{"id":"2af967d6-e706-4df6-8945-3b25c579b794","arxiv_id":"2506.00601","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A dual-UAV scheme with a cooperative jamming drone jointly optimizes beamforming and trajectories to maximize the average covert rate in air-to-ground ISAC networks under covertness and sensing constraints.","lead":"This paper designs a covert wireless system with two drones: one drone sends a secret message while a second drone emits noise that hides the message and also helps locate ground targets. It matters because it shows how a second drone can simultaneously improve stealth and sensing in air-to-ground integrated sensing and communication networks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (39) is not a valid first-order Taylor expansion: the gradient of Alice's trajectory objective omits factor-2 terms, so Algorithm 1's surrogate and convergence claim are unsupported.","rationale":"The paper's central assertion rests on Algorithm 1. The SCA trajectory update is not a minor heuristic detail; it is the mechanism that produces the optimized trajectories in the simulations. The derivative algebra in Eq. (39) is concretely wrong: the term zeta1*(u-v_b) should carry a factor of 2 because d^2*zeta1 is differentiated with respect to u, and the term -2(u-v_b)/(ln2*d^2) is required for the second log term. Since the paper provides no code and no convergence proof, this is a checkable defect rather than a matter of presentation. The reader's weakest assumption about unproved convexity is related but not identical; the gradient error would matter even if the objective were well behaved. I still credit the paper for a well-posed problem, a plausible system model, and simulation comparisons. The concern does not by itself prove the proposed scheme is bad; it shows the optimization claims are currently unsupported. That is consistent with a conditional verdict pending a numerical verification and correction. If the finite-difference check passes and revised simulations reproduce the figures, acceptance would be appropriate.","tokens_in":22314,"tokens_out":15493,"duration_ms":159493,"concrete_test":"At a feasible iterate from Algorithm 1 with Table I parameters, choose a small displacement delta with ||delta|| <= psi_a, e.g., 0.1 m. Numerically evaluate R_hat from Eq. (32) at u_a+delta and compare it with alpha + rho^H delta from Eqs. (38)-(39); for a true first-order expansion the residual should be O(||delta||^2). If instead ((R_hat(u+delta)-R_hat(u)) - rho^H delta)/||delta|| does not tend to 0 as ||delta|| tends to 0, Eq. (39) is not the gradient. Then rerun Algorithm 1 with the corrected gradient (including the factor-2 terms) and check whether the returned trajectories and average covert rates in Figs. 4-7 change materially; also verify that the true covertness constraint in Eq. (31b) is satisfied at every returned point.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the trajectory-update SCA in Sec. III-A. Eq. (39) defines the FOT coefficient for Alice's objective as rho = gamma_ab/(ln2 * zeta2) + zeta1*(u_a-v_b)/ln2 * (1/zeta2 - 1/(d^2*zeta1)). From Eq. (32), however, R_hat = log2(zeta2) - log2(d^2*zeta1), with zeta2 = eta_ab + d^2*zeta1 and nabla_u zeta2 = gamma_ab + 2*zeta1*(u-v_b). The true gradient is therefore (gamma_ab + 2*zeta1*(u-v_b))/(ln2*zeta2) - 2*(u-v_b)/(ln2*d^2). Eq. (39) contains only half of the two zeta1-dependent terms, so it is not the first-order Taylor expansion claimed. Thus the 'lower bound' in Eq. (37) is not a valid linearization even locally, and the statement that Algorithm 1 converges by increasing the surrogate has no basis. A parallel issue affects Jack's trajectory update in Eq. (53). Because the central claim is that the co-designed trajectories maximize the average covert rate under the covertness and sensing constraints, this algebraic mismatch directly undermines the reported gains in Figs. 4-7 unless the algorithm is corrected and re-simulated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper considers covert communication in an air-to-ground ISAC network with two UAVs: Alice, a dual-functional BS transmitting to Bob while sensing ground targets, and Jack, a cooperative jammer whose artificial noise both confuses Willie and serves as a bistatic sensing illumination. The authors formulate two average-covert-rate maximization problems for the communication-only (CCO) and communication-plus-sensing (CCS) phases, with transmit power, maneuver, KL-divergence-based covertness, and distance-normalized beampattern sum-gain sensing constraints. A BCD method is proposed, alternating between SDR-based beamforming and trust-region SCA trajectory updates for Alice and Jack; the CCS phase selects sensing slots by a weighted-distance greedy algorithm and optimizes the dual-functional beamformers. Simulations compare the proposed scheme with fly-hover-fly and single-UAV benchmarks for different flight times, sensing thresholds, covertness levels, and residual SIC levels. The central claim is that the proposed co-design yields the highest ACR and sensing performance while satisfying all constraints.","tokens_in":22666,"tokens_out":15282,"duration_ms":132847,"significance":"The motivating idea of reusing a cooperative jammer's AN as a bistatic sensing waveform is attractive and is a reasonable extension of the single-UAV ISAC covert-communication literature. The system model is fairly complete: imperfect SIC is incorporated, and the covertness condition is derived from a standard KL-divergence bound rather than imposed ad hoc. The benchmarks and parameter sweeps in Figs. 4-7 provide concrete, falsifiable predictions, and no parameters are fitted to produce the reported curves. However, the algorithmic core of the paper, which generates those predictions, contains demonstrable algebraic errors in the claimed first-order Taylor expansions and provides no convergence proof. The numerical gains are therefore not presently supported. If the derivations are corrected and the simulations regenerated, the paper could be a useful contribution.","major_comments":[{"comment":"The coefficient rho_a^(t1)[n] in Eq. (39) is not a valid first-order Taylor expansion of \\hat R_b^cco[n] in Eq. (32). With d^2 = A_a^2 + ||u_a - v_b||^2 and zeta2 = eta_ab + d^2 zeta1, the true gradient is \\nabla_{u_a}\\hat R = (\\gamma_ab + 2 zeta1 (u_a - v_b))/(ln2 * zeta2) - 2 (u_a - v_b)/(ln2 * d^2). Eq. (39) simplifies to \\gamma_ab/(ln2 * zeta2) + zeta1 (u_a - v_b)/(ln2 * zeta2) - (u_a - v_b)/(ln2 * d^2), i.e., only half of the zeta1-dependent and distance-dependent terms. Hence Eq. (37) is not even a local linearization, and the inequality \\hat R >= \\tilde R is unsupported. Since Algorithm 1 updates Alice's trajectory by maximizing this surrogate in (P4.t1), the reported trajectory gains in Figs. 4-7 do not follow from the stated derivation.","section":"III-A, Eq. (39)"},{"comment":"Jack's trajectory update has the same defect. For zeta3 and zeta4 defined in Eqs. (49)-(50), a correct first-order expansion of \\breve R_b^cco gives gradient terms [\\varpi_jb \\gamma_jb + 2(\\sigma_b^2/\\beta + K)(u_j - v_b)]/(ln2 * zeta4) - [\\varpi_jb \\gamma_jb + 2(\\sigma_b^2/\\beta)(u_j - v_b)]/(ln2 * zeta3), where K = tr(W_a A(u_a,v_b))/d^2(A_a,u_a,v_b). Eq. (53), as printed, lacks the vector (u_j - v_b) in the second term, and the coefficient structure does not match this gradient. Therefore the surrogate in Eq. (51) is not a first-order lower bound, and subproblem (P5.t2) is not the SCA subproblem claimed.","section":"III-B, Eq. (53)"},{"comment":"The linearized covertness constraint (42) is also not the first-order expansion of (36). Expanding (36) at u_a^(t1) yields a linear coefficient \\gamma_aw + 2(1-\\kappa)(tr(W_j A(u_j,v_w))/d^2(A_j,u_j,v_w) + \\sigma_w^2/\\beta)(u_a^(t1) - v_w). Eq. (44) instead contains an undefined symbol \\gamma_rw and a coefficient without the required factor 2. Thus (42) can admit trajectories that violate the original covertness constraint (31b); the same problem affects Jack's constraint approximation in (57)-(59). Feasibility of the Algorithm 1 output with respect to the covertness constraint is therefore not guaranteed.","section":"III-A, Eqs. (42)-(44)"},{"comment":"The convergence claim for Algorithm 1 is unsupported. The paper never establishes that \\hat R_b^cco or \\breve R_b^cco is convex or concave in the UAV positions, so the first-order expansions in (37) and (51) are not proved to be lower bounds; even with a correct gradient, monotonic increase of the surrogate subproblems does not imply monotonic increase of the true ACR. In addition, the trust-region radii \\psi_a and \\psi_j are reduced geometrically in every iteration without an acceptance/rejection test based on true-objective improvement, so the sentence 'By iteratively updating ... convergence way' at the end of Section III-A has no basis. Because the simulation results in Figs. 4-7 are produced by this algorithm, the central numerical claim is not currently established.","section":"III-D, Algorithm 1"}],"minor_comments":[{"comment":"In the definition of the detection error probability, the second term is written as Pr(D1|H1), but it should be Pr(D0|H1).","section":"II-C, Eq. (20)"},{"comment":"Under H1, the jamming signal from Jack should arrive through channel h_jw, but Eq. (19) writes h_aw^H w_j s_j; this is inconsistent with Eq. (26) and with Eq. (18).","section":"II-A, Eq. (19)"},{"comment":"The symbol A(u_m,v) is introduced as a^H(u_m,v)a(u_m,v), which is a scalar; in the trace expressions such as tr(W_a A(u_a,v_b)) it must be the rank-one matrix a(u_m,v)a^H(u_m,v).","section":"III-A, Eq. (30)"},{"comment":"In Table I, both Alice and Jack final locations are labeled u_F_j; one of the two entries should be Alice's final location u_F_a, and the printed coordinates should be checked.","section":"Table I"},{"comment":"Algorithm 1's stopping-criterion indices appear inconsistent: line 5 compares \\bar R^{(t3+1)} - \\bar R^{(t1)} with a threshold, although t1 is not yet defined in the inner loop; this should be t3.","section":"III-D, Algorithm 1"},{"comment":"The sensing performance is measured by the same distance-normalized beampattern sum-gain that is imposed as constraint (28b); the reported sensing gains are therefore partly by construction. An independent sensing metric, such as detection probability or Cramér-Rao bound, would substantially strengthen the claim.","section":"IV-B, Figs. 5-7"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and I see no reason to suspect data fabrication. However, the algebraic errors in the core SCA derivations affect all reported performance numbers, so a corrected derivation and regenerated simulations are necessary before publication. The novelty of the dual-UAV jammer-as-bistatic-sensor concept is sufficient that a careful revision could make the paper acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the system idea is genuinely new — a cooperative jamming UAV whose artificial noise doubles as a bistatic sensing waveform for an A2G-ISAC network — and the paper does a decent job of setting up the covertness and sensing constraints. But the optimization core has an algebraic bug that undercuts the claimed convergence, and the simulations can't rescue it until that's fixed.\n\nWhat's new: prior covert A2G-ISAC work uses a single UAV, and stationary-jammer work doesn't reuse the AN for sensing. The hybrid monostatic-bistatic radar model and the distance-normalized beampattern sum-gain are a sensible way to avoid an intractable CRB. The problem formulation, with imperfect SIC, is coherent. The greedy slot-selection heuristic is a reasonable engineering shortcut. Credit where due: the authors write out the signal model and the KL-divergence covertness constraint, and the simulation comparisons against FHF and single-UAV schemes are meaningful.\n\nThe soft spots are in the SCA. Eq. (39) is supposed to be the first-order Taylor coefficient of Alice's rate in Eq. (32). Starting from R = log2(ζ2) − log2(d^2 ζ1) with ζ2 = η + d^2 ζ1 and ζ1 independent of u_a, the exact gradient is (γ + 2ζ1(u−v))/(ln2·ζ2) − 2(u−v)/(ln2·d^2). Eq. (39) contains only half of the ζ1-dependent terms, so it is not the gradient, not even locally. The same issue appears in Jack's update (Eq. (53)). That means the \"lower bounds\" in Eqs. (37) and (42) are not valid linearizations, and the statement that Algorithm 1 converges monotonically has no basis. The simulation gains in Figs. 4–7 are therefore not supported until the algorithm is corrected and re-run. This is not a minor typo: it is the load-bearing step of the trajectory optimization.\n\nOther issues are smaller. There is no convergence proof for the BCD outer loop, the trust-region radii are decreased with no rule that guarantees feasibility of the surrogate, and the sensing metric used as the constraint is the same metric used to evaluate performance, which makes the sensing gains partly circular. No code or error bars are provided, so the quantitative claims are hard to assess separately.\n\nBottom line: the system concept is worth a serious referee, and the paper could be salvageable with a corrected algorithm and re-simulated results. As it stands I would not cite the trajectory-optimization result, but I would mention the system model in related work.","headline":"A genuinely new dual-UAV covert ISAC concept with a coherent model, but the SCA trajectory update has a missing-factor gradient error that undercuts the main simulation claims until fixed.","tokens_in":23128,"tokens_out":3309,"would_cite":false,"duration_ms":30078,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Co-designing two drone trajectories and beamformers, with a jammer's artificial noise reused as a bistatic sensing waveform, maximizes average covert rate and sensing performance in an air-to-ground integrated sensing and communication…","keywords":["covert communications","integrated sensing and communication","UAV trajectory optimization","cooperative jamming","hybrid monostatic-bistatic radar","beampattern gain","successive interference cancellation","block coordinate descent"],"falsifier":"Run Algorithm 1 on a small instance, say ten time slots and two targets, from many random initial trajectories and check whether the surrogate value at each iteration bounds the true objective and whether all runs converge to the same average covert rate; alternatively, evaluate the inequalities in Eqs. (37) and (42) on a grid of UAV positions to find any point where the alleged lower bound exceeds the true rate or the alleged upper bound falls below the true covertness term.","tokens_in":22162,"feed_emoji":"📡","tokens_out":5704,"duration_ms":54593,"temperature":0.7,"pith_summary":"This paper proposes a covert air-to-ground integrated sensing and communication network with two drones: one source UAV carries the legitimate link and radar, while a second jamming UAV flies as a cooperative jammer. The paper's central claim is that the jammer's artificial noise can do double duty—confuse the ground warden's detector and illuminate ground targets for the source UAV's hybrid monostatic-bistatic radar—so that jointly optimizing both drones' trajectories and beamformers yields a higher average covert rate and better sensing than single-drone or fly-hover-fly designs. The authors formulate a non-convex average covert rate maximization problem under covertness, sensing, power, and mobility constraints, and solve it by block coordinate descent with trust-region successive convex approximation and semidefinite relaxation. If the claim holds, cooperative jamming in this setting need not cost sensing capability: the same waveform that hides the communication also feeds the radar.","feed_headline":"A jamming UAV can lift covert rate and sensing together","feed_subtitle":"Co-designing two drone paths and beams turns artificial noise into a radar illumination signal.","key_machinery":"The load-bearing object is the distance-normalized beampattern sum-gain, which measures the sensing power arriving at each ground target from both the source UAV and the jamming UAV, normalized by squared slant distances. This quantity couples the jamming beamformer into the sensing constraint and turns the jammer's artificial noise into a sensing resource. The covertness requirement is expressed through a Kullback-Leibler divergence bound derived from the warden's Neyman-Pearson detector, rewritten as a linear inequality in the source beamformer, jamming beamformer, and sensing covariance. The optimization is carried by block coordinate descent over the source trajectory, jammer trajectory, and beamformers, with trust-region successive convex approximation handling the non-concave trajectory subproblems and semidefinite relaxation with a nuclear-norm penalty enforcing the rank-one beamformer structure. Sensing-location selection is a greedy weighted-distance minimization that chooses time slots where the drones are close to both the user and the targets.","core_discovery":"The paper asserts that a dual-UAV configuration, where the source UAV transmits a dual-functional waveform and the jamming UAV transmits artificial noise, can enhance covertness and sensing simultaneously. The artificial noise is included in the sensing beampattern gain, effectively forming a hybrid monostatic-bistatic radar in which the source UAV receives both its own target-echoed waveform and the jammer's scattered noise. The design maximizes the time-averaged covert rate from the source UAV to the ground user while keeping the warden's minimum detection error probability above a required level and the distance-normalized beampattern sum-gain toward each target above a sensing threshold. Imperfect successive interference cancellation at the user is modeled through residual interference levels, which the simulations show degrade the covert rate. The numerical results indicate that the co-designed scheme achieves the highest average covert rate and sensing gain among the compared schemes, and that these gains increase with the number of antennas and with a looser covertness requirement.","pith_inferences":["A natural extension is to optimize the jammer's artificial noise covariance as a full-rank matrix rather than a single rank-one beam, which could confuse the warden more effectively while adding spatial diversity to the sensing illumination. ","The greedy sensing-slot selection assumes an equal number of slots per target and static target positions; unequal target priorities or moving targets would require an online variant of the weighted-distance minimization. ","Because the covertness guarantee is built on a lower bound of the detection error probability rather than the exact minimum, the design is conservative, and the actual detection probability may be even lower than the constraint suggests. ","The same hybrid monostatic-bistatic idea could apply to passive sensing scenarios where the jamming UAV illuminates targets without receiving echoes, provided synchronization and clock-offset effects are modeled."],"forward_implications":["Covert integrated sensing and communication can use a second UAV as a jammer without sacrificing sensing, because the artificial noise wave is also a radar illumination signal. ","Jointly optimizing trajectories and beamformers outperforms fly-hover-fly trajectories even when those trajectories are followed by optimized beams. ","The proposed scheme maintains a positive average covert rate at high sensing thresholds where the fly-hover-fly benchmarks drop to zero, so sensing constraints need not eliminate covert communication. ","Imperfect successive interference cancellation is a first-order performance factor: better SIC quality directly increases the achievable covert rate. ","Increasing the number of antennas on the UAVs improves both the average covert rate and the sensing performance under the co-designed scheme. ","The simulation results show that the dual-UAV cooperative design achieves a higher average covert rate than the single-UAV scheme across the tested covertness and residual-interference ranges."],"supporting_citations":[{"why":"Supplies the transmit beampattern gain derivation and the joint maneuver-beamforming design that the paper's sensing metric and Eq. (35) build on.","marker":"[10]"},{"why":"Provides the single-UAV covert ISAC trajectory and beamforming baseline that this work extends to a dual-UAV architecture with cooperative jamming.","marker":"[16]"},{"why":"Establishes covert wireless communication with artificial noise generation, the basis for using the jammer's AN to confuse the warden.","marker":"[21]"},{"why":"Shows how distributed cooperative jamming aids covertness over fading channels, supporting the dual-UAV jamming design.","marker":"[22]"},{"why":"Defines the multiwaveform multiband hybrid multistatic radar model that the paper adapts into its monostatic-bistatic sensing formulation.","marker":"[27]"},{"why":"Provides the hybrid bistatic-monostatic radar technique for combining echoes from two separate transmitters at one receiver.","marker":"[28]"},{"why":"Supplies the successive interference cancellation model whose residual interference terms appear in the user's signal-to-interference-plus-noise ratios.","marker":"[34]"},{"why":"Gives the Neyman-Pearson detection formulation used to derive the warden's minimum detection error probability and the Kullback-Leibler divergence covertness constraint.","marker":"[35]"}],"fun_headline_variants":["Jamming drone turns noise into covert sensing signal","Dual drones boost covert comms and sensing at once","Artificial noise becomes radar aid for covert UAV link","Co-designing two UAV paths lifts covert rate and radar","Dual-UAV scheme makes jamming noise sense targets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The trust-region successive convex approximation assumes that the first-order Taylor expansions in Eqs. (37) and (42) are valid lower and upper bounds for the rate and covertness functions of the UAV positions, but the paper does not establish the needed convexity or concavity; if those bounds fail, the optimized trajectories may not increase the average covert rate and Algorithm 1 may not converge.","fun_headline_variants_meta":{"raw":{"variants":["Jamming drone turns noise into covert sensing signal","Dual drones boost covert comms and sensing at once","Artificial noise becomes radar aid for covert UAV link","Co-designing two UAV paths lifts covert rate and radar","Dual-UAV scheme makes jamming noise sense targets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000232,"raw_usage":{"total_tokens":1529,"prompt_tokens":1026,"completion_tokens":503,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":642,"completion_tokens_details":{"reasoning_tokens":426}},"tokens_in":642,"tokens_out":503,"duration_ms":4907,"temperature":1.0,"reasoning_tokens":426,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:02:28.524007+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1 on a small instance, say ten time slots and two targets, from many random initial trajectories and check whether the surrogate value at each iteration bounds the true objective and whether all runs converge to the same average covert rate; alternatively, evaluate the inequalities in Eqs. (37) and (42) on a grid of UAV positions to find any point where the alleged lower bound exceeds the true rate or the alleged upper bound falls below the true covertness term.","supporting_citations":[{"cited_title":"Joint maneuver and beamformin g design for UA V-enabled integrated sensing and communication,","cited_arxiv_id":null,"evidence_quote":"Supplies the transmit beampattern gain derivation and the joint maneuver-beamforming design that the paper's sensing metric and Eq. (35) build on."},{"cited_title":"Joint beamforming and UA V trajectory optimization for covert communications in ISAC networks,","cited_arxiv_id":null,"evidence_quote":"Provides the single-UAV covert ISAC trajectory and beamforming baseline that this work extends to a dual-UAV architecture with cooperative jamming."},{"cited_title":"Covert wireless communi- cation with artificial noise generation,","cited_arxiv_id":null,"evidence_quote":"Establishes covert wireless communication with artificial noise generation, the basis for using the jammer's AN to confuse the warden."},{"cited_title":"Wireless covert communications aided by distributed cooperative jamming over slow fading c hannels,","cited_arxiv_id":null,"evidence_quote":"Shows how distributed cooperative jamming aids covertness over fading channels, supporting the dual-UAV jamming design."},{"cited_title":"Improved targ et localization in multiwaveform multiband hybrid multistatic radar netwo rks,","cited_arxiv_id":null,"evidence_quote":"Defines the multiwaveform multiband hybrid multistatic radar model that the paper adapts into its monostatic-bistatic sensing formulation."},{"cited_title":"A hybrid bistaticmonosta tic radar tech- nique for calibration-free estimation of lossy wall parame ters,","cited_arxiv_id":null,"evidence_quote":"Provides the hybrid bistatic-monostatic radar technique for combining echoes from two separate transmitters at one receiver."},{"cited_title":"Bidirectional integrated sensing and commu- nication: Full-duplex or half-duplex?","cited_arxiv_id":null,"evidence_quote":"Supplies the successive interference cancellation model whose residual interference terms appear in the user's signal-to-interference-plus-noise ratios."},{"cited_title":"Active RIS-aided covert communications for MISO-NOMA systems,","cited_arxiv_id":null,"evidence_quote":"Gives the Neyman-Pearson detection formulation used to derive the warden's minimum detection error probability and the Kullback-Leibler divergence covertness constraint."}],"review_version":1}