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REVIEW 2 major objections 5 minor 21 references

FAS for Secure and Covert Communications

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Fluid antennas can raise the secrecy rate of a covert wireless link by jointly optimizing beamforming and antenna positions, outperforming fixed-position arrays in simulation.

desk verdict A promising FAS secrecy/covertness formulation is undermined by a wrong quadratic form in the position subproblem; the reported gains are not yet supported, but the idea is sound and fixable. read the letter →

arxiv 2411.09235 v1 pith:3L2S6V25 submitted 2024-11-14 eess.SP

Junteng Yao , Liangxiao Xin , Tuo Wu , Ming Jin , Kai-Kit Wong , Chau Yuen , Hyundong Shin This is my paper · ORCID
classification eess.SP
keywords fluidantennasystemcovertcommunicationphysicallayersecuritybeamformingalternatingoptimizationmajorization-minimizationsecrecyrateposition
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 proposes a fluid antenna system (FAS) transmitter whose multiple movable antennas are jointly optimized with the transmit beamforming to maximize the secrecy rate against an eavesdropper while keeping the transmission undetectable by a warden. The central claim is that adjusting antenna positions adds a spatial degree of freedom that significantly improves secure and covert communication performance compared to fixed-position antennas (FPA). The paper develops an alternating optimization algorithm that alternates between a penalty-based beamforming update and a majorization-minimization position update, and simulations show higher secrecy rates than FPA, random-position, and exhaustive-search benchmarks under equal power and covertness constraints. If correct, this establishes FAS as a practical physical-layer technique for communication that must remain both secret and hidden.

What carries the argument

The central object is the transmit field response vector $f_k(t_n) = [e^{jrac{2\pi}{\lambda}\rho_{k,1}(t_n)}, \ldots]^T$ with $\rho_{k,l}(t_n) = x_n\sin\theta^t_{k,l}\cos\phi^t_{k,l} + y_n\cos\theta^t_{k,l}$, which makes each antenna position affect the channel only through path phases. On this basis the algorithm alternates: a penalty-based semidefinite program relaxes the rank-one beamforming constraint, and an MM-based position update uses first-order and second-order Taylor expansions to build concave lower bounds for the legitimate link and convex upper bounds for the eavesdropper and warden links, ensuring each subproblem is convex and solvable by CVX.

What would settle it

Measure the actual channel response of a physical fluid antenna as a function of position and compare the achieved secrecy rate under the optimized positions with the phase-only model's prediction; if the realized channels differ enough to break the assumed phase-only relationship, the algorithm's performance advantage over FPA would not reproduce.

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Extended reading notes

Core claim

Under a planar far-field response model in which moving a fluid antenna changes only the phase of each multipath component, the paper shows that jointly designing the transmit beamforming vector and the fluid antennas' positions can maximize the secrecy rate subject to a covertness constraint expressed as a bound on the Kullback-Leibler divergence at the warden. The optimization problem is non-convex, so the paper decomposes it into subproblems: a penalty-based rank-one approximation handles beamforming, while majorization-minimization constructs concave lower bounds and convex upper bounds for the channel terms as functions of antenna position. Simulation results demonstrate that the proposed scheme outperforms FPA, RPA, and EAS benchmarks, with the gain growing in maximum transmit power and tolerated detection coefficient.

Load-bearing premise

The design assumes that moving a fluid antenna changes only the phase of each multipath component, leaving amplitudes and angles unchanged; if real antennas also change amplitude, mutual coupling, or near-field behavior, the secrecy and covertness gains shown in simulation may shrink.

Editorial extensions

If this is right

  • For a fixed covertness requirement, adding movable antennas at the transmitter yields a higher secrecy rate than an equal-power fixed-position array, because position optimization creates channel diversity that can be steered against the eavesdropper.
  • The secrecy-rate gain of FAS over FPA grows with the maximum transmit power and with the tolerated detection coefficient, since both factors relax the constraints that position optimization exploits.
  • The proposed algorithm provides a concrete, converging design procedure: each iteration solves two convex programs, so system designers can compute locally optimal beamforming vectors and antenna positions without global search.
  • The covertness constraint is handled analytically through Pinsker's inequality and the Lambert W function, giving a closed-form upper bound on the warden's received power that any feasible solution must satisfy.

Reading between the lines

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

  • A natural testable extension is to replace the simulated channel model with measured or full-wave-computed channel responses from a physical fluid antenna prototype; the algorithm's structure would remain unchanged, but the phase-only assumption could be validated or refuted.
  • Because the covertness guarantee relies on a lower bound from Pinsker's inequality, a tighter bound or an exact detection-error-probability expression could change the feasible set and the optimal positions, so the design's margin under exact detection is open.
  • The same alternating optimization framework could apply to other reconfigurable geometries, such as movable antenna arrays at the receiver or intelligent reflecting surfaces, wherever channel phase is a tunable function of position.
  • The paper uses a local search, so the reported gains may depend on initialization; testing random restarts or a coarse grid of starting positions would reveal the robustness of the advantage over FPA.
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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

2 major / 5 minor

Summary. This letter studies a fluid-antenna-system (FAS)-aided transmitter that serves a legitimate receiver while an eavesdropper overhears and a warden tries to detect the transmission. The authors formulate a secrecy-rate maximization problem subject to a covertness constraint derived from Pinsker's inequality, a transmit power constraint, antenna minimum-distance constraints, and a rank-one beamforming constraint. They propose an alternating optimization algorithm that uses a penalty-based convex update for the beamforming matrix and a majorization-minimization (MM) update for the antenna positions. Simulation results in Figs. 1 and 2 compare the proposed scheme with fixed-position-antenna (FPA), random-position-antenna (RPA), and exhaustive-antenna-selection (EAS) benchmarks and report significant gains from the fluid antenna system.

Significance. If the algebraic derivations were correct, the paper would provide a reasonable first extension of FAS to the joint secure-and-covert setting, with a transparent coordinate-descent structure and comparisons against external benchmarks rather than fitted data. The MM and penalty elements are standard, and the problem formulation is sensible. However, the central identity used for the position subproblem in Section III-B is incorrect as written: the matrix Φ_k used throughout the MM bounds is not the matrix that appears in Tr(H_kV) under the paper's own channel model. This error invalidates the feasibility guarantees of the surrogate constraints (26)-(28) and therefore the simulation evidence for the claimed FAS gains. The error is localized and appears fixable by replacing Φ_k with the correct Gram-type matrix, but the numerical results would need to be regenerated before the central claim can be accepted.

major comments (2)
  1. [III-B, Eq. (18)] Eq. (18) sets Φ_k=Σ_k^HΣ_k and expands Tr(H_kV) as α_k+β_k(t_n)+2Re{f_k^H(t_n)Ω_k}. With the channel h_k^H=1^HΣ_kF_k(¯t) from Eq. (3), however, Tr(H_kV)=||1^HΣ_kF_k(¯t)v||^2=v^H F_k^H(¯t)Σ_k^H 1 1^H Σ_k F_k(¯t)v. The matrix that must appear in the expansion is therefore Φ_k=Σ_k^H11^HΣ_k, not Σ_k^HΣ_k. These two choices agree only when L_r^k=1, whereas Section IV explicitly sets L_r^k=L_t^k=4. Consequently, α_k, β_k(t_n), Ω_k, Ψ_k, and the bounds in (19)-(25) are not bounds on the actual Tr(H_kV), and the surrogate constraints (26)-(28) do not enforce the covertness constraint (9) or the auxiliary constraints (11b)-(11c). Solving the position subproblem (30) as written can produce antenna positions that violate Problem (10). This is a load-bearing error for the claimed FAS gains in Figs. 1 and 2; the definition of Φ_k should be corrected and the simulations rerun.
  2. [Appendix A, Eq. (33)] The partial derivative with respect to y_t^n is printed with a factor cos φ^t_{k,l}; from the definition ρ_{k,l}(t_n)=x_t^n sinθ^t_{k,l} cosφ^t_{k,l}+y_t^n cosθ^t_{k,l} in Section II, the y-derivative of the phase is proportional to cosθ^t_{k,l}, not cosφ^t_{k,l}. Since ∇β_k(t_n) is used in both the lower bound (20) and the upper bound (24), the printed gradient would invalidate the MM inequalities even after the Φ_k correction. Please correct the formula and verify the signs and coefficients in (32) and (33).
minor comments (5)
  1. [III-B, Eq. (18)] In the middle term of the right-hand side of Eq. (18), the subscript is printed as β_b(t_n); it should be β_k(t_n) for consistency with the surrounding notation.
  2. [III-B] The notation v(n) and v_n is used interchangeably for the elements of the beamforming vector; please unify the notation.
  3. [III-B, Eq. (29)] Eq. (29) is dimensionally consistent as printed: the denominator ||t_n^m−t_v|| makes the left-hand side a scalar distance, which is then compared with D. No correction is needed here, but the sentence could clarify that this is the standard first-order lower bound of the convex norm ||t_n−t_v||.
  4. [IV] The y-axis labels in Figs. 1 and 2 are given as 'Secrecy rate' without units; bits/s/Hz would be the conventional unit for the secrecy rate.
  5. [III] The paper states only the convergence accuracy 10^{-4} and does not describe the stopping criterion for the AO loop or the penalty update rule. A brief statement on the convergence criterion would improve reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the FAS secure/covert gains are supported by an externally benchmarked simulation, with only minor background self-citations.

full rationale

The paper's derivation chain starts from the channel model in Eqs. (1)-(3), the secrecy-rate objective (10), the relaxed problem (11), and an AO decomposition into beamforming (16) and position (30) subproblems. The MM inequality used to bound Tr(H_k V) in Eq. (22) is explicitly attributed to [19], an external reference, and the planar far-field response model is likewise cited to [19]; neither is a self-citation. The authors' own prior works [12], [16], [18] appear only as background examples of FAS applications in the introduction and play no load-bearing role in deriving the algorithm or in interpreting the simulations. The central claim that FAS outperforms FPA is tested against FPA, RPA, and EAS benchmarks in Figs. 1-2, with channel matrices drawn from a randomized path-response model rather than fitted to the algorithm's outputs; there is no fitted parameter that is later renamed as a prediction. No uniqueness theorem or ansatz is imported from the authors' prior work to force the chosen formulation. The algebraic discrepancy in Eq. (18) noted by the skeptic (Phi_k = Sigma_k^H Sigma_k rather than Sigma_k^H 1 1^H Sigma_k for L_r > 1) is a correctness/validity concern about whether the surrogate constraints (26)-(28) bound the true Tr(H_k V), but it is not a circularity: it is not an equivalence by construction nor a fitted-input-called-prediction. Accordingly, the circularity score is low and reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim does not rely on fitted physical quantities; the algorithm's penalty factor eta is a hand-chosen hyperparameter. The main load-bearing assumptions are the far-field phase-only channel model and the MM inequality from prior work. No new physical entities are introduced.

free parameters (1)
  • Penalty factor eta = initial 1, multiplied by 1.5 per iteration
    Hand-chosen in Section IV; controls the rank-one enforcement in the beamforming subproblem. No sensitivity analysis is provided, and the final result may depend on this schedule.
assumptions (4)
  • domain assumption Planar far-field response model: antenna position changes only the phase of each path, not AoA/AoD or amplitude
    Assumed in Section II to express the field response vectors in (1); the entire FAS position optimization is built on this.
  • standard math Pinsker's inequality lower bound on DEP
    Used in Section II to replace the intractable DEP with the KL divergence constraint (8), a standard step in covert communications.
  • standard math MM majorization inequality (22) for quadratic forms
    Cited from reference [19] and used in Section III-B to construct the upper bound on Tr(H_k V) for the position optimization.
  • domain assumption Channel path responses follow Sigma_k[l,l] ~ CN(0, g0 d_k^{-alpha}/L)
    Simulation channel model in Section IV; no real channel measurements or hardware validation are provided.

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Pith. "Pith review of FAS for Secure and Covert Communications." pith.science (2026). https://pith.science/paper/3L2S6V25

@misc{pith2026241109235,
  author       = {Pith},
  title        = {Pith review of: FAS for Secure and Covert Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3L2S6V25}},
  note         = {Machine review of arXiv:2411.09235}
}
read the original abstract

This letter considers a fluid antenna system (FAS)-aided secure and covert communication system, where the transmitter adjusts multiple fluid antennas' positions to achieve secure and covert transmission under the threat of an eavesdropper and the detection of a warden. This letter aims to maximize the secrecy rate while satisfying the covertness constraint. Unfortunately, the optimization problem is non-convex due to the coupled variables. To tackle this, we propose an alternating optimization (AO) algorithm to alternatively optimize the optimization variables in an iterative manner. In particular, we use a penalty-based method and the majorization-minimization (MM) algorithm to optimize the transmit beamforming and fluid antennas' positions, respectively. Simulation results show that FAS can significantly improve the performance of secrecy and covertness compared to the fixed-position antenna (FPA)-based schemes.

Figures

Figures reproduced from arXiv: 2411.09235 by the authors.

Figure 1
Figure 1. The maximum transmit power of Alice Pmax versus the secrecy rate. 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Secrecy rate Proposed EAS RPA FPA [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The tolerated detection coefficient ǫ versus the secrecy rate. proposed scheme consistently demonstrates superior perfor￾mance compared to the benchmark schemes. As ǫ increases, the secrecy rate also rises for all the schemes. This is because a higher ǫ relaxes the constraint in (9), allowing more spatial resource to be allocated to enhance the secrecy rate. This trend underscores the trade-off between the desired l… view at source ↗

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