{"id":"aa5adf59-c4a8-497b-9d51-fc119486855d","arxiv_id":"2501.15410","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A movable-antenna cooperative ISAC design is claimed to cut transmit power by 30-40% under CSI and time-synchronization errors, but the proof of its worst-case rate constraint has a central gap.","lead":"This paper proposes using movable antennas in a cooperative integrated sensing and communication network to reduce transmit power when channel state information and time synchronization are imperfect, and solves the resulting resource allocation problem with a constrained deep reinforcement learning agent. The paper claims 30-40% power savings over fixed-antenna baselines, but the central worst-case rate derivation is not sound.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1's robustness bound (47) is derived from an expression that is not the squared CSI error; the missing subtracted channel term makes the bound false unless an unstated small-angle restriction is imposed, so the power-savings claim is not established.","rationale":"The reader's verdict identifies the right locus: Appendix A's derivation of Eq. (47) is the load-bearing step. I checked the algebra and agree with the diagnosis, with one clarification. The fact that Eq. (45) is nonzero at zero error is not by itself fatal, because an upper bound may be loose; what is fatal is that the omitted subtractive term is not merely a missing tightening but the only term that removes the estimated channel, so the expression in Eq. (45) is not the squared error and is not guaranteed to bound it. The explicit N=1, L=1 counterexample at delta = pi/2 shows Eq. (47) can fail, and since Theorem 1 and the optimization problem (26) use Eq. (47) as a worst-case bound, the robust power-minimization result and the reported 30%-40% power savings are not supported. I recommend rejection rather than conditional acceptance because the paper does not state or verify any small-angle assumption that would make Eq. (47) valid, and the HCRLB portion in Appendix B is also only sketched with the tightness claim deferred to [30]. The concrete numerical check proposed would show whether a repaired proof is likely; if the bound survives over the simulation parameter grid, the central conclusion might be salvaged with an explicit assumption and corrected derivation, but as submitted the main theorem is not established. This is a structural concern about the argument, not an assessment of author intent.","tokens_in":24474,"tokens_out":13279,"duration_ms":123767,"concrete_test":"Compute the exact field-response error in Eq. (44) for N=8, L=3 and compare the maximum over the uncertainty set in Eq. (12), with |Delta theta| <= epsilon_theta, |Delta phi| <= epsilon_phi, and ||Delta tilde h|| <= bar_epsilon, against the right-hand side of Eq. (47). Start with the adversarial point: one path with delta = pi/2, Delta tilde h = 0, and nonzero |hat h|; if the true squared error exceeds N||hat tilde h||^2 + 2 N L bar_epsilon, Theorem 1 is false. Then repeat the maximization over the small-error grid used in Fig. 6 (bar_epsilon = 0.01, sigma_xi = 100 ns) to determine whether adding an explicit small-angle assumption could rescue the bound.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing failure is in Appendix A, Eqs. (44)-(47). Eq. (44) correctly writes the squared error as sum over antennas of |sum_i e^{j phi(theta_hat+Delta theta, phi_hat+Delta phi)}(hat h_i + Delta h_i) - e^{j phi(theta_hat, phi_hat)} hat h_i|^2. The transition to Eq. (45) drops the second, subtracted term: the expression in (45) is, before the Taylor expansion, |sum_i e^{j phi(theta_hat+Delta theta, phi_hat+Delta phi)}(hat h_i + Delta h_i) + e^{j phi(theta_hat, phi_hat)} Delta h_i|^2, not the squared channel error. At Delta theta = Delta phi = Delta h = 0, Eqs. (45)-(46) therefore evaluate to N||hat h||^2 instead of 0. A loose nonzero bound at the zero-error point would be acceptable, but the real problem is that the omitted term is essential for controlling the error at nonzero phase errors. With N=1, L=1, Delta h=0, and a phase error delta = pi/2, the true error is ||Delta h||^2 = |e^{j delta} - 1|^2 |hat h|^2 = 2|hat h|^2, while Eq. (47) gives |hat h|^2. Thus Eq. (47) is false in the generality stated; Theorem 1 and the problem (26) contain no small-angle restriction. Since A(w), B(w), and every simulated power saving inherit this bound, the claimed worst-case robust guarantee and the reported 30%-40% power savings are not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":24774,"tokens_out":10780,"duration_ms":94461,"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":[{"comment":"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.","section":"Appendix A, Eqs. (44)-(47)"},{"comment":"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.","section":"Sec. IV-A, Eqs. (10) and (13)"},{"comment":"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.","section":"Appendix A, Eq. (46)"},{"comment":"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.","section":"Sec. IV-B and Appendix B, Eqs. (25), (27), (57)-(64)"}],"minor_comments":[{"comment":"The organization paragraph places the conclusion in Section VI, but the actual Conclusion is Section VII; the section numbering should be corrected.","section":"Section I and Section VII"},{"comment":"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.","section":"Problem (26) and Section VI"},{"comment":"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).","section":"Algorithm 1"},{"comment":"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.","section":"Figs. 4 and 8"},{"comment":"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.","section":"Sec. V-B"},{"comment":"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.","section":"Abstract and Sec. VI"}],"recommendation":"major_revision","confidential_remarks":"The paper is in scope for a communications/signal-processing journal, and the general direction is acceptable for a revision. I recommend major revision rather than rejection because the faulty bound in Appendix A is a localizable mathematical error that could in principle be repaired with a correct derivation and a small-angle assumption. However, I would ask the editor to require a full re-derivation of Theorem 1, a correction of the SINR expression in Eq. (10), and a rerun of the numerical results before the paper is reconsidered; if the authors cannot supply a valid CSI error bound, the paper should be rejected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper's central robustness claim rests on a bound that does not hold, so the 30–40% power saving headline is not supported by the proof. The stress-test note is correct. In Appendix A, Eq. (44) writes the squared CSI error correctly, but the transition to Eq. (45) drops the subtracted estimated-channel term. What is bounded in Eq. (47) is not the squared error. At zero angle/gain error the expression evaluates to N||hat h||^2, not zero, and the omitted term is essential for controlling the error at nonzero phase errors. With N=1, L=1, Delta h=0, and a phase error of pi/2, the true error is 2|hat h|^2 while Eq. (47) gives |hat h|^2. Since Theorem 1 and every simulation figure inherit this bound, the robust optimality and the reported power savings are not established.\n\nWhat the paper does well: the combination of movable-antenna positioning with a robust C-ISAC design under both CSI and TS errors is a fair extension beyond prior work. The HCRLB analysis with TS errors is a useful addition, and the CDRL/DDPG formulation is a sensible way to attack the non-convex problem, even if it is not conceptually new. The simulation setup is plausible and the comparison against FPA, SDR, and ZF is reasonable.\n\nSoft spots beyond the main flaw: the HCRLB tightness assumption is imported from [30] without verification for this specific model, and the paper does not provide error bars or code/data, which would be needed to trust the numerical gains. The literature review is adequate; the novelty claim is a bit overstated given [8] already handles robust C-ISAC with imperfect CSI and TS, but the MA part is a legitimate addition.\n\nWho this is for: researchers working on MA-aided ISAC or robust resource allocation in C-ISAC. If the bound in Theorem 1 is repaired, the paper could be a useful incremental contribution. As it stands, the central technical result is not proven, so the numerical conclusions are not trustworthy.\n\nMy recommendation: send it to reviewers only if the authors can fix the bound or explicitly impose and justify a small-angle restriction. Without that repair, I would reject. The paper deserves a serious referee because the topic is relevant and the combination is worth examining, but the current form should not be accepted.","headline":"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.","tokens_in":25419,"tokens_out":2271,"would_cite":false,"duration_ms":21480,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Movable antennas can cut transmit power by 30–40% in cooperative ISAC networks under channel and clock errors.","keywords":["movable antennas","cooperative integrated sensing and communication","imperfect channel state information","time synchronization error","hybrid Cramér-Rao lower bound","worst-case robust beamforming","constrained deep reinforcement learning","power minimization"],"falsifier":"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.","tokens_in":1776,"feed_emoji":"📡","tokens_out":7221,"duration_ms":114344,"temperature":0.7,"pith_summary":"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.","feed_headline":"Movable antennas save 30–40% power in ISAC networks","feed_subtitle":"Robust beamforming keeps rate and sensing accuracy when channel and clock errors hit cooperative ISAC.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the networked-ISAC model with imperfect CSI and time synchronization that this paper extends by adding movable antennas.","marker":"[8]"},{"why":"Provides the worst-case robust optimization technique and the actual-versus-estimated CSI relation used to derive Theorem 1.","marker":"[28]"},{"why":"Establishes the hybrid Cramér-Rao lower bound and its asymptotic tightness, which the sensing-accuracy constraint relies on.","marker":"[30]"},{"why":"Gives the field-response channel model that expresses movable-antenna channels through angles and antenna positions.","marker":"[24]"},{"why":"Defines the time-synchronization error model and propagation-delay structure used in the sensing signal and HCRLB.","marker":"[25]"},{"why":"Motivates the angle and gain error model for movable-antenna channel estimation that underlies the CSI error bound.","marker":"[29]"},{"why":"Supplies the deep deterministic policy gradient actor-critic baseline on which the constrained solver is built.","marker":"[34]"}],"fun_headline_variants":["Movable antennas slash ISAC power 30–40% despite errors","Robust ISAC: movable antennas offset CSI and sync faults","Movable antennas cut power in cooperative ISAC with errors","C-ISAC robustness: movable antennas save 30–40% power","Movable antennas tame imperfect CSI and sync in ISAC"],"cache_read_input_tokens":27392,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Movable antennas slash ISAC power 30–40% despite errors","Robust ISAC: movable antennas offset CSI and sync faults","Movable antennas cut power in cooperative ISAC with errors","C-ISAC robustness: movable antennas save 30–40% power","Movable antennas tame imperfect CSI and sync in ISAC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000595,"raw_usage":{"total_tokens":2790,"prompt_tokens":953,"completion_tokens":1837,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":569,"completion_tokens_details":{"reasoning_tokens":1748}},"tokens_in":569,"tokens_out":1837,"duration_ms":11843,"temperature":1.0,"reasoning_tokens":1748,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:20:10.751931+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Coordinated transmit beamforming for networked ISAC with imperfect CSI and time synchronization,","cited_arxiv_id":null,"evidence_quote":"Supplies the networked-ISAC model with imperfect CSI and time synchronization that this paper extends by adding movable antennas."},{"cited_title":"Notes on the tightness of the hybrid Cramer–Rao lower bound,","cited_arxiv_id":null,"evidence_quote":"Establishes the hybrid Cramér-Rao lower bound and its asymptotic tightness, which the sensing-accuracy constraint relies on."},{"cited_title":"Flexible precoding for multi-user movable antenna communications,","cited_arxiv_id":null,"evidence_quote":"Gives the field-response channel model that expresses movable-antenna channels through angles and antenna positions."},{"cited_title":"Cooperative time syn- chronization and robust clock parameters estimation for time-sensitive cell-free massive MIMO systems,","cited_arxiv_id":null,"evidence_quote":"Defines the time-synchronization error model and propagation-delay structure used in the sensing signal and HCRLB."},{"cited_title":"Channel estimation for movable antenna communication systems: A framework based on compressed sensing,","cited_arxiv_id":null,"evidence_quote":"Motivates the angle and gain error model for movable-antenna channel estimation that underlies the CSI error bound."}],"review_version":1}