-terrestrial nodes or power constraints.

Load-bearing premise

The GNN-based framework can effectively capture the network topology and solve the non-convex joint beamforming problem in an online manner to deliver the claimed EE gains.

What would settle it

Numerical experiments in which the GNN solution produces no increase in 5th-percentile EE relative to a baseline terrestrial network without HAPS would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2606.00244 by Animesh Yadav, Halim Yanikomeroglu, Lavanya S S Anjapuli.

Figure 1
Figure 1. Figure 1: System architecture of the network considered. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Proposed GNN-based optimization architecture [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Flow diagram of GNN optimization Fig.2 which is a detailed representation of second stage in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: CDF vs. EE with NOMA and OMA techniques across [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: CDF vs. EE for different solution approaches and cell [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

In terrestrial networks, especially in urban areas, cell-edge users often face significant capacity limitations due to high path loss, shadowing, and inter-cell interference (ICI). This paper proposes integrating a high-altitude platform station (HAPS) into terrestrial networks, where terrestrial base stations (BS) can alleviate these issues by relaying data intended for cell-edge users via HAPS, thereby leveraging line-of-sight (LoS) links. We formulate an energy-efficiency (EE) maximization problem to jointly design beamforming vectors at the BS and HAPS with the goal of improving cell-edge user performance. Since the resulting problem is non-convex, we develop an online optimization framework based on a graph neural networks (GNN), which effectively captures the network topology. Numerical results show that the proposed HAPS-assisted architecture improves network performance, particularly by increasing the 5th-percentile EE, thereby enhancing service for cell-edge users.

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 / 1 minor

Summary. The paper proposes integrating a high-altitude platform station (HAPS) into terrestrial networks to relay data for cell-edge users via LoS links, alleviating path loss, shadowing, and ICI. It formulates a non-convex energy-efficiency (EE) maximization problem for joint beamforming at terrestrial BSs and the HAPS, and develops a GNN-based online optimization framework to solve it by capturing network topology. Numerical results are claimed to demonstrate that the HAPS-assisted architecture improves network performance, especially the 5th-percentile EE for cell-edge users.

Significance. If the numerical results hold with appropriate baselines and verification, the work could contribute to NTN beamforming by showing how GNNs enable topology-aware online solutions to non-convex joint optimization problems, with potential benefits for edge-user EE in integrated terrestrial-NTN setups.

major comments (2)
  1. [Abstract] Abstract: The central claim rests on 'numerical results' showing 5th-percentile EE gains, but the text provides no details on baselines, simulation parameters, error bars, convergence, or how the GNN addresses non-convexity; this is load-bearing for the performance improvement assertion and prevents verification.
  2. [Problem Formulation / GNN Framework] Problem formulation and GNN framework: The non-convex EE maximization is stated to be solved via GNN online optimization, but without equations, architecture details, or proof of topology capture, it is impossible to assess whether the framework delivers the claimed gains or reduces to standard methods.
minor comments (1)
  1. [Abstract] Abstract: Consider expanding the abstract with one sentence on key simulation parameters or baseline comparisons to better support the numerical claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We agree that additional details are needed to support the claims and will revise the manuscript accordingly to improve verifiability while preserving the core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim rests on 'numerical results' showing 5th-percentile EE gains, but the text provides no details on baselines, simulation parameters, error bars, convergence, or how the GNN addresses non-convexity; this is load-bearing for the performance improvement assertion and prevents verification.

    Authors: We agree the abstract is overly concise and will revise it to include brief references to the baselines (e.g., no-HAPS ZF and WMMSE), key parameters (HAPS altitude, user density, power budgets), and the GNN's unsupervised training approach for the non-convex EE problem. Due to length limits, error bars and convergence curves will be explicitly cross-referenced to Section IV rather than duplicated in the abstract. revision: yes

  2. Referee: [Problem Formulation / GNN Framework] Problem formulation and GNN framework: The non-convex EE maximization is stated to be solved via GNN online optimization, but without equations, architecture details, or proof of topology capture, it is impossible to assess whether the framework delivers the claimed gains or reduces to standard methods.

    Authors: The manuscript contains a formulation section with the EE objective (sum-rate over total power) and power constraints, plus a GNN section describing the graph (nodes as BS/HAPS, edges as interference/LoS links) and message-passing layers. To address the concern, we will insert the explicit loss function, layer update equations, and a short paragraph explaining topology capture via permutation-equivariant aggregation; we will also add a table comparing GNN output to WMMSE to demonstrate it does not reduce to standard methods. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The manuscript abstract and context present a problem formulation for EE maximization followed by a GNN-based solver and numerical validation, but contain no equations, derivations, or self-citations that reduce any claimed prediction or result to its own inputs by construction. The central performance claim is supported by simulation outcomes rather than any self-definitional mapping, fitted-input renaming, or load-bearing self-citation chain, rendering the approach self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that the GNN solves the non-convex problem effectively.

pith-pipeline@v0.9.1-grok · 5698 in / 1007 out tokens · 21691 ms · 2026-06-28T19:37:24.835411+00:00 · methodology

discussion (0)

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