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arxiv: 2505.22286 · v4 · submitted 2025-05-28 · 💻 cs.IT · eess.SP· math.IT

Wireless Communication for Low-Altitude Economy with UAV Swarm Enabled Two-Level Movable Antenna System

Haiquan Lu , Yong Zeng , Shaodan Ma , Bin Li , Shi Jin , Rui Zhang This is my paper

Pith reviewed 2026-05-19 13:16 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords UAV swarmmovable antennalow-altitude economymulti-user communicationposition optimizationinterference-free communicationbeamforming
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The pith

A UAV swarm with two-level movable antennas maximizes the minimum rate for multiple ground users by jointly optimizing swarm positions, local antenna placements, and beamforming.

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

The paper proposes a system in which UAVs coordinate to form a large-scale movable antenna array while each UAV also adjusts its own local antenna positions. This two-level mobility is used to maximize the lowest achievable rate across ground user equipments through joint optimization of three-dimensional UAV placements, individual antenna locations, and receive beamforming. For the two-user case with single-antenna UAVs, closed-form positions are derived that eliminate inter-user interference when the uniform plane wave model applies, by arranging the swarm into a uniform sparse array that meets minimum safety distances. Numerical evaluations confirm higher rates than benchmark schemes that lack either level of mobility.

Core claim

By treating the UAV swarm as a coordinated large movable antenna system in which each UAV also hosts its own movable antenna array, the minimum rate for ground users can be substantially increased through joint three-dimensional placement, local antenna positioning, and beamforming; in the two-user single-antenna case this yields closed-form interference-free positions under the uniform plane wave assumption.

What carries the argument

Two-level movable antenna system: UAV swarm coordination for large-scale array movement combined with per-UAV local antenna position adjustment, which together enable the joint optimization problem.

If this is right

  • For a single user the optimization reduces to simple geometric placement of the swarm.
  • For two users the derived uniform sparse array placement achieves zero inter-user interference under the stated model.
  • For arbitrary numbers of users an alternating optimization algorithm efficiently solves the non-convex problem.
  • Equipping each UAV with multiple antennas extends the same two-level mobility gains to richer local arrays.

Where Pith is reading between the lines

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

  • The interference-free placement rule could be adapted to slowly moving users by periodic re-optimization of swarm geometry.
  • Similar two-level mobility ideas might apply to other aerial platforms where individual vehicles can both translate and reconfigure their antenna elements.
  • Real-world validation would require checking whether the uniform plane wave approximation remains accurate at the short ranges typical of low-altitude UAV operations.

Load-bearing premise

The uniform plane wave model holds for the air-to-ground channels, which permits closed-form derivation of swarm positions that remove inter-user interference.

What would settle it

Field measurements in which inter-user interference persists or minimum rates fail to exceed those of fixed-antenna benchmarks even after the swarm is placed according to the derived uniform sparse array positions would falsify the claimed performance gains.

Figures

Figures reproduced from arXiv: 2505.22286 by Bin Li, Haiquan Lu, Rui Zhang, Shaodan Ma, Shi Jin, Yong Zeng.

Figure 1
Figure 1. Figure 1: Wireless communication with a low-altitude UAV swar [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The channels’ squared-correlation coefficient [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Convergence behaviour of Algorithm 1. V. NUMERICAL RESULTS In this section, numerical results are provided to verify the performance of the proposed low-altitude UAV swarm enabled MA system. The channel power at the reference distance of d0 = 1 m is β0 = −61.4 dB, and the noise power is σ 2 = −94 dBm. The minimum distance to avoid the collision among UAVs is dmin = 1 m. Moreover, the minimum distance to av… view at source ↗
Figure 5
Figure 5. Figure 5: The SNR loss factor versus the transmit power for the t [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The minimum achievable rate versus the transmit powe [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The minimum achievable rate versus the number of UEs i [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The minimum achievable rate versus the normalized mo [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the minimum achievable rate for the ca [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original abstract

Unmanned aerial vehicle (UAV) is regarded as a key enabling platform for low-altitude economy, due to its advantages such as 3D maneuverability, flexible deployment, and LoS air-to-air/ground communication links. In particular, the intrinsic high mobility renders UAV especially suitable for operating as a movable antenna (MA) from the sky. In this paper, by exploiting the flexible mobility of UAV swarm and antenna position adjustment of MA, we propose a novel UAV swarm enabled two-level MA system, where UAVs not only individually deploy a local MA array, but also form a larger-scale MA system with their individual MA arrays via swarm coordination. We formulate a general optimization problem to maximize the minimum achievable rate over all ground user equipments (UEs), by jointly optimizing the 3D UAV swarm placement positions, their individual MAs' positions, and receive beamforming for different UEs. To gain useful insights, we first consider the special case where each UAV has only one antenna, under different scenarios of one single UE, two UEs, and arbitrary number of UEs. In particular, for the two-UE case, we derive the optimal UAV swarm placement positions in closed-form that achieves IUI-free communication when the uniform plane wave (UPW) model holds, where the UAV swarm forms a uniform sparse array (USA) satisfying minimum safe distance constraint. While for the general case with arbitrary number of UEs, we propose an efficient alternating optimization algorithm to solve the formulated non-convex optimization problem. Then, we extend the results to the case where each UAV is equipped with multiple antennas. Numerical results verify that the proposed low-altitude UAV swarm enabled MA system significantly outperforms various benchmark schemes, thanks to the exploitation of two-level mobility to create more favorable channel conditions for multi-UE communications.

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 proposes a UAV swarm-enabled two-level movable antenna (MA) system for low-altitude economy wireless communications. UAVs form a swarm that acts as a large-scale MA while each UAV deploys its own local MA array. The central optimization maximizes the minimum achievable rate over ground UEs by jointly tuning 3D swarm positions, individual MA positions, and receive beamforming. Closed-form optimal swarm positions are derived for the two-UE single-antenna case that achieve IUI-free reception when the uniform plane wave (UPW) model holds and the swarm forms a uniform sparse array respecting minimum safe distance. An alternating optimization algorithm is given for the general multi-UE case, with extension to multi-antenna UAVs; numerical results claim significant gains over benchmarks due to the two-level mobility.

Significance. If the modeling assumptions hold, the work supplies useful analytical insight via the closed-form two-UE solution and a practical alternating algorithm, together with numerical evidence that two-level mobility can improve multi-user channel conditions in low-altitude settings. The explicit derivation of IUI-free placements under UPW and the reproducible numerical comparisons constitute concrete strengths.

major comments (2)
  1. [Two-UE special case] Two-UE special case (abstract and corresponding derivation): the closed-form optimal swarm positions that achieve IUI-free communication are obtained under the uniform plane wave (UPW) model. In low-altitude regimes the relevant distances are often comparable to array aperture or wavelength, so spherical-wave curvature is expected; the paper should quantify the resulting residual IUI or demonstrate that the claimed channel-condition advantage survives under a near-field model.
  2. [Numerical results] Numerical results section: the reported outperformance is interpreted as arising from the two-level mobility creating favorable channels, yet the simulations appear to retain the UPW assumption used in the closed-form case. Adding a near-field propagation comparison (or an error analysis when UPW is relaxed) is needed to confirm that the performance gap persists when the central modeling assumption is removed.
minor comments (2)
  1. [Algorithm description] The transition from the special-case closed-form results to the general alternating algorithm could be clarified with a brief statement on how the two-UE insight informs the initialization or interpretation of the numerical optimizer.
  2. [System model] Notation for the two-level MA (swarm-level versus per-UAV MA positions) should be introduced once with a clear diagram or table to avoid ambiguity in later sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments regarding the modeling assumptions and numerical validation. We address each major comment below and indicate the planned revisions.

read point-by-point responses

  1. Referee: [Two-UE special case] Two-UE special case (abstract and corresponding derivation): the closed-form optimal swarm positions that achieve IUI-free communication are obtained under the uniform plane wave (UPW) model. In low-altitude regimes the relevant distances are often comparable to array aperture or wavelength, so spherical-wave curvature is expected; the paper should quantify the resulting residual IUI or demonstrate that the claimed channel-condition advantage survives under a near-field model.

    Authors: We agree that the UPW model is an approximation and spherical-wave curvature can be relevant in low-altitude regimes. The closed-form solution is derived under UPW to obtain analytical insight into IUI-free placements. In the revision we will add an analysis (new subsection or appendix) that quantifies residual IUI for the derived positions under the spherical-wave model and shows that the claimed channel-condition advantage largely persists for typical low-altitude distances. revision: yes

  2. Referee: [Numerical results] Numerical results section: the reported outperformance is interpreted as arising from the two-level mobility creating favorable channels, yet the simulations appear to retain the UPW assumption used in the closed-form case. Adding a near-field propagation comparison (or an error analysis when UPW is relaxed) is needed to confirm that the performance gap persists when the central modeling assumption is removed.

    Authors: We acknowledge that the current numerical results rely on the UPW model. To verify robustness, we will add a near-field comparison in the revised numerical results section using the spherical-wave propagation model, confirming that the performance gains from two-level mobility remain significant when the UPW assumption is relaxed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained under stated assumptions

full rationale

The paper formulates a joint optimization over UAV positions, MA positions, and beamforming to maximize min rate. For the two-UE special case it derives closed-form positions that null IUI under the explicit UPW assumption by constructing a uniform sparse array obeying the min-distance constraint. This is a direct algebraic consequence of the plane-wave phase model rather than a fit or self-definition. The general case uses a standard alternating optimization algorithm on the non-convex problem. No load-bearing self-citations, uniqueness theorems imported from the same authors, or ansatz smuggling appear in the derivation chain. Numerical verification compares against benchmarks and is independent of the closed-form special case. The UPW assumption is stated openly and the near-field concern is an external modeling question, not a circularity inside the paper's own equations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the UPW model for closed-form results and standard assumptions in wireless optimization such as LoS links and minimum distance constraints; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Uniform plane wave (UPW) model holds for channel modeling in the two-UE case
    Invoked to derive optimal UAV swarm placement positions achieving IUI-free communication with uniform sparse array.
  • domain assumption LoS air-to-air/ground communication links and 3D maneuverability of UAVs
    Background assumption enabling the two-level MA system formulation.

pith-pipeline@v0.9.0 · 5882 in / 1361 out tokens · 32973 ms · 2026-05-19T13:16:55.025237+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

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    Relation between the paper passage and the cited Recognition theorem.

    for the two-UE case, we derive the optimal UAV swarm placement positions in closed-form that achieves IUI-free communication when the uniform plane wave (UPW) model holds, where the UAV swarm forms a uniform sparse array (USA) satisfying minimum safe distance constraint

What do these tags mean?
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supports
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extends
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uses
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contradicts
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Reference graph

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