Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization

Ahmad Bazzi; Chadi Assi; Lin Zhang; Ning Wei; Ran Yang; Wanting Lyu; Yue Xiu; Zheng Dong

REVIEW 2 major objections 5 minor 19 references

Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization

T0 review · 2 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper shows that moving antennas — not just steering beams — lets a dual radar-communication base station send more covert data while preserving radar quality and hiding from the warden.

desk verdict Adds movable antennas to covert DFRC with a standard optimization stack; the SCA feasibility bound is under-proven and needs fixing before the algorithm's guarantees can be trusted. read the letter →

arxiv 2510.09949 v2 pith:Q4YVP5OV submitted 2025-10-11 eess.SP

Ran Yang , Zheng Dong , Lin Zhang , Wanting Lyu , Yue Xiu , Ning Wei , Ahmad Bazzi , Chadi Assi This is my paper · ORCID

classification eess.SP

keywords movableantennasdual-functionalradar-communicationcovertcommunicationbeamformingoptimizationantennapositionsemidefiniterelaxationblockcoordinatedescentphysicallayersecurity

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 takes up a security question inside integrated sensing and communication: when the radar target is also a warden trying to detect the base station's covert data traffic, can physically moving the antennas help? Its answer is yes. The authors formulate a joint design of beamformers, receive filter, and continuous antenna positions that maximizes covert sum rate under a radar signal-to-noise floor and a covertness constraint expressed as a bound on the warden's likelihood-ratio statistic. They solve it with a block-coordinate descent algorithm that alternates closed-form updates with semidefinite relaxation, projected gradient descent, and successive convex approximation, and their simulations show the movable-antenna design consistently out-rates fixed-position arrays and discrete antenna-selection baselines. The upshot is that antenna movement is a usable degree of freedom for hiding communications, not just for array gain.

What carries the argument

The load-bearing objects are the field-response matrix G_k(t) — whose entries e^{j(2π/λ)t_n cosψ} convert antenna positions into channel phases — and the covertness constraint (16f), η1/η0 ≤ κ, which via Pinsker's inequality turns Willie's minimum detection error probability into a simple power-ratio bound. Around these, the algorithm rotates: closed-form updates for ρ_k and υ_k, SDR for beamforming with the rank-one construction (20) that preserves feasibility and optimality, and PGD-with-SCA surrogates for the position variables t and r. The radar SNR constraint (16b) and the covertness constraint (16f) are where antenna movement does its work, because moving antennas changes both the user

What would settle it

Optimize the design for a nominal warden angle φ, then evaluate the actual radar SNR and warden's KL divergence at φ+3° (a small mismatch); if the covertness constraint η1/η0 ≤ κ fails at the true warden location while a fixed-position beamformer would still satisfy it, the perfect-knowledge assumption is exposed as the load-bearing premise.

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Extended reading notes

Core claim

The paper's central claim is that a dual-functional radar-communication base station with N movable transmit and receive antennas can maximize its covert sum rate by jointly optimizing the transmit beamforming matrix, the receive filter, and the continuous one-dimensional positions of the antennas, while keeping the radar signal-to-noise ratio above a threshold Γ and the warden's detection error probability near chance. Antenna positions enter through the field-response matrices G_k(t) and steering vectors a_t(φ,t), a_r(φ,r), so the optimizer gains spatial degrees of freedom that fixed λ/2-spaced arrays do not have. The covertness requirement is reduced, via Pinsker's inequality, to the powe

Load-bearing premise

The design assumes the warden/target is quasi-static and its angle φ and reflection amplitude |α| are known exactly from a prior tracking stage, so the steering vectors used in the radar and covertness constraints are exact; if the angle estimate is off, the promised radar SNR and covertness are not guaranteed.

Editorial extensions

If this is right

If the central claim holds, a movable-antenna DFRC base station can deliver higher covert sum rates than fixed-position arrays at the same transmit power, radar SNR threshold, and covertness level.
The performance gap over fixed arrays widens as the radar SNR requirement Γ grows, suggesting antenna movement is most valuable when sensing constraints are tight.
The algorithm's mostly closed-form updates and empirical convergence in under eight iterations make the joint design computationally feasible for moderate antenna counts.
Because the covertness guarantee is expressed as the ratio η1/η0 ≤ κ, the same constraint machinery can be reused for other warden models or other system parameterizations without re-deriving the detection analysis.
The dedicated radar waveform doubles as the cover signal, so the design naturally balances sensing and hiding; the reported rate loss relative to an unconstrained upper bound is moderate.

Reading between the lines

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

The covertness guarantee is built on Pinsker's inequality, a lower bound on the warden's detection error probability; a direct Monte Carlo check of the achieved DEP on the optimized η0 and η1 would tell whether the promised ε is conservative or optimistic.
The assumption that the target's angle φ and reflection amplitude |α| are exactly known from prior tracking is the fragile part; a robust formulation that optimizes against an angular uncertainty interval would be the natural next step, and the trade-off between robustness and covert rate is left open.
The position-dependent field response used here is a general mechanism: the same optimization machinery could be applied to secrecy-rate maximization or anti-jamming problems, where antenna positions are not yet standard decision variables.
The SDR and BCD steps only guarantee a local optimum; a small-scale exhaustive search over positions for N=2 or N=3 could quantify the gap to the global optimum and show whether the reported gains are conservative or optimistic.

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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

This paper combines movable antennas with covert dual-functional radar-communication, which is a new system model. The solution machinery is standard from existing work: Lagrangian dual transform, BCD, SDR, PGD, and SCA. Credit where due: the problem is well posed, the rank-one recovery proof in Appendix A is a clean Cauchy-Schwarz argument and appears correct, and the gradient derivation in Appendix B is explicit and checkable. Simulations show a consistent rate gain over fixed-position antennas.

The main soft spot is real. The SCA surrogate for the radar SNR constraint uses a quadratic lower bound of the form SNR0(t) >= SNR0(t_l) + grad^T (t - t_l) - (delta0/2)||t - t_l||^2, with delta0 supposedly chosen so that delta0 I >= Hessian(SNR0). For that quadratic to be a uniform lower bound, you need the Hessian's most negative eigenvalue to be at least -delta0, not just its largest eigenvalue bounded above. Since the steering-vector quadratic form can have strongly negative Hessian eigenvalues, the surrogate can be feasible while the true constraint is violated. The construction of delta0 and delta1 is outsourced to the authors' own unreleased preprint [19] without derivation or flagging. That is a load-bearing correctness issue, independent of the simulation results.

Other issues are smaller. The problem in (19) is not a standard SDP; the objective is concave in R, making it a convex problem with LMI constraints, and the label should match. The simulations lack error bars, statistical robustness checks, and released code. The system model assumes phi and |alpha| are exactly known from a prior tracking stage; no sensitivity analysis is given for errors in those parameters, which matter because the covertness constraint depends on the steering direction.

These are all addressable. The paper deserves a serious referee, but the referee should require a correct statement of the curvature bound (or a derivation) and at least a basic sensitivity analysis before acceptance. It's a reasonable incremental contribution for readers working on MA-aided ISAC or covert communications, not a breakthrough.

Referee Report

2 major / 5 minor

Summary. This paper studies a movable-antenna dual-functional radar-communication (DFRC) system with covert users. The BS jointly optimizes transmit beamforming vectors, the radar covariance matrix, the receive filter, and the transceiver antenna positions to maximize the covert sum rate under a radar SNR constraint and a low-probability-of-detection (covertness) constraint. The authors reformulate the problem with Lagrangian and quadratic transformations and solve it by block coordinate descent: closed-form updates for auxiliary variables, semidefinite relaxation with a rank-one recovery step for beamforming, projected gradient descent with successive convex approximation for antenna positions, and an eigenvector update for the receive filter. Simulations compare the proposed method with an upper-bound scheme, fixed-position antennas, and greedy antenna selection.

Significance. The problem is timely and the proposed decomposition is plausible: combining continuous antenna-position optimization with covert DFRC is a natural extension of the movable-antenna literature. The main technical strength is the rank-one recovery argument in Appendix A, which shows that the SDR relaxation can be made tight without changing the objective value. The Lagrangian/quadratic transformations and the SDR formulation in Section III-B are otherwise sound. The central weakness is the SCA step for antenna positions: the curvature bound in Eq. (23) is stated in the wrong direction and is outsourced to an overlapping-author preprint, so the feasibility of Algorithm 1 is not currently established. If this is corrected and the practical sensitivity to target parameters is addressed, the paper would make a solid contribution.

major comments (2)

[§III-C, Eqs. (23) and (25c)] The quadratic lower bound in Eq. (23) is not implied by the stated condition 'δ0 I_N ⪰ ∇²SNR0(t)'. For the bound SNR0(t) ≥ SNR0(t_l)+∇SNR0(t_l)^T(t−t_l) − (δ0/2)||t−t_l||² to hold uniformly, one needs ∇²SNR0(t) ⪰ −δ0 I_N, i.e., a bound on the negative curvature. The stated inequality only upper-bounds the largest eigenvalue. This matters because SNR0(t) ∝ a_t(φ,t)^H R0 a_t(φ,t) is a sum of sinusoids; e.g., for N=2 the Hessian can have eigenvalues 0 and −4|R0(1,2)|(2π/λ cosφ)^2 cos(·), so the negative eigenvalue is active. If δ0 is chosen only to satisfy δ0 I_N ⪰ ∇²SNR0(t), then (25c) can be feasible while the original radar constraint (16b) is violated. The construction of δ0 is deferred to [19], an overlapping-author preprint; it must be derived in the paper or the bound must be reformulated. The same issue applies to the analogous r-update in §III-D.
[§II-B and §IV] Constraints (16b) and (16f) depend on the target angle φ and reflection amplitude |α| through a_t(φ,t). The paper assumes these are exactly known from a prior tracking stage. If φ is mismatched, the actual radar SNR and warden detection probability can differ from the values used in the optimization, so the claims of radar and covertness guarantees are ideal-case. The paper gives no sensitivity analysis or robust formulation. I recommend adding a numerical study with mismatched φ/|α| (e.g., a few degrees of angle error) and, if robust operation is intended, a robust reformulation; at minimum the ideal-case nature of the guarantees should be stated explicitly.

minor comments (5)

[§III-C, Eq. (22)] The notation 'v_k' in Eq. (22) is not defined; it should be the auxiliary variable υ_k introduced in Eq. (17).
[General] Typos and formatting: 'INTRODUTION', 'matirx', 'decesions', 'covergence', 'Apendix', and 'exist conditions' in Algorithm 1 should be corrected.
[§IV] No Monte Carlo details are given. Specify the number of channel realizations over which the curves are averaged and provide error bars or standard deviations.
[Algorithm 1] Convergence of the BCD/PGD-SCA loops is not proven; Fig. 2(a) only shows monotonic increase in one scenario. The authors should state precisely what convergence guarantee, if any, the iterates enjoy.
[§III-B and Appendix A] The paper calls (19) an SDP after dropping the rank constraints, but the objective is concave rather than linear; the problem is convex and CVX-solvable, but the label is imprecise. In addition, the rank-one recovery (20) assumes h_k^H \tilde{R}_k h_k > 0; the zero-rate corner case should be mentioned.

Circularity Check

1 steps flagged · score 4.0 of 10

SCA feasibility constants δ0/δ1 are outsourced to the authors' own unreleased preprint [19], making a load-bearing step of Algorithm 1 depend on self-citation; no other circular reduction found.

self citation load bearing [Section III-C, equations (23)-(25) and reference [19]]
"Note that the positive real numbers δ0 and δ1 are selected to satisfy δ0IN ⪰ ∇²SNR0(t) and δ1IN ⪰ ∇²G(t), with ∇²SNR0(t) and ∇²G(t) being the Hessian matrices, respectively. Please refer to the appendix in [19] for the construction of δ0 and δ1."

The SCA step replaces the radar SNR constraint (16b) with the surrogate (25c), which is only guaranteed feasible if SNR0(t) is globally lower-bounded by the quadratic in (23). That lower bound requires δ0 to dominate the negative curvature of SNR0(t); the paper supplies no construction, only the condition δ0IN ⪰ ∇²SNR0(t), and defers the actual construction to [19], an unreleased preprint by overlapping authors. Algorithm 1's feasibility and the central claim of a valid MA-enhanced covert design therefore rest on this self-citation. Since [19] is not machine-checked or independently derived here, the proof step is imported rather than established.

full rationale

I walked the derivation chain. The Lagrangian dual transformation (17), quadratic transformation, SDR relaxation (19), rank-one reconstruction (20) with Appendix A proof, and gradient derivation in Appendix B are all derived in-paper from standard external results; no fitted parameter is renamed as a prediction, no constant is fit to data, and no external empirical benchmark is used. The only load-bearing step that is not self-contained is the SCA bound in (23)-(24): the constants δ0 and δ1 that make the surrogate constraints valid are not constructed in this paper but are referred to the authors' own unpublished arXiv preprint [19]. Moreover the stated condition 'δ0IN ⪰ ∇²SNR0(t)' is not by itself the standard majorization condition for the quadratic lower bound (which needs ∇²SNR0(t) ⪰ -δ0 I), so the deferred construction is essential to the algorithm's feasibility guarantee. This is a self-citation load-bearing step, but it does not make the whole derivation equivalent to its inputs; the beamforming and antenna-position optimization otherwise has independent content. Hence score 4, not higher.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The derivations rest on standard far-field MA channel modeling, Gaussian signaling, and Bayesian detection theory. The only ad hoc element is the SCA Hessian bound construction, borrowed from the authors' own prior arXiv work. No new physical entities are introduced; all free parameters are algorithm or simulation settings, not fitted physical constants.

free parameters (5)

δ0, δ1 (SCA curvature bounds)
Positive constants in (23)-(24) chosen so δ0 I_N ⪰ ∇²SNR0(t) and δ1 I_N ⪰ ∇²G(t); construction outsourced to [19], not specified.
PGD step length η = backtracking line search (values not given)
Used in (21a) to update antenna positions; no step-size range or backtracking parameters specified, affecting convergence and final solution.
Nesterov acceleration initialization α1 = 0.1
Set in §III-C for momentum update; no justification or sensitivity analysis.
Convergence criteria
Algorithm 1 stops when 'exist conditions are met' but no tolerance, max iterations, or objective-change threshold is stated, so the reported converged rates cannot be exactly reproduced.
Simulation scenario parameters = C0=-30 dB, path-loss exponent 3.2, L=6, D=10λ, Γ=15 dB, ϵ varied, etc.
These describe the test scenario, not fitted values; the claimed relative gains depend on them, and no averaging/seed information is provided.

assumptions (6)

domain assumption Far-field propagation with constant AoA/AoD/amplitudes and identical number of paths L for all links
Section II-A, Eqs. (1)-(3); relies on [12]. If near-field effects or unequal path counts occur, the channel model and gradient derivations break.
domain assumption Target (Willie) is quasi-static and its parameters φ and |α| have been roughly estimated and are known
Section II-B, paragraph after Eq. (8). Beamforming and covertness constraints use a_t(φ,t) and A(r,t).
standard math Willie uses the optimal likelihood ratio test with equal priors and known noise variance; DEP bound via Pinsker's inequality is sufficient
Section II-C, Eqs. (10)-(15); standard detection theory.
domain assumption s(m) and r(m) are independent Gaussian with known covariance; R0 can be realized as a radar probing signal
Section II-A, Eqs. (4)-(5); relies on [16].
ad hoc to paper There exist δ0,δ1 satisfying the Hessian majorization conditions
Section III-C, Eqs. (23)-(24); the existence and construction are cited to [19], an overlapping-author preprint not included here.
domain assumption The SCA approximations (23)-(24) are accurate enough that the projected gradient iterations converge to a local optimum
No convergence proof is given; only numerical evidence in Fig. 2(a).

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Cite this review

Pith. "Pith review of Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization." pith.science (2026). https://pith.science/paper/Q4YVP5OV

@misc{pith2026251009949,
  author       = {Pith},
  title        = {Pith review of: Movable Antenna Enhanced Covert Dual-Functional Radar-Communication: Joint Beamforming and Antenna Position Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q4YVP5OV}},
  note         = {Machine review of arXiv:2510.09949}
}

read the original abstract

Movable antenna (MA) has emerged as a promising technology to flexibly reconfigure wireless channels by adjusting antenna placement. In this paper, we study a secured dual-functional radar-communication (DFRC) system enhanced by movable antennas. To ensure communication security, we aim to maximize the achievable sum rate by jointly optimizing the transmit beamforming vectors, receiving filter, and antenna placement, subject to radar signal-to-noise ratio (SNR) and transmission covertness constraints. To tackle this challenging optimization problem, we first employ a Lagrangian dual transformation process to reformulate it into a more tractable form. Subsequently, the problem is solved by employing a block coordinate descent (BCD) procedure, incorporating semidefinite relaxation (SDR), projected gradient descent (PGD), and successive convex approximation (SCA) techniques. Simulation results demonstrate that the proposed method can significantly improve the covert sum rate, and achieve a satisfactory balance between the communication and radar performance compared with existing benchmark schemes by leveraging the flexibility of movable antennas.

Figures

Figures reproduced from arXiv: 2510.09949 by the authors.

**Figure 2.** (a) Convergence behavior. (b) Covert sum rate versus transmit [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** (a) Trade-off between covert sum rate and radar SNR [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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