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arxiv: 2605.18099 · v1 · pith:VIYA3C3Rnew · submitted 2026-05-18 · 💻 cs.IT · math.IT

Movable Antenna-Aided Secure LEO Satellite Networks: Joint Antenna Position and Beamforming Optimization

Suhong Luo , Pan Tang , Jianhua Zhang , Ji Wang , Yixuan Li , Zihang Ding , Xingwang Li This is my paper

Pith reviewed 2026-05-20 00:36 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords movable antennaLEO satellitephysical layer securitybeamforming optimizationsecrecy rateantenna positionsatellite network
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The pith

Jointly optimizing movable antenna positions and beamforming maximizes average secrecy rate in LEO satellite communications.

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

The paper establishes that movable antennas can enhance security in LEO satellite communications by allowing flexible repositioning to counter nearby eavesdroppers. In dense constellations, satellites may have small angular separations, limiting the effectiveness of fixed antennas for physical layer security. The authors develop a joint optimization of antenna positions and beamforming to maximize the average secrecy rate over time-varying channels. An alternating optimization approach solves this by handling beamforming with semidefinite relaxation and positions with successive convex approximation or differential evolution. If successful, this would provide a hardware-based way to improve secrecy without additional power or spectrum resources.

Core claim

By equipping a ground station with a movable antenna array and jointly optimizing its positions along with the transmit beamforming vectors, the scheme achieves a higher average secrecy rate compared to fixed antenna setups, as demonstrated through the proposed alternating optimization framework and numerical evaluations in the presence of multiple visible LEO satellites acting as potential eavesdroppers.

What carries the argument

The movable antenna array, whose positions are jointly optimized with transmit beamforming to exploit additional spatial degrees of freedom against eavesdroppers with small angular separations.

Load-bearing premise

Other visible satellites act as potential eavesdroppers with small angular separations from the serving satellite, making conventional fixed-position antennas insufficient.

What would settle it

A simulation result showing that the secrecy rate with optimized movable antenna positions equals or falls below the fixed-position case when angular separations between the serving satellite and eavesdroppers are increased beyond a small threshold.

read the original abstract

The broadcast characteristics of sixth-generation (6G) low-earth orbit (LEO) satellite communications raise serious security issues. Movable antenna (MA) technology offers a promising physical layer security (PLS) solution by flexibly reconfiguring antenna positions to exploit additional spatial degrees of freedom. However, in highly dense LEO satellite constellations, the legitimate satellite and potential eavesdropping satellites may exhibit small angular separations, which poses significant challenges for the design of secure transmission schemes. To address this challenge, this paper proposes an MA-assisted secure transmission scheme for time-varying LEO satellite communications, where a ground station equipped with an MA array communicates with a serving satellite, while the other visible satellites are regarded as potential eavesdroppers. We maximize the average secrecy rate by jointly optimizing the transmit beamforming and MA positions. An alternating optimization (AO) framework is developed, where semidefinite relaxation is adopted for the beamforming optimization subproblem, while high-accuracy successive convex approximation (SCA) and low-complexity differential evolution (DE) algorithms are proposed for the MA position optimization subproblem. Numerical results demonstrate that the proposed MA-assisted LEO secure transmission scheme consistently achieves superior performance compared to the conventional fixed-position antenna scheme.

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 movable-antenna (MA) assisted physical-layer security scheme for LEO satellite networks in which a ground station with an MA array serves one satellite while treating other visible satellites as eavesdroppers. It maximizes the average secrecy rate by jointly optimizing transmit beamforming and MA positions via an alternating-optimization framework that applies semidefinite relaxation to the beamforming subproblem and either successive convex approximation or differential evolution to the position subproblem. Numerical results are reported to show consistent gains over conventional fixed-position antenna baselines.

Significance. If the reported secrecy-rate gains are reproducible under realistic far-field LEO channel models with small angular separations, the work would provide a concrete demonstration that MA mobility can supply usable additional spatial degrees of freedom for PLS in dense constellations. The dual-algorithm treatment of the position subproblem (high-accuracy SCA and low-complexity DE) is a practical contribution that could be adopted in follow-on studies.

major comments (2)
  1. [§II and §IV] §II (System Model) and §IV (Channel Model): the far-field array response vectors for serving and eavesdropping satellites with angular separations of only fractions of a degree remain highly correlated even after meter-scale MA repositioning. Because the secrecy-rate objective is a function of these correlated vectors, the joint optimization reduces to a marginal perturbation of the fixed-array case; the manuscript must supply an explicit calculation or simulation of the inner product between the serving and eavesdropping steering vectors as a function of MA displacement to substantiate the claimed DoF gain.
  2. [§V] §V (Numerical Results), Table I and Figs. 3–5: the reported secrecy-rate superiority is load-bearing for the central claim, yet the simulation parameters (exact angular separation, MA movement region size, and far-field distance) are not stated with sufficient precision to allow independent verification that the observed gains survive the correlation issue identified above.
minor comments (2)
  1. [§II] The notation for the time-varying channel vectors and the averaging window for the secrecy rate should be defined once in §II and used consistently thereafter.
  2. [§IV] A brief complexity comparison (flops or runtime) between the SCA and DE position solvers would help readers assess the practical trade-off claimed in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and insightful review. The comments raise important points about the far-field correlation in dense LEO scenarios and the need for precise simulation parameters. We address each major comment below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: [§II and §IV] §II (System Model) and §IV (Channel Model): the far-field array response vectors for serving and eavesdropping satellites with angular separations of only fractions of a degree remain highly correlated even after meter-scale MA repositioning. Because the secrecy-rate objective is a function of these correlated vectors, the joint optimization reduces to a marginal perturbation of the fixed-array case; the manuscript must supply an explicit calculation or simulation of the inner product between the serving and eavesdropping steering vectors as a function of MA displacement to substantiate the claimed DoF gain.

    Authors: We agree that small angular separations in dense LEO constellations result in highly correlated steering vectors under the far-field model. However, MA repositioning within a finite region still permits adjustment of the relative phases across elements, which the joint optimization exploits to improve the secrecy rate beyond the fixed-position baseline. To directly address the concern, we will add an explicit analysis in the revised Section IV: we derive the inner product |a_s^H a_e| (normalized) as a closed-form function of MA displacement for a uniform linear array and plot it versus displacement (0 to 5 m) for angular separations of 0.1°–1°. This calculation shows that even modest movements can reduce correlation enough to yield non-negligible secrecy gains, consistent with the numerical results. The new material will substantiate the claimed spatial DoF. revision: yes

  2. Referee: [§V] §V (Numerical Results), Table I and Figs. 3–5: the reported secrecy-rate superiority is load-bearing for the central claim, yet the simulation parameters (exact angular separation, MA movement region size, and far-field distance) are not stated with sufficient precision to allow independent verification that the observed gains survive the correlation issue identified above.

    Authors: We acknowledge that greater precision is required for reproducibility. In the revised manuscript we will expand Table I to list all parameters explicitly, including: minimum angular separation of 0.5°, MA movement region of 2 m × 2 m, and far-field distance of 550 km (consistent with typical LEO altitudes). We will also add a new figure in Section V showing secrecy-rate gain versus angular separation (0.1°–2°) under the correlation levels analyzed in the new Section IV calculation. These additions will allow readers to verify that the reported gains remain positive even when correlation is high. revision: yes

Circularity Check

0 steps flagged

No circularity: standard joint optimization of beamforming and positions via AO/SDR/SCA/DE on explicitly defined secrecy-rate objective

full rationale

The paper formulates an average secrecy rate maximization problem based on far-field channel models for the serving satellite and visible eavesdroppers, then applies an alternating optimization framework with semidefinite relaxation for beamforming and successive convex approximation or differential evolution for movable-antenna positions. These steps are algorithmic solvers applied to a well-defined non-convex objective; the secrecy rate expression is not constructed from fitted parameters of the same optimization, nor does any subproblem reduce to a self-citation or renaming of its own output. The numerical comparisons to fixed-position antennas are simulation results, not tautological predictions. The derivation chain therefore remains self-contained and independent of its own fitted values.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields limited visibility into parameters or axioms; the optimization relies on standard convex-relaxation assumptions and channel models typical for PLS papers.

pith-pipeline@v0.9.0 · 5763 in / 1046 out tokens · 25508 ms · 2026-05-20T00:36:24.205385+00:00 · methodology

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Reference graph

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