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REVIEW 4 major objections 6 minor 2 cited by

Movable Antenna-Aided Cooperative ISAC Network with Time Synchronization error and Imperfect CSI

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Movable antennas can cut transmit power by 30–40% in cooperative ISAC networks under channel and clock errors.

desk verdict The paper combines MA positioning with robust C-ISAC under both CSI and time-synchronization errors, but its central worst-case rate constraint rests on an invalid bound, so the headline power-savings claim is not established. read the letter →

arxiv 2501.15410 v1 pith:EHSO6JNL submitted 2025-01-26 eess.SP

Yue Xiu , Yang Zhao , Ran Yang , Dusit Niyato , Jing Jin , Qixing Wang , Guangyi Liu , Ning Wei This is my paper · ORCID
classification eess.SP
keywords movableantennascooperativeintegratedsensingandcommunicationimperfectchannelstateinformationtimesynchronizationerrorhybridCramér-Raolowerboundworst-caserobustbeamformingconstraineddeepreinforcementlearningpowerminimization
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 tries to establish that movable antennas can rescue cooperative integrated sensing and communication (C-ISAC) networks from two practical imperfections that fixed-antenna designs cannot absorb: channel state information (CSI) estimation error and inter-base-station time synchronization (TS) error. It models both errors explicitly—CSI error as a bounded channel perturbation, TS error as a random clock offset entering the sensing delay—and derives a worst-case achievable rate constraint plus a hybrid Cramér-Rao lower bound (HCRLB) on target localization accuracy. On those constraints it builds a power-minimization problem over beamforming, base-station selection, and antenna positions, and solves it with a constrained deep reinforcement learning algorithm. The payoff claimed is a 30–40% transmit-power reduction relative to existing algorithms, with reliable communication at TS-error variance of 100 ns and CSI-error level of 0.01, and fewer antennas or base stations needed than fixed-antenna or simpler movable-antenna schemes.

What carries the argument

The load-bearing objects are: (i) the field-response channel model, which expresses movable-antenna channels through angle of departure, angle of arrival, and antenna position; (ii) the worst-case CSI error bound of Eq. (47), $\| \Delta h_{b,u} \|^2 \le N \| \hat{\tilde h}_{b,u} \|^2 + 2N L_{b,u} \bar{\epsilon}_{b,u}$, which turns the uncertain rate constraint into the deterministic worst-case constraint of Theorem 1; (iii) the hybrid Cramér-Rao lower bound (HCRLB), which turns TS-error variance into a trace constraint on target-position estimation; and (iv) a constrained Markov decision process solved by a primal-dual deep deterministic policy gradient with a Wolpertinger action-selection architecture. The power-minimization problem is the point where all four meet.

What would settle it

Evaluate Eq. (44) with all estimation errors set to zero—$\Delta\theta=0$, $\Delta\phi=0$, and $\Delta\tilde h=0$. The true squared error is zero, but the right-hand side of Eq. (47) is $N \| \hat{\tilde h}_{b,u} \|^2$, which is positive; if that is what the derivation yields, the inequality is not a valid bound on the error, and the worst-case rate constraint built from it would be over-conservative or invalid. Recomputing Theorem 1 with a corrected error bound would settle the paper's central claim.

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Extended reading notes

Core claim

The central claim is that movable antennas give a quantifiable robustness gain in C-ISAC: by physically reconfiguring transmit and receive antenna positions, the system can compensate for both channel-estimation and time-synchronization impairments at lower transmit power than fixed-position antennas. The paper derives this through a worst-case robust reformulation: Theorem 1 converts the uncertain rate constraint into a deterministic lower bound that depends on estimated channel gains and known error bounds, and the HCRLB converts TS-error uncertainty into a sensing-accuracy constraint. The optimization then minimizes total transmit power while satisfying both constraints, and the proposed constrained deep reinforcement learning solver is shown in simulation to need only 3 base stations where an adaptive-portable-antenna scheme needs 4–5 and a fixed-antenna scheme needs 6, and to achieve a 30–40% power saving over existing algorithms.

Load-bearing premise

The load-bearing premise is that the inequality in Eq. (47), $\| \Delta h_{b,u} \|^2 \le N \| \hat{\tilde h}_{b,u} \|^2 + 2N L_{b,u} \bar{\epsilon}_{b,u}$, truly bounds the channel-estimation error; if this bound is not valid, the worst-case communication-rate constraint and the 30–40% power-saving result built on it are not established.

Editorial extensions

If this is right

  • If the worst-case rate bound is valid, a C-ISAC operator can certify a minimum throughput for every user even when the channel estimate is off by the stated error magnitude.
  • The same worst-case reformulation lets the network minimize transmit power, with simulated savings of 30–40% against existing algorithms.
  • Movable antennas reduce infrastructure cost: 16 MAs are claimed to match the performance of 32 fixed antennas under CSI error, and 20 MAs under TS error.
  • The robust design cuts the number of active base stations: 3 BSs under TS errors where fixed-antenna systems need 6.
  • The HCRLB-based sensing constraint lets the network treat TS error as a resource cost, so improving synchronization accuracy could be traded directly against transmit power.

Reading between the lines

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

  • An extension not made in the paper would be to test whether the 30–40% power saving persists when Eq. (47) is replaced by a tighter statistical model of CSI error, since a looser bound directly inflates the power needed to satisfy the worst-case constraint.
  • The same worst-case-plus-HCRLB template could be applied to multi-target tracking or to other reconfigurable-antenna systems, where each antenna's position becomes a continuous decision variable.
  • A testable prediction on small instances (for example, 2 BSs and 1 user) is that an exhaustive or semidefinite-relaxation solver should find a lower transmit power than the trained reinforcement-learning policy; the gap would quantify solver suboptimality separately from the robustness model.
  • If the bound in Eq. (47) is as loose as the derivation in Appendix A suggests, then the reported power numbers are conservative rather than optimistic, and a corrected error characterization would likely improve the claimed savings.
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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 / 6 minor

Summary. The paper considers a cooperative integrated sensing and communication (C-ISAC) network in which multiple dual-function radar and communication base stations, equipped with movable antennas, serve downlink users while locating a target. It models imperfect CSI through angle and gain errors and models time-synchronization errors through a Gaussian random variable, then derives a worst-case communication rate constraint and a hybrid Cramer-Rao lower bound (HCRLB) sensing constraint. The resulting transmit-power minimization problem over beamforming, BS selection, and MA positions is solved with a constrained deep reinforcement learning algorithm based on a modified DDPG with a Wolpertinger architecture. Simulations claim 30%-40% power savings over fixed-position-antenna baselines under CSI error 0.01 and TS error 100 ns.

Significance. The problem is timely, and combining movable antennas with robust C-ISAC under imperfect CSI and time-synchronization errors is a reasonable and potentially useful direction. The paper also gives a concrete non-convex formulation and a constrained-DRL solution method, which is a plausible algorithmic contribution. However, the central worst-case rate result in Theorem 1 is built on an invalid CSI-error bound in Appendix A, and the SINR expression in Eq. (10) does not describe the actual user rate. These issues are load-bearing: the power-minimization problem, the CDRL solution, and the claimed savings are all evaluated using these incorrect constraints. If the derivations can be corrected and the simulations redone, the framework would be worth reconsidering; as written, the quantitative claims are not established.

major comments (4)
  1. [Appendix A, Eqs. (44)-(47)] The bound in Eq. (47) is not a valid bound on the CSI estimation error. Eq. (44) correctly starts from |Δh|² = |Σ_i e^{jφ(θ̂+Δθ,φ̂+Δφ)}(ĥ_i+Δĥ_i) − Σ_i e^{jφ(θ̂,φ̂)}ĥ_i|², but the transition to Eq. (45) drops the subtracted estimated-channel term and instead adds a spurious +Σ_i e^{jφ(θ̂,φ̂)}Δĥ_i term. As a result, at Δθ = Δϕ = Δĥ = 0 the expression in Eqs. (45)-(46) evaluates to N‖ĥ‖² rather than 0. More seriously, for N=1, L=1, Δĥ=0 and a phase error δ=π/2, the true squared error is |e^{jδ}−1|²|ĥ|² = 2|ĥ|², while Eq. (47) gives |ĥ|². Since Theorem 1 and problem (26) impose no small-angle restriction, the worst-case rate constraint (14) and every simulation result built on it are not established.
  2. [Sec. IV-A, Eqs. (10) and (13)] The communication rate expression is not the SINR of user u. The interference term is written as Σ_{u′≠u} |c_{b,u′} h_{b,u′} w_{b,u′}|², which uses the channel of the interfering user u′ instead of the channel h_{b,u} of the user whose rate is being computed; the correct interference from beamformer w_{b,u′} at user u is |h_{b,u}^H w_{b,u′}|². In addition, the noise term is σ_b², which is a BS-side noise, rather than the user noise σ_u². Because this incorrect SINR enters Theorem 1 and constraint (26c), the robust rate guarantee is not the guarantee claimed for the actual system.
  3. [Appendix A, Eq. (46)] The step Σ_j |Σ_i e^{j(...)} ĥ_i|² = N‖ĥ‖² is not valid for L > 1. For a fixed antenna j, Cauchy-Schwarz gives |Σ_i e^{j(...)} ĥ_i|² ≤ L Σ_i |ĥ_i|², so summing over N antennas yields at most N L ‖ĥ‖², not N‖ĥ‖² unless all path phases are identical. Thus Eq. (47) is too tight even independently of the error in Eq. (45), further invalidating Theorem 1.
  4. [Sec. IV-B and Appendix B, Eqs. (25), (27), (57)-(64)] The sensing constraint is not rigorously established. Eq. (25) contains an undefined block Ξ^b_{ΔξΔu_b}, and the derivation of the HCRLB relies on a matrix-inversion formula and a tightness result from [30] without verifying that the model here satisfies the required conditions. The final trace constraint (26b) is therefore not shown to be a valid lower bound on the position-estimation MSE. This is load-bearing because the sensing accuracy constraint is one of the two core constraints in the power-minimization problem.
minor comments (6)
  1. [Section I and Section VII] The organization paragraph places the conclusion in Section VI, but the actual Conclusion is Section VII; the section numbering should be corrected.
  2. [Problem (26) and Section VI] The symbol γ_b is used for both the sensing accuracy threshold in (26b) and the communication rate threshold in (26c), and Section VI writes “communication rate γ_b = 2 bit/s/Hz”; this overloading makes the constraints difficult to read.
  3. [Algorithm 1] Line 4 of Algorithm 1 refers to Eq. (32) for action selection, but Eq. (32) defines target reward and cost values; action selection is given in Eq. (31).
  4. [Figs. 4 and 8] The captions of Fig. 4 state “Number of BSs” although the panels show cumulative reward and cost versus episodes, and the captions of Fig. 8 are interchanged with the text describing 100 ns and 200 ns cases.
  5. [Sec. V-B] The “Wolpertinger architecture” is mentioned several times but never defined; the action-selection procedure in Eqs. (30)-(31) does not explain how the discrete/continuous Wolpertinger action set is constructed.
  6. [Abstract and Sec. VI] The text reports “TS error variance of 100 ns”; since σ_ξ = 100 ns is used as a standard deviation, the quantity should be described as a standard deviation, or the variance should be stated with ns² units.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the worst-case rate and HCRLB derivations are self-contained, and the power-savings claim is an optimization result rather than a relabeled fit.

full rationale

The manuscript does not exhibit a circular derivation in the sense defined here. Theorem 1 is proved in Appendix A using triangle inequality, Cauchy-Schwarz, and a Taylor expansion; although the transition from Eq. (44) to Eq. (45) appears to drop the subtracted estimated-channel term and is a serious mathematical validity concern, that is an error in the bounding argument, not a construction in which the conclusion is identical to an input. The HCRLB constraint is a standard application of the hybrid Fisher information matrix, with the derivation of the required derivatives given in Appendix B; the TS-error component in Eq. (25) is the usual Schur-complement extra term. The CDRL algorithm is trained and evaluated on the same simulated channel model, which limits independent external validation, but no fitted parameter is renamed as a prediction and no benchmark is used to force the reported 30%-40% power savings. Self-citations to [19], [21], and [28] appear in the literature review and in the citation for the worst-case robust optimization template, but Theorem 1's derivation is reproduced in the manuscript, so the central claim does not reduce to an unverified self-citation chain. The Appendix A flaw, if confirmed, undermines the correctness of the robust guarantee, but that is a correctness risk rather than a circularity under the criteria of this analysis.

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

The central claim rests on several domain assumptions: fixed point-target LoS sensing, Gaussian TS errors with known variance, bounded CSI errors, and HCRLB tightness. The simulation scenario parameters are hand-chosen and affect the quantitative power-savings claim. No new physical entities are introduced.

free parameters (4)
  • CSI error bound \bar\epsilon_{b,u} = 0.01 default, scanned to larger values in Fig. 6a
    Hand-chosen uncertainty radius; the required transmit power increases with it, so it directly shapes the main quantitative claim.
  • TS error standard deviation \sigma_\xi = 100 ns default, 200 ns in Fig. 8b
    Assumed Gaussian clock-error prior; the HCRLB and the power cost scale with this parameter.
  • Sensing accuracy threshold \gamma_b = 0.05
    User-selected constraint in problem (26b); determines how tight the HCRLB requirement is.
  • Communication rate threshold \gamma_u = 2 bit/s/Hz
    User-selected QoS constraint in problem (26c); higher thresholds increase transmit power in the simulations.
assumptions (5)
  • domain assumption Time synchronization errors are zero-mean Gaussian with known variance sigma_xi^2 and are the only source of synchronization mismatch.
    Invoked in Section III-B, Eq. (8). If the error model is wrong, the HCRLB and the resulting power-minimization constraints are not valid.
  • domain assumption The HCRLB is treated as an achievable constraint: requiring tr{HCRLB_b(p)} <= gamma_b is assumed to control the true MSE of target position estimation.
    Used in problem (26b). The paper cites asymptotic tightness [30] but does not verify that a specific unbiased estimator attains the bound in the simulated regime.
  • domain assumption The sensing channel is a LoS, clutter-free, point-target model with known single-bounce geometry.
    Stated in Section III, Eqs. (2)-(7) and surrounding text. Real ISAC environments with clutter and extended targets are excluded from the model.
  • domain assumption The field-response channel can be reconstructed from AoA, AoD, and gain estimates, with errors confined to small bounded intervals.
    Assumed in Section IV-A, Eqs. (11)-(12), citing [29]. The Appendix A Taylor expansions rely on these error intervals being small enough for first-order approximation.
  • standard math Standard linear algebra inequalities and first-order Taylor expansions are applicable to the CSI-error derivation.
    Used in Appendix A, Eqs. (38)-(46). The Taylor expansion is applied without an explicit smallness condition, and the subtraction error suggests the expansion is used incorrectly.

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Cite this review

Pith. "Pith review of Movable Antenna-Aided Cooperative ISAC Network with Time Synchronization error and Imperfect CSI." pith.science (2026). https://pith.science/paper/EHSO6JNL

@misc{pith2026250115410,
  author       = {Pith},
  title        = {Pith review of: Movable Antenna-Aided Cooperative ISAC Network with Time Synchronization error and Imperfect CSI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHSO6JNL}},
  note         = {Machine review of arXiv:2501.15410}
}
read the original abstract

Cooperative-integrated sensing and communication (C-ISAC) networks have emerged as promising solutions for communication and target sensing. However, imperfect channel state information (CSI) estimation and time synchronization (TS) errors degrade performance, affecting communication and sensing accuracy. This paper addresses these challenges {by employing} {movable antennas} (MAs) to enhance C-ISAC robustness. We analyze the impact of CSI errors on achievable rates and introduce a hybrid Cramer-Rao lower bound (HCRLB) to evaluate the effect of TS errors on target localization accuracy. Based on these models, we derive the worst-case achievable rate and sensing precision under such errors. We optimize cooperative beamforming, {base station (BS)} selection factor and MA position to minimize power consumption while ensuring accuracy. {We then propose a} constrained deep reinforcement learning (C-DRL) approach to solve this non-convex optimization problem, using a modified deep deterministic policy gradient (DDPG) algorithm with a Wolpertinger architecture for efficient training under complex constraints. {Simulation results show that the proposed method significantly improves system robustness against CSI and TS errors, where robustness mean reliable data transmission under poor channel conditions.} These findings demonstrate the potential of MA technology to reduce power consumption in imperfect CSI and TS environments.

Figures

Figures reproduced from arXiv: 2501.15410 by the authors.

Figure 1
Figure 1. Illustration of the MA-enabled C-ISAC system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The proposed robust algorithm based on CDRL. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. (a) Cumulative reward of the CDRL versus epochs. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (5 more)
Figure 3
Figure 3. Figure 3: Simulation setup of the MA-enabled C-ISAC system. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png]
Figure 5
Figure 5. Figure 5: (a) Average transmit power versus the number of MAs [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: (a) Average transmit power versus the communica [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 6
Figure 6. Figure 6: (a) Average transmit power versus the CSI error. (b) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 8
Figure 8. Figure 8: (a) BS selection versus the proposed algorithm and [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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Forward citations

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.