Energy-Efficient Secure Communications via Joint Optimization of UAV Trajectory and Movable-Antenna Array Beamforming

Jinu Gong; Joonhyuk Kang; Sanghyeok Kim

REVIEW 4 major objections 3 minor 1 cited by

Energy-Efficient Secure Communications via Joint Optimization of UAV Trajectory and Movable-Antenna Array Beamforming

T0 review · 4 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read UAVs with movable-antenna arrays can raise secrecy energy efficiency by about 40 percent over fixed-antenna jammers, via joint optimization of flight path, antenna orientation, and beamforming.

desk verdict The paper's novel scenario is undercut by an invalid worst-case bound on Eve's rate, so the reported 40% secrecy-energy-efficiency gain is likely an artifact. read the letter →

arxiv 2507.20489 v1 pith:RE4EKRZ5 submitted 2025-07-28 eess.SP

Sanghyeok Kim , Jinu Gong , Joonhyuk Kang This is my paper · ORCID

classification eess.SP

keywords Movable-antennaarrayUAVtrajectoryoptimizationSecrecyenergyefficiencyPhysicallayersecurityBeamformingCooperativejammingAlternatingLine-of-sightchannel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a UAV carrying a movable-antenna array can act as an energy-efficient friendly jammer, and that the key to making it work is to optimize its flight path, array orientation, and beamforming jointly. In the simulated setup, the proposed joint optimization reaches roughly 40% higher secrecy energy efficiency than a fixed-antenna jammer and roughly 10% higher than a strategy that simply aims the array at the eavesdropper. The practical stake is that physical-layer security can be bought with antenna flexibility instead of extra flight distance or transmit power.

What carries the argument

The load-bearing object is the movable-antenna array mounted on the UAV's underside, whose orientation is described by rotations about three local axes. Because the aerial-ground channels are modeled as pure line-of-sight, the array response vector is a deterministic function of the rotation angles, which means steering the beam and digging nulls can be done by rotating the panel. Around this object the paper builds an alternating optimization: trajectory updates use successive convex approximation and the Dinkelbach method for the fractional objective, orientation updates use projected gradient ascent with backtracking line search, and beamforming updates use rank-relaxed semidefinite programming with Gaussian randomization to recover the beamforming vector.

What would settle it

Run the same optimization with the LoS channel replaced by a Rician or multipath channel in which the direct component contributes only part of the received power; if the roughly 40% secrecy-energy-efficiency gain over fixed antennas drops toward zero, the central claim's reliance on deterministic LoS array responses is confirmed.

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Extended reading notes

Core claim

The central claim is that movable antennas give a jamming UAV a spatial degree of freedom that fixed antenna panels do not: by rotating the panel, the UAV can point a strong jamming beam at the eavesdropper while steering a null at the legitimate user, all without changing its position. This lets the UAV follow a shorter, less curved trajectory than a fixed-antenna jammer, which must fly around the user to avoid harming its reception. The paper makes the optimization tractable by bounding the worst-case eavesdropper rate over an uncertainty region, and by solving the resulting fractional, non-convex problem with alternating updates of trajectory, orientation angles, and beamforming vector. The simulation comparison shows the proposed MA-based method outperforming both the fixed-antenna and the Eve-oriented baselines in secrecy energy efficiency.

Load-bearing premise

The aerial-ground channels are modeled as strictly line-of-sight, so the array response is a deterministic function of the panel orientation; if multipath is present, the deep nulls and beam alignment that generate the reported gains would be degraded.

Editorial extensions

If this is right

A jamming UAV can trade flight distance for antenna steering, so secrecy constraints no longer force long detours around the legitimate user.
Adding movable antennas to existing UAV jamming platforms can raise secrecy energy efficiency by about 40% in LoS-dominated settings without requiring more transmit power.
The worst-case bound on the eavesdropper's rate means the gains are promised even when only an approximate eavesdropper position is known.
The same alternating, Dinkelbach-based structure can be reused for other fractional secrecy objectives in UAV-enabled networks.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the LoS assumption is relaxed to a multipath or Rician channel, the reported 40% gain is likely to shrink, but the relative value of MA rotation should persist whenever the direct path dominates.
The approach could naturally extend to multiple users or eavesdroppers by scheduling rotation angles across time slots to shape several beams and nulls over the flight.
A prototype test with measured array responses and real actuation costs would be the cleanest way to tell how much of the gain survives outside the simulation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Hey,

The headline: the paper's novel piece is a rotatable (they call it movable) antenna array on a jamming UAV, optimized jointly with trajectory and beamforming for secrecy energy efficiency. That scenario doesn't appear in the prior work they cite, and the system model is assembled carefully enough. But the central numerical result—about 40% SEE gain over fixed antennas—is not supported, because the worst-case Eve rate bound in Eq. (8) is not a valid bound.

Here's the problem. The actual Eve SINR uses |h_{B,e}^H wB|^2 and |h_{J,e}^H wJ|^2, which include array gains. The bound replaces them with path-loss-only terms: it drops the BS array gain (at least 6 dB for 4 antennas, possibly more) and assumes the jammer's interference is at its worst-case path-loss level, ignoring that wJ can null Eve. Both errors make the Eve rate smaller than it can actually be, which inflates the secrecy rate used as the objective. The paper never checks (8) against the exact maximization in (7). There's also an exponent inconsistency: (8) uses free-space distance-squared loss, while the channel model in Table I uses α=3.5 and 2.8 for those links. So the reported gains may be artifacts of the surrogate bound.

Other issues are secondary. Section III-B describes projected gradient descent for the MA angles, but Algorithm 1 says "two-phase approach." The reformulated rate in Eq. (16) appears without derivation. There's no code and no sensitivity analysis; the conclusions rest on a single deterministic scenario. On the plus side, the authors engage with the right literature, and the energy consumption model is standard. If the bound were fixed, this could be a modest but useful extension to UAV-PLS work.

Who is this for? Readers who want to see how antenna orientation could be added to UAV jamming formulations. The system model is worth a look, but don't take the numbers at face value.

I'd send it to peer review because the technical flaw warrants expert scrutiny, but I would not accept it in this form. If the authors can provide a valid bound or directly evaluate the worst-case rate, the paper might become publishable.

Referee Report

4 major / 3 minor

Summary. The manuscript proposes a framework for secure UAV-assisted communications in which a rotary-wing UAV equipped with a movable-antenna (MA) array acts as a friendly jammer. The authors jointly optimize the UAV trajectory, the MA orientation angles, and the jamming beamforming vector to maximize the sum secrecy energy efficiency (SEE), subject to the UAV's velocity constraint, MA angle limits, and a transmit power constraint. The formulation uses a worst-case lower bound on secrecy capacity built from upper-bounding the eavesdropper's rate via simplified path-loss terms. An alternating optimization algorithm is developed, and simulations report roughly 40% SEE improvement over a fixed-antenna baseline and about 10% over an Eve-oriented baseline. The paper is a candidate for IEEE Wireless Communications Letters and is the first to consider an MA-equipped UAV as a jammer.

Significance. If the technical formulation were correct, the paper would make a novel and relevant contribution: combining UAV mobility with movable-antenna array reconfigurability for physical-layer security, and demonstrating energy-efficiency gains. The related work is appropriately cited, and the idea of exploiting MA orientation to form deep nulls and directional beams is timely. However, the central technical validity is compromised by an incorrect worst-case bound, and the numerical results are obtained by optimizing a surrogate objective that is not a valid lower bound on secrecy capacity. The paper also contains internal algorithm inconsistencies and an underived reformulation. These issues are load-bearing and must be resolved before the claims can be trusted.

major comments (4)

[II.B] The claimed upper bound on Eve's rate in Eq. (8) is not valid. The actual numerator of gamma_e in Eq. (6) is PB |h_{B,e}^H w_B|^2, which includes the channel array gain |g_{B,e}^H w_B|^2; with MRT toward the legitimate user this gain can be as large as N_B (here 4), and it can be even larger if the BS beam illuminates Eve. The proposed bound uses only the scalar path-loss term tilde{h}_{B,e}, omitting this array gain and therefore underestimating the numerator. Conversely, the denominator of gamma_e contains PJ |h_{J,e}^H w_J|^2, which the optimizer can drive toward zero by forming a null toward Eve; replacing it with a strictly positive path-loss term tilde{h}_{J,e} overestimates the jamming interference at Eve and underestimates Eve's rate. Both effects inflate the secrecy-capacity lower bound (13)-(14) that is the optimization objective. Since Section IV reports performance of this surrogate objective, the claimed 40% and 10% SEE improvements may be artifacts of the invalid bound rather than of MA orientation. The paper does not validate Eq. (8) against the exact max_{qe} in Eq. (7).
[III.A] The reformulated secrecy rate expression in Eq. (16) is presented without any derivation, and its equivalence to the original rbar_sec is not established. Some terms use channel vectors h (e.g., the second term uses h_{J,e}^H w_J) while others use array-response vectors g (e.g., the first and third terms), and the auxiliary variables mu[n], nu[n], tau[n], chi[n] are introduced without explaining how they transform the objective and constraints. This makes the trajectory subproblem (18) unjustified; a reader cannot verify that maximizing (18) indeed maximizes (15). The authors should provide a clear derivation, including the exact substitutions and the reasons for the claimed convex behaviour.
[Algorithm 1] Line 10 of Algorithm 1 states that the MA orientation angles are updated using a 'two-phase approach', but Section III-B describes a projected gradient (feasible direction) method with backtracking line search. These are not the same method, and the paper does not explain what the two-phase approach is or how it relates to the projected gradient update in Eq. (21). The convergence statement in Section III-B relies on the Armijo-Goldstein condition, but if a different update is used in the actual implementation, the convergence guarantee does not apply. Please clarify which method is implemented in the simulations and provide a consistent description.
[III] The removal of the non-negative operator [.]^+ from the objective in Eq. (14) is justified solely by a reference to [4], with no proof for the MA-equipped system considered here. The claim that 'the optimization always leads to a non-negative objective value' is not self-evident, especially because the worst-case bound in Eq. (8) is not a true upper bound; if the bound is corrected, the secrecy lower bound can become negative. The paper should either prove the non-negativity for the actual objective or retain the [.]^+ operator and handle it in the optimization.

minor comments (3)

[IV] The numerical results are reported in vague terms ('around 40% improvement', 'about 10% higher') without exact numbers, confidence intervals, or a sensitivity analysis. Since the central claim is empirical, the paper should provide the precise SEE values and ideally some variation of parameters (e.g., epsilon, N_B, PJ) to show the robustness of the gains.
[II.B.2] There is a grammatical error in the sentence 'The total energy consumption is consists of propulsion power...' It should read 'consists of' or 'is composed of'.
[IV] The descriptions of Figures 1 and 2 are sparse; the text mentions energy consumption and efficiency plots but does not clearly state the axes, units, or the exact metrics displayed. Please add appropriate captions and refer to specific curves in the body.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is a self-contained optimization/simulation study, with no fitted input relabeled as a prediction.

full rationale

I walked the paper's derivation chain from the system model to the reported results. The SEE objective (13) is constructed directly from the received-signal model (5)-(6), the worst-case secrecy rate bound (8), and the energy model (10)-(12). No parameter is fitted to a subset of data and then reported as a prediction; the optimized quantities are the UAV trajectory, MA orientation angles, and beamforming vector, all evaluated by simulation against standard baselines. The reformulations in (16)-(18) and (23)-(24) are algebraic manipulations with auxiliary variables and successive convex approximation / Dinkelbach linearizations of the same objective, not independent predictions that could reduce to their inputs. The cited prior results ([4], [13], [14]) supply standard trajectory, rotorcraft-energy, and MA-power models, and they are not authored by the present authors; none is invoked to forbid an alternative in a way that collapses the derivation. The main substantive concern is that Eq. (8) is a questionable worst-case bound: it omits the BS array gain and replaces the jammer gain at Eve with a path-loss-only term, so the surrogate objective may not be a true lower bound on secrecy capacity. That is a modeling/correctness defect of the surrogate objective, not circular reasoning: the reported gains are computed from that surrogate rather than from a fitted parameter later relabeled as a prediction. No circular step meets the evidence bar, so the circularity score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper relies on standard physical-layer and UAV energy models from prior literature, plus several domain assumptions about LoS channels, eavesdropper uncertainty, and MRT at the BS. The only hand-picked free parameters are the MA power consumption coefficients, which are simulation settings, not fitted to data. No new physical entities are introduced.

free parameters (3)

P_base = 2 W
Hand-chosen simulation parameter for MA power consumption model in Eq. (11); affects the energy denominator and thus the reported SEE percentages.
zeta = 0.05 W/rad
Hand-chosen coefficient for the elevation-angle-dependent MA power consumption in Eq. (11); impacts the energy model and the optimization trade-off.
xi = 0.03 W/rad
Hand-chosen coefficient for the azimuth-angle-dependent MA power consumption in Eq. (11); another free parameter in the energy model.

assumptions (6)

domain assumption Aerial-ground links are LoS with no multipath.
Invoked in Section II.A.2 to write the channel vector as a deterministic function of array orientation and distance, which underpins the beamforming and null-steering analysis.
domain assumption The eavesdropper's location is bounded by a disc of radius epsilon around the estimate.
Used in Section II.A to define the uncertainty region and to derive the worst-case secrecy capacity bound in Eq. (7)-(8).
domain assumption The BS employs maximum ratio transmission (MRT) beamforming towards the legitimate user.
Stated in Section III.C; this fixes wB and reduces the optimization to trajectory, MA angles, and the jammer beamforming vector.
ad hoc to paper The optimization always leads to a non-negative objective value, so the [.]^+ operator can be dropped.
Stated in Section III without derivation, citing reference [4]. This is essential for removing the max(0,.) operator and simplifying the problem.
domain assumption The antenna array is rigid and rotates about three axes; individual elements do not move within the array plane.
Section II.A.1 models orientation via rotation matrices while element positions in local coordinates remain fixed, meaning the 'movable-antenna' is actually a rotatable array.
domain assumption MA power consumption is modeled as linear in the angle changes.
Eq. (11) in Section II.B.2; this simple linear model is assumed for the energy consumption of the antenna rotation mechanism.

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Cite this review

Pith. "Pith review of Energy-Efficient Secure Communications via Joint Optimization of UAV Trajectory and Movable-Antenna Array Beamforming." pith.science (2026). https://pith.science/paper/RE4EKRZ5

@misc{pith2026250720489,
  author       = {Pith},
  title        = {Pith review of: Energy-Efficient Secure Communications via Joint Optimization of UAV Trajectory and Movable-Antenna Array Beamforming},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RE4EKRZ5}},
  note         = {Machine review of arXiv:2507.20489}
}

read the original abstract

This paper investigates the potential of unmanned aerial vehicles (UAVs) equipped with movable-antenna (MA) arrays to strengthen security in wireless communication systems. We propose a novel framework that jointly optimizes the UAV trajectory and the reconfigurable beamforming of the MA array to maximize secrecy energy efficiency, while ensuring reliable communication with legitimate users. By exploiting the spatial degrees of freedom enabled by the MA array, the system can form highly directional beams and deep nulls, thereby significantly improving physical layer security. Numerical results demonstrate that the proposed approach achieves superior secrecy energy efficiency, attributed to the enhanced spatial flexibility provided by the movable antenna architecture.

Figures

Figures reproduced from arXiv: 2507.20489 by the authors.

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Forward citations

Cited by 1 Pith paper

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Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [4]

Securing UA V Communications via Joint Trajectory and Power Control,

G. Zhang et al. , “Securing UA V Communications via Joint Trajectory and Power Control,” IEEE Transactions on Wireless Communications , vol. 18, no. 2, pp. 1376–1389, Jan. 2019

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[3] [2]

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S. Hong, C. Pan, H. Ren, K. Wang, and A. Nallanathan, “Arti ﬁcial- Noise-aided Secure MIMO Wireless Communications via Intel ligent Reﬂecting Surface,” IEEE Transactions on Communications , vol. 68, no. 12, pp. 7851–7866, Sep. 2020

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X. Zhou, Q. Wu, S. Y an, F. Shu, and J. Li, “UA V -Enabled Secu re Communications: Joint Trajectory and Transmit Power Optim ization,” IEEE Transactions on V ehicular Technology , vol. 68, no. 4, pp. 4069– 4073, Apr. 2019

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6DMA Enhanced Wireless Network wit h Flexible Antenna Position and Rotation: Opportunities and Challenges,

X. Shao and R. Zhang, “6DMA Enhanced Wireless Network wit h Flexible Antenna Position and Rotation: Opportunities and Challenges,” IEEE Communications Magazine , vol. 63, no. 4, pp. 121–128, May 2025

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W. Liu, X. Zhang, H. Xing, J. Ren, Y . Shen, and S. Cui, “UA V - Enabled Wireless Networks with Movable-Antenna Array: Flexible Be amforming and Trajectory Design,” IEEE Wireless Communications Letters , Mar. 2024

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L.-H. Shen and Y .-H. Chiu, “RIS-Aided Fluid Antenna Arra y-Mounted UA V Networks,” IEEE Wireless Communications Letters , Apr. 2025

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