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REVIEW 4 major objections 5 minor 53 references

Does Movable Antenna Present A Dual-edged Nature? From the Perspective of Physical Layer Security: A Joint Design of Fixed-position Antenna and Movable Antenna

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Hybrid fixed-plus-movable antenna arrays can raise physical-layer secrecy rates by 42% over fixed-only jamming.

desk verdict The FMA co-design concept is new and worth attention, but the MA beamforming and gradient derivations are wrong, so the reported secrecy-rate gains are unsupported as written. read the letter →

arxiv 2507.05784 v1 pith:73DZO55S submitted 2025-07-08 cs.IT math.IT

Kan Yu , Wenxu Wang , Xiaowu Liu , Yujia Zhao , Qixun Zhang , Zhiyong Feng , Dong Li This is my paper · ORCID
classification cs.ITmath.IT
keywords physicallayersecuritymovableantennasecrecyratemaximizationjointFPA-MAdesignartificialnoisebeamformingInternetofVehiclesprojectedgradientascentalternatingoptimization
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

The paper asks whether movable antennas help or hurt physical-layer security, and answers that the two antenna types should not be rivals. It argues that fixed-position arrays, used alone for artificial-noise jamming, leave spatial blind spots that mobile eavesdroppers can exploit, while movable-antenna arrays used alone cannot guarantee a stable link in fast-moving vehicle networks. The proposed FMA co-design splits the job: the fixed array beamforms the confidential signal and the movable array repositions itself to direct jamming noise at eavesdroppers. Jointly optimizing the movable positions and both beamformers, the simulations report secrecy-rate improvements of 42.34% over isolated fixed-antenna AN generation and 9.12% over isolated movable-antenna confidential transmission. A sympathetic reader would take the paper's central truth to be that spatial flexibility and baseline coverage are complementary security resources, not substitutes.

What carries the argument

The object that carries the argument is the FMA array: $N$ fixed antennas at half-wavelength spacing handle the confidential signal, while $N$ movable antennas, each restricted to the interval $[0,L]$ and mutually separated by at least $d_{\min}$, generate artificial noise. The secrecy-rate objective is the sum over $Q$ time slots of $\log_2(1+\mathrm{SINR}_b) - \log_2(1+\mathrm{SINR}_{e^*})$ against colluding eavesdroppers. The movable-antenna steering vector $\mathbf{a}(\mathbf{x}_{\mathrm{MA}}[t],\theta)$ has entries $\exp(j\frac{2\pi}{\lambda} x_n[t]\cos\theta)$, and the position-update gradient is built from diagonal matrices $\mathbf{D}_i$ and $\boldsymbol{\Lambda}_i$ containing sine and cosine terms of those phases. Algorithmically, the FPA beamformer comes from a generalized eigenvalue problem, the MA beamformer is assigned a generalized eigenvector by analogy to the same derivation, and MA positions are updated by a momentum-accelerated projected gradient ascent whose projection enforces the minimum-distance and boundary constraints.

What would settle it

Re-run the paper's four-time-slot scenario replacing the MA beamformer from Eq. (31) with a direct numerical maximizer of the subproblem objective in Eq. (30) under the same power constraint; if the numerical maximizer beats the eigenvector-based update, or if the reported 31.1 bps/Hz result cannot be reproduced with the published update, the central algorithmic claim is refuted.

Watch

Extended reading notes

Core claim

The central discovery is that a co-designed fixed-plus-movable array—fixed elements carrying the confidential beam, movable elements generating adaptive artificial noise—achieves higher average secrecy rate than either technology alone in a high-mobility vehicular setting. The paper formulates the maximization of the time-averaged secrecy rate over MA positions, FPA beamforming, and MA beamforming, and solves it with alternating optimization: closed-form generalized-eigenvector beamformers for both arrays and a momentum-accelerated projected-gradient ascent for MA positions. In the simulated four-slot highway scenario with two colluding eavesdroppers, the FMA co-design reaches the highest initial secrecy rate (31.1 bps/Hz versus 18.0 bps/Hz for the fixed-only AN baseline and 20.4 bps/Hz for the movable-only confidential-signal baseline), which the abstract summarizes as 42.34% and 9.12% improvements over the respective baselines.

Load-bearing premise

The load-bearing premise is that the movable-antenna beamformer given by the generalized eigenvector actually maximizes the secrecy objective, even though that objective is a ratio of two signal-to-noise-plus-interference terms and is not a Rayleigh quotient.

Editorial extensions

If this is right

  • A base station serving vehicles could keep a low-latency confidential link on its fixed array while its movable elements continuously re-aim jamming noise at eavesdroppers, without moving the whole aperture.
  • The reported convergence of the momentum-accelerated position search within tens of iterations (versus roughly 88 for plain projected gradient ascent) suggests MA repositioning can keep pace with millisecond-scale beam reconfiguration in high-mobility links.
  • The beam-pattern results show the movable-array noise can hold interference at the legitimate receiver below $-100$ dB while delivering several dB of jamming gain at each eavesdropper angle, a decoupling the fixed-array-only AN baseline cannot achieve.
  • The alternating-optimization template—closed-form beamforming plus momentum-accelerated position search—extends to other MA-aided secrecy problems where eavesdropper angles are known.

Reading between the lines

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

  • A fair next comparison would be an MA-only jammer (movable antennas generating noise without a fixed confidential array); this would isolate whether the reported gain comes from the hybrid split or simply from having movable jammers.
  • Because the MA beamforming update in Eq. (31) is justified by analogy to the FPA Rayleigh-quotient derivation, checking it against a numerical maximizer of the actual fractional objective in Eq. (30) would settle whether the convergence results reflect the true subproblem optimum.
  • If eavesdropper CSI becomes imperfect, the same framework would likely need robust or statistical position planning; the paper's perfect-CSI setting is the optimistic boundary of the design space.
  • The movable elements could be reused for legitimate beamforming in the absence of eavesdroppers, suggesting a mode-switching protocol that this paper does not develop.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a hybrid fixed-position antenna (FPA) and movable-antenna (MA) array for physical-layer security in high-mobility IoV scenarios. The FPA array transmits the confidential signal while the MA array generates artificial noise (AN); the authors jointly optimize MA positions, the FPA beamformer, and the MA beamformer by alternating optimization, with a Nesterov momentum-based projected gradient ascent (NMPGA) for the position subproblem. The central claimed result is that this FMA co-design achieves 42.34% and 9.12% secrecy-rate gains over FPA-only AN generation and MA-only confidential-information baselines, respectively.

Significance. If the proposed method were correct, the FMA co-design would be a timely and practically motivated contribution to MA-assisted physical-layer security, combining the coverage stability of fixed antennas with the spatial flexibility of movable antennas. The paper is not circular: the secrecy rates are computed from the stated channel model, and no constants are fitted to match a target. The simulation setup is described in detail, including Table 2 parameters and pseudocode for both algorithms, which is a strength. However, the algorithmic derivations contain load-bearing errors: the MA beamforming update is not a valid solution to the stated subproblem, and the NMPGA gradient does not match the objective's derivative. These errors directly undermine the reported performance gains and the convergence claims, so the central contribution is not established as written.

major comments (4)
  1. [§4.3, Eqs. (30)–(31)] The proposed MA beamforming update does not solve subproblem (P4). Setting w_MA = sqrt(P_MA) z with ||z||=1 transforms Eq. (30) into F(z) = [1 + G_b/(sigma^2 + P_MA |a_b^H z|^2)] / [1 + G_e/(sigma^2 + P_MA z^H K_e z)], which is not a Rayleigh quotient and cannot be maximized by the generalized eigenvector of the matrix pair in Eq. (31). In particular, the matrices Q_b = I + G_b(sigma^2 I + P_MA K_b)^{-1} and Q_e = I + G_e(sigma^2 I + P_MA K_e*)^{-1} yield z^H Q_b z = 1 + G_b/sigma^2 - G_b P_MA |a_b^H z|^2/[sigma^2(sigma^2 + P_MA ||a_b||^2)], which is not the term 1 + G_b/(sigma^2 + P_MA |a_b^H z|^2) appearing in the objective; the analogous mismatch holds for Q_e. Since Algorithm 2 updates w_MA with Eq. (31) and the reported secrecy-rate gains in Figs. 5–6 and in the abstract are attributed to this AN beamformer, the central quantitative claim is not supported by the described algorithm.
  2. [§4.2, Eqs. (22) and (28)] The NMPGA gradient is not the derivative of the objective in Eq. (19). For the Bob term, d/dgamma0 log2(1 + G_b/(gamma0+sigma^2)) = -G_b/[ln2 (gamma0+sigma^2)(gamma0+sigma^2+G_b)], whereas Eq. (22) uses denominator (gamma0+sigma^2)(1+G_b), which is numerically different and dimensionally inconsistent. The Eve term has the same problem. Eq. (28) additionally reverses the sign of the terms involving D0 and Lambda0 relative to Eq. (27), and its denominator (gamma0+sigma^2)(1+1/G_b) does not match either expression. Consequently, the position update in Eqs. (20a)–(20d) is not a valid gradient ascent for (P3), so the convergence and speed claims of NMPGA in Fig. 4 are not established.
  3. [§3.4, Eqs. (9)–(10)] The reduction from (P1) to (P1*) by omitting the [.]^+ operator is not generally equivalence-preserving. Maximizing sum_t [R_bob[t] - R_eve[t]]^+ differs from maximizing sum_t (R_bob[t] - R_eve[t]) whenever any per-slot difference is negative, because the latter penalizes negative terms instead of clipping them to zero. The cited Lemma 1 in [37] may apply to a different setting; no argument specific to this FPA-MA problem is provided. Since Algorithm 2 optimizes (P1*) while the evaluation metric is the average of the clipped per-slot rates, the connection between the solved problem and the reported average secrecy rate is missing.
  4. [§4.4, Convergence] The monotone-convergence argument for Algorithm 2 is invalid as written. It assumes that each AO subproblem increases the objective, but the MA beamforming update from Eq. (31) is not a maximizer of (P4) and may decrease the secrecy rate, and the NMPGA gradient from Eqs. (22)/(28) is not the correct ascent direction. Without valid monotone steps, the boundedness-plus-monotone-convergence argument does not apply, and the termination criteria in Algorithm 2 do not guarantee convergence to a local optimum.
minor comments (5)
  1. [Algorithm 2, line 5] Line 5 of Algorithm 2 says 'Update w_i_MA[t] by Eq. (30)', but Eq. (30) is the objective of subproblem (P4); the update formula is Eq. (31).
  2. [§4.2, Eq. (23)] The sentence following Eq. (23) is incomplete: 'where ∈ [0, 1, 2, . . . , M]' is missing the variable it quantifies; it should be 'where i ∈ {0,1,...,M}'.
  3. [§5, Fig. 7] Fig. 7 compares the FMA co-design with N=5 antennas to an MA-Only baseline with 10 antennas, while the system model and Table 2 specify N=5 for all schemes; the baseline antenna count and power allocation should be clarified.
  4. [Abstract and Introduction] The text contains typographical and grammatical errors, including 'the solution employs' (lowercase after a period), 'more higher spatial degree of freedom', 'FP A-MA', and 'FPA-MA co-designfor', which should be corrected.
  5. [§5.3] The text alternates between 'PGA algorithm' and 'the proposed PGA algorithm' when describing the baseline; it should be made explicit that the baseline uses the PGA method from [10, 48, 49], not the proposed NMPGA.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the derivation is self-contained and the reported gains are simulation outputs, not fitted targets.

full rationale

The paper's derivation chain is not circular. The secrecy-rate objective (P1) is constructed from the channel model in Eqs. (5)-(8), and the reported gains, including the 42.34% and 9.12% improvements, are computed by running the proposed AO/NMPGA algorithm rather than by fitting constants to match benchmark outputs. The FPA and MA beamforming updates are obtained from standard Rayleigh-quotient/eigenvector results, and the MA position update uses gradients of the same objective; none of these steps presupposes the final secrecy-rate values. The only self-citation is the authors' prior work [15], which appears in the related-work discussion as background and is not load-bearing for the new derivation. A skeptical reader's concern that Eq. (31) may not actually maximize the Eq. (30) objective would be a correctness or derivation error, not circularity: a wrong or mismatched update would not make the reported result equivalent to its inputs by construction. The paper is therefore self-contained against external benchmarks, and no circular step is identified.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a set of idealizations (perfect CSI, LoS-only channels, stationary MA within time slots) and on two unproved mathematical steps: the removal of the [·]⁺ operator and the generalized-eigenvector solution for the MA beamforming subproblem. The algorithmic free parameters are left unspecified, and the simulations appear to use a different channel normalization than the model states.

free parameters (4)
  • NMPGA step-size schedule δ = unspecified
    Algorithm 1 adapts δ 'slightly' up or down based on secrecy-rate trends, but no concrete schedule or initial value is given; the reported convergence speed and final secrecy rate depend on this tuning.
  • NMPGA momentum coefficient ζ = unspecified
    Momentum coefficient is adapted heuristically in Algorithm 1; no value is stated, and the convergence trajectories in Fig. 4 depend on it.
  • Sliding-window trend threshold = unspecified
    Algorithm 1 uses a 'trend by slide windows' to decide between decreasing step size and decaying velocity; the window length and threshold are not defined.
  • Effective channel gain in simulations = implicitly 1 (path-loss factor omitted)
    Reported secrecy rates near 31 bps/Hz require unity channel gain, whereas Eq. (1) with Table 2 parameters gives κ0/d^α ≈ 1.6×10^-9 at d=100m; the simulator appears to drop the path-loss scaling.
assumptions (5)
  • domain assumption Perfect CSI of both Bob and all colluding Eves is available at the BS for all time slots.
    Stated in Section 3.4 and acknowledged as a limitation in Section 6; the MA AN beamforming relies on knowing Eve angles exactly.
  • domain assumption Line-of-sight channel with steering vectors depending only on angle, with κ0/d^α path loss.
    Section 3.2, Eqs. (1)-(3); ignores multipath, blockage, and antenna coupling beyond the minimum-distance constraint.
  • domain assumption MA positions are stationary within each time slot and CSI is constant over Ttotal/Q.
    Section 3.1; the time discretization with Q=4 slots in the simulations is a simplification of continuous vehicle motion.
  • ad hoc to paper Removing the [x]⁺ operator from the objective does not change the optimal solution.
    Section 3.4, after Eq. (9): the paper asserts this citing Lemma 1 of [37], but provides no proof for this problem; at unconstrained optima with negative R_bob - R_eve, the ceiling operator would matter.
  • ad hoc to paper The MA beamforming subproblem (P4) is solved by the generalized eigenvector of the matrix product in §4.3.
    The claimed Rayleigh-quotient reduction is not valid for the objective in Eq. (30), so this is an unproved premise of the algorithm.

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Cite this review

Pith. "Pith review of Does Movable Antenna Present A Dual-edged Nature? From the Perspective of Physical Layer Security: A Joint Design of Fixed-position Antenna and Movable Antenna." pith.science (2026). https://pith.science/paper/73DZO55S

@misc{pith2026250705784,
  author       = {Pith},
  title        = {Pith review of: Does Movable Antenna Present A Dual-edged Nature? From the Perspective of Physical Layer Security: A Joint Design of Fixed-position Antenna and Movable Antenna},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/73DZO55S}},
  note         = {Machine review of arXiv:2507.05784}
}
read the original abstract

In conventional artificial noise (AN)-aided physical-layer security systems, fixed-position antenna (FPA) arrays exhibit inherent vulnerability to coverage gaps due to their static spatial configuration. Adversarial eavesdroppers can strategically exploit their mobility to infiltrate these spatial nulls of AN radiation patterns, thereby evading interference suppression and successfully intercepting the confidential communication. To overcome this limitation, in this paper, we investigate a hybrid antenna deployment framework integrating FPA arrays and movable antenna (MA) arrays (denoted by FMA co-design) to address the security performance in dynamic wireless environments, based on the fact that MA arrays enable channel reconfiguration through localized antenna repositioning, achieving more higher spatial degree of freedom (DoF). Enabled by FMA co-design framework, FPA arrays ensure baseline connectivity for legitimate links while MA arrays function as dynamic security enhancers, replacing conventional static AN generation. Furthermore, we formulate a non-convex optimization problem of the secrecy rate maximization through jointly optimizing MA positioning, FPA beamforming, and MA beamforming under practical constraints. the solution employs a dual-algorithm approach: Nesterov momentum-based projected gradient ascent (NMPGA) accelerates convergence in continuous position optimization, while alternating optimization (AO) handles coupled beamforming design. Experimental evaluations demonstrate that the proposed FMA co-design framework achieves significant secrecy performance gains over individual optimization benchmarks, yielding 42.34% and 9.12% improvements in secrecy rate compared to isolated FPA for AN generation and MA for confidential information baselines, respectively.

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.