{"id":"6788b067-9a37-4a96-b74c-dc8aa6c78d15","arxiv_id":"2506.13137","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"An iterative optimization algorithm jointly schedules user offloading, user access, radar beamforming, and drone trajectory to minimize ground-user energy consumption in a secure UAV-aided ISCC system.","lead":"This paper designs a drone's flight path, user scheduling, offloading decisions, and radar beam pattern to serve ground users while jamming a suspected eavesdropper, aiming to minimize the total energy used by user devices. It shows how standard optimization tools can be applied to a secure integrated sensing, communication, and computing scenario for 6G networks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The convexity claim underpinning the trajectory subproblem (Section III-D) is false, so the SCA reformulation of P4.2 and the convergence proof are not established.","rationale":"The paper's core claim is that the proposed alternating optimization algorithm solves the original problem by successively solving convex subproblems, with P4.2 being the trajectory subproblem. The weakest assumption is precisely the convexity of d_sk^{-2}[n] and Z1[n] d_se^{-4}[n] used in Section III-D. The reader correctly identifies that these functions are not convex: 1/(||q - q_k||^2 + H^2) has an indefinite Hessian, and the same is true for 1/(||q - q_e||^2 + H^2)^2. This is not a cosmetic oversight; it invalidates the claim that P4.2 is a convex problem and consequently undermines the SCA inner-approximation argument and the convergence proof of Algorithm 1. Other issues, such as the statistical approximation of the wiretap SINR in equation (12) and the freezing of steering vectors during trajectory optimization, are secondary because the trajectory subproblem's convexity is the explicit foundation for the algorithm's theoretical guarantee. The proposed concrete test is a direct Hessian computation plus a CVX feasibility check, which would settle whether the concern lands. Since the reader's verdict of CONDITIONAL already accounts for this load-bearing gap, my stress-test does not alter the verdict; it reinforces the need for the authors to correct or restructure the trajectory subproblem before the paper can be accepted.","tokens_in":19347,"tokens_out":4385,"duration_ms":41256,"concrete_test":"Compute the Hessian of f(q) = 1/(||q - q_k||^2 + H^2) and g(q) = Z1/(||q - q_e||^2 + H^2)^2 at two sample points, for example q = q_k + (1,0)^T and q = q_k + (1,1)^T, with H = 0 and H = 50 m. If either Hessian has a negative eigenvalue, the convexity assertion in Section III-D is false. Then feed constraints (39), (40), and (41) with fixed Z1 into CVX and check whether the solver accepts them as a disciplined convex program; if the model is rejected, or the iterates of Algorithm 1 fail to converge when initialized at a feasible point, P4.2 is not convex as claimed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The trajectory subproblem P4.2 is claimed to be convex, and this claim rests on the assertion in Section III-D that d_sk^{-2}[n] and Z1[n] d_se^{-4}[n] are convex functions of the UAV trajectory q_s[n]. That assertion is false. The function f(q) = 1/(||q - q_k||^2 + H^2) has an indefinite Hessian over its domain: for H = 0, the Hessian is (2/||q - q_k||^4) * (4(q - q_k)(q - q_k)^T - ||q - q_k||^2 I), whose eigenvalues are 6/||q - q_k||^4 (along q - q_k) and -2/||q - q_k||^4 (orthogonal to q - q_k). For H > 0, the Hessian remains indefinite when ||q - q_k||^2 < H^2 and also has a negative eigenvalue along directions orthogonal to q - q_k. Similarly, g(q) = Z1/(||q - q_e||^2 + H^2)^2 is not convex; for H = 0 its Hessian is (4/||q - q_e||^6) * (3(q - q_e)(q - q_e)^T - ||q - q_e||^2 I), which is indefinite. Consequently, constraint (40) is not a convex constraint as written, and the Taylor-based surrogate (41) does not produce a valid convex inner approximation for (39). Since P4.2 is the only subproblem whose convexity is supposed to be established through these two functions, the proof in Section III-E that the objective is non-increasing after each iteration (equation 53) does not follow. The numerical results may still be reproducible, but the paper does not establish the algorithmic guarantee it claims.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a secure UAV-aided integrated sensing, communication, and computing (ISCC) system. A UAV equipped with a uniform planar array serves as an aerial edge server, transmits radar sensing signals to localize and jam a potential eavesdropper with uncertain location, and receives partial offloading from ground users. The total user energy consumption is minimized by jointly optimizing the offloading ratio, user scheduling, transmit beamforming, and UAV trajectory, subject to secrecy, sensing, propulsion-energy, and computational-delay constraints. The authors propose a block-coordinate-descent algorithm with successive convex approximation, decomposing the problem into four subproblems: an offloading-ratio LP, a user-scheduling LP, a beamforming SDP, and a trajectory SCA problem. Numerical results over three geometric scenarios show convergence and lower energy consumption than three benchmark schemes.","tokens_in":19768,"tokens_out":14171,"duration_ms":163016,"significance":"If the theoretical guarantees were valid, the paper would be a useful combination of ISCC, UAV trajectory design, and physical-layer security, with a tractable decomposition into convex subproblems. The system model is reasonably rich, including an uncertain eavesdropper region, rotary-wing propulsion energy, and partial computation offloading, and the numerical study covers three distinct user/eavesdropper geometries. However, the paper does not provide reproducible code or machine-checked proofs, and the convergence and optimality guarantees rest on a small number of hand-verified convexity claims. Those claims are incorrect in a load-bearing way: the trajectory subproblem P4.2 is not convex as stated, and the stochastic approximation in Eq. (12) is not a valid expectation approximation. The numerical results may well be reproducible, but they do not by themselves establish the algorithmic guarantees claimed in Sections III-D and III-E. The paper also does not discuss how the relaxed scheduling variables in P2.1 are mapped back to a feasible binary schedule.","major_comments":[{"comment":"The assertion above Eqs. (39)-(40) that d_sk^{-2}[n] and Z1[n]d_se^{-4}[n] are convex functions of the UAV position q_s[n] is false. For f(q)=1/(||q-q_k||^2+H^2), the Hessian is -2I/x^2 + 8(q-q_k)(q-q_k)^T/x^3 with x=||q-q_k||^2+H^2, so its eigenvalue in any direction orthogonal to q-q_k is -2/x^2<0; the function is not convex over its domain. The same indefiniteness holds for Z1/(||q-q_e||^2+H^2)^2. Consequently constraint (40) is not convex, and the first-order Taylor replacement in (41) is not a valid convex inner approximation of (39): for a nonconvex function the tangent is not a global underestimator, so the surrogate may admit points that violate the original constraint. Therefore P4.2 is not a convex problem as claimed, and the convergence step (53) in Section III-E, which depends on the convexity of P4.2 and on the validity of the SCA surrogates, is not established.","section":"Section III-D, Eqs. (39)-(41)"},{"comment":"Equation (12) approximates the random SINR gamma_ek[n] by replacing only the numerator |hek|^2 with its expectation, while the denominator still contains the random variables |hei[n]|^2. This is not an approximation of E[gamma_ek[n]] in general (E[X/Y] is not E[X]/E[Y]), and, more importantly, the resulting expression remains random. Constraint (25i), which uses this expression, is therefore stochastic as written rather than a deterministic worst-case constraint over the eavesdropper location. Since (25i) is inherited by every subproblem that enforces secrecy, this issue affects the feasibility of P0 and the validity of the reported numerical feasibility checks. A consistent treatment would approximate the whole ratio, e.g., by replacing all random channel powers by their means or by using an outage or Jensen-based bound.","section":"Section II-A, Eq. (12)"},{"comment":"The claim that P2.1 is a linear program after relaxing theta_k[n] to [0,1] is inconsistent with the problem as written. The constraints (25h) and (25i) are ratios of affine functions of theta, with theta_r[n]=sum_k theta_k[n] appearing in the denominators through P_ses[n] and hse[n]^H W[n] hse[n]; the objective also includes terms theta_k[n] E_offload_k[n] whose rate Rhat_sk[n] depends on theta_r[n]. These are nonlinear in the relaxed variable. Furthermore, the paper does not describe a rounding or penalty step that recovers a binary schedule from the continuous solution, so the monotonicity argument in (51) for Step 2 is not justified. This is a load-bearing issue because Step 2 is one of the four blocks on which the BCD convergence proof rests.","section":"Section III-B, P2.1"}],"minor_comments":[{"comment":"The text alternates between 'uncrewed' and 'unmanned' aerial vehicle, and the symbol 'UAV' is frequently typeset as 'UA V'; these should be made consistent.","section":"Abstract and throughout"},{"comment":"Constraint (22) multiplies by theta_k[n] a quantity T_offload_k[n] that already contains theta_k[n] by definition (18), producing a quadratic term under the relaxed scheduling variable. For binary theta this is harmless, but it is inconsistent with the LP claim for P2.1 and should be clarified.","section":"Section II-B, Eq. (22)"},{"comment":"The convergence condition in Algorithm 1 writes E(A^(m),...)-E(A^(m-1),...) ≻ epsilon; this should be a scalar inequality, and the loop should specify whether the absolute value or the difference itself is tested.","section":"Section III-E, Algorithm 1"},{"comment":"The rotor solidity entry 's 0.05 m3' appears to have an incorrect unit; solidity is dimensionless.","section":"Table III"},{"comment":"The footnote describing the approximation of random power gains by their expectation is grammatically incomplete and does not state whether Eq. (12) approximates the expectation of the ratio or the ratio of expectations.","section":"Footnote 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on the authors' own recent papers ([31]-[33], [41], [42], [49]) for core modeling and approximation steps. This is not disqualifying, but the cited works should be checked to confirm that they actually justify the approximations used here, especially Eq. (12). The main obstacle to acceptance is technical: the trajectory subproblem's convexity claim is false, and the secure-rate constraints are stochastic as written. These are fixable in principle with a careful reformulation, but the current manuscript does not provide it."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is: the paper has a genuinely new problem combination and a clean presentation, but the main algorithmic guarantee rests on a false convexity claim in Section III-D. The trajectory subproblem P4.2 is not convex as claimed. The functions 1/||q - q_k||^2 and Z1/||q - q_e||^4 have indefinite Hessians over their domains (for any positive altitude), so the assertion that they are convex is wrong. That means the SCA lower bound in (41) is not a valid inner approximation, constraint (40) is not convex as written, and the convergence proof in Section III-E does not follow. This is load-bearing, not cosmetic. The numerical results are therefore not supported by the stated algorithm; CVX would not accept P4.2 as written.\n\nWhat is new: the joint formulation—user scheduling, offloading ratio, sensing beamforming, trajectory—with a worst-case uncertain eavesdropper region is not in the cited prior work, and Table I is a fair comparison. The system model is coherent, and the simulations cover three scenarios with three benchmarks; the convergence plots and the scheduling/rate figures are informative. Credit where due: if the convexity issues were fixed, this would be a useful systems paper for the UAV-aided ISCC subfield.\n\nOther soft spots: Eq. (12) approximates a ratio of random variables by replacing only the numerator with its expectation; the denominator remains random, so the worst-case eavesdropping constraint is a heuristic, not a bound. Section III-B claims P2.1 is an LP, but constraints (25h) and (25i) contain theta in the denominator through theta_r and the interference terms; as written it is not linear. The binary relaxation also produces fractional schedules with no rounding or feasibility argument. These are significant but secondary to the P4.2 issue. The citation pattern looks fine; the self-citations are standard in this area.\n\nBottom line: this is a paper for readers working on secure UAV-aided ISCC. It deserves a serious referee only if the authors can rework the trajectory subproblem and the scheduling subproblem. As submitted, I would not accept. If I were editor, I would not desk-reject it outright; I would send it out with a clear request to fix the math, because the problem is relevant and the empirical setup is careful. After a major revision, it could be acceptable.","headline":"A well-motivated and cleanly presented secure UAV-aided ISCC optimization paper whose central trajectory convexity claim is false, so the proposed algorithm's guarantee does not hold as written.","tokens_in":20262,"tokens_out":10654,"would_cite":false,"duration_ms":120893,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that a single drone can simultaneously provide edge computing, radar sensing, and secure jamming, and that jointly optimizing offloading ratio, scheduling, beamforming, and trajectory minimizes total ground-user energy.","keywords":["integrated sensing communication and computing","ISCC","physical-layer security","UAV trajectory optimization","mobile edge computing","offloading ratio","sensing beamforming","block coordinate descent"],"falsifier":"Compute the Hessian of $f(x,y)=1/((x-x_k)^2+(y-y_k)^2+H^2)$ at a point horizontally offset from the user, say $(x,y)=(1,0)$ with $H=1$; its eigenvalues are $0.5$ and $-0.5$, which is indefinite, showing the claimed convexity fails. The same second-order test applied directly to constraint (39) of the paper settles whether the trajectory subproblem is convex as claimed.","tokens_in":19195,"feed_emoji":"📡","tokens_out":8591,"duration_ms":91758,"temperature":0.7,"pith_summary":"The paper argues that a single drone can serve as an aerial base station, a mobile edge-computing host, and a radar jammer at the same time, and that these roles should be planned jointly rather than separately. Its central claim is that by jointly optimizing the fraction of each user's task that is offloaded, which users are served in each time slot, the radar beamforming weights, and the drone's flight trajectory, the total energy consumed by the ground users is minimized while secure offloading, sensing, and drone-energy constraints are respected. Because the variables are tightly coupled and the problem is non-convex, the paper decomposes it into four subproblems and solves them alternately, using successive convex approximation to turn the non-convex parts into convex ones. Numerical results show the iterative algorithm converging in about ten iterations and producing lower user energy consumption than three fixed-strategy baselines. The contribution, if it holds, is a design principle for secure aerial computing: trajectory, scheduling, offloading, and jamming are one coupled resource-allocation problem.","feed_headline":"Drone radar jams eavesdroppers while cutting user energy","feed_subtitle":"Jointly optimizing offload ratio, scheduling, beamforming, and flight path minimizes ground users' total energy.","key_machinery":"Three named mechanisms carry the argument. Block coordinate descent (BCD) cycles through four subproblems so each variable block is updated while the others are frozen, which makes the objective non-increasing at each step. Successive convex approximation (SCA) replaces non-convex constraints with first-order Taylor expansions around the current iterate; this is applied to the offloading-rate expression, the inverse-distance terms in the secure-rate and sensing constraints, and the propulsion-power function, producing convex subproblems P1.1, P2.1, P3.2, and P4.2. The third mechanism is the sensing beampattern gain $P[n] = a_{\\mathrm{T}}^H[n]\\,W[n]\\,a_{\\mathrm{T}}[n]$, a quadratic form of the beamforming matrix that appears in both the sensing-threshold constraint and the eavesdropper-suppression constraint, thereby coupling beamforming and trajectory design.","core_discovery":"The paper's own claim is that the non-convex central problem, which minimizes total user energy consumption under secure-communication, sensing, and drone-energy constraints, can be solved near-optimally by alternating among four convex subproblems. The offloading proportion is a linear program; user scheduling is a linear program after relaxing binary variables; beamforming is a semidefinite program after dropping the rank-one constraint and recovering it later; and the trajectory subproblem is built from successive convex approximations of rate expressions, inverse-distance terms, and the rotary-wing propulsion model. The paper asserts the resulting objective sequence is non-increasing and bounded below, so the alternating procedure converges, and the simulations display optimized trajectories that stay close to the users while keeping distance from the estimated eavesdropper region. The sensing beam plays a dual role: it provides the radar return for locating the eavesdropper and it suppresses the eavesdropper's signal-to-interference-plus-noise ratio, which is why the secure offloading rate can stay above its threshold.","pith_inferences":["The claimed convexity of the trajectory subproblem should be checked before relying on the numerical gains; a corrected surrogate for the inverse-distance terms, such as a second-order-cone reformulation, would put the successive-convex-approximation step on firmer ground.","The same joint-design logic suggests a testable extension to multiple eavesdroppers or to three-dimensional trajectories: the jamming-versus-service trade-off should become sharper because the drone has more spatial degrees of freedom.","A natural empirical check is to compare the proposed scheme against a greedy scheduling policy in a hardware-in-the-loop testbed; the predicted energy gap should grow as users move closer to the eavesdropper.","The result also implies that sensing quality and communication secrecy are not competing objectives in this setting: the radar signal is itself the jamming signal, so better sensing and better secrecy improve together."],"forward_implications":["Users located close to the eavesdropper can still offload the bulk of their computation, because the radar beam suppresses the eavesdropper's rate instead of forcing local computation.","The optimized trajectory will approach users during their scheduled slots and keep distance from the estimated eavesdropper region, so flight path becomes a security resource as well as a communication resource.","Because the alternating algorithm converges in a handful of iterations, the joint design is computationally cheap enough to re-run as user positions or threat estimates change.","User energy consumption increases with user transmit power and with the number of users, but is nearly insensitive to the size of the eavesdropper-location uncertainty, suggesting the design is robust to imperfect localization."],"supporting_citations":[{"why":"Supplies the adaptive ISAC beamforming-and-trajectory design used as a comparison baseline and as a model for SCA-based trajectory updates.","marker":"[7]"},{"why":"Provides the periodic sensing-and-communication framework whose beampattern-gain sensing metric the paper adopts.","marker":"[9]"},{"why":"Offers a multi-UAV ISAC trajectory, association, and beamforming design used as a Benchmark 3 baseline.","marker":"[12]"},{"why":"Establishes the joint trajectory-and-offloading formulation for multi-UAV ISCC systems that this paper extends with secrecy constraints.","marker":"[23]"},{"why":"Provides the secure UAV-ISAC secrecy-rate formulation and multiple-eavesdropper benchmark for secure trajectory design.","marker":"[27]"},{"why":"Supplies the partial-offloading model and UAV mobile-edge-computing setup for user tasks.","marker":"[31]"},{"why":"Supports the time-slot trajectory model and the approximation of probabilistic LoS channels by a LoS benchmark.","marker":"[32]"},{"why":"Provides the imperfect-eavesdropper-location uncertainty model used for worst-case secrecy constraints.","marker":"[34]"},{"why":"Defines the sensing threshold constraint that the beampattern gain must satisfy.","marker":"[43]"},{"why":"Gives the rotary-wing UAV propulsion power model used for the drone energy constraint.","marker":"[48]"}],"fun_headline_variants":["Drone radar both finds and jams eavesdroppers, saving user power","Radar on drone jams eavesdroppers and trims user energy","Dual-purpose drone radar: sense, jam, and cut user power","How drone radar does double duty: jam eavesdroppers, save energy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the inverse-squared-distance functions used in the secure-rate and sensing constraints are convex functions of the drone's horizontal position, so that the first-order approximations in the trajectory subproblem are valid; the function $1/(\\|q_s-q_k\\|^2+H^2)$ is not actually convex, so the trajectory subproblem's convexity is not established.","fun_headline_variants_meta":{"raw":{"variants":["Drone radar both finds and jams eavesdroppers, saving user power","Radar on drone jams eavesdroppers and trims user energy","Dual-purpose drone radar: sense, jam, and cut user power","How drone radar does double duty: jam eavesdroppers, save energy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000631,"raw_usage":{"total_tokens":2915,"prompt_tokens":950,"completion_tokens":1965,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":566,"completion_tokens_details":{"reasoning_tokens":1885}},"tokens_in":566,"tokens_out":1965,"duration_ms":13831,"temperature":1.0,"reasoning_tokens":1885,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:36:12.005032+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the Hessian of $f(x,y)=1/((x-x_k)^2+(y-y_k)^2+H^2)$ at a point horizontally offset from the user, say $(x,y)=(1,0)$ with $H=1$; its eigenvalues are $0.5$ and $-0.5$, which is indefinite, showing the claimed convexity fails. The same second-order test applied directly to constraint (39) of the paper settles whether the trajectory subproblem is convex as claimed.","supporting_citations":[{"cited_title":"Beamforming design and trajectory optimization for UA V-empowered adaptable integrated sensing and com- munication,","cited_arxiv_id":null,"evidence_quote":"Supplies the adaptive ISAC beamforming-and-trajectory design used as a comparison baseline and as a model for SCA-based trajectory updates."},{"cited_title":"Throughput maximization for UA V-enabled integrated periodic sensing and commu- nication,","cited_arxiv_id":null,"evidence_quote":"Provides the periodic sensing-and-communication framework whose beampattern-gain sensing metric the paper adopts."},{"cited_title":"A joint UA V trajectory, user association, and beamforming design strategy for multi-UA V-assisted ISAC systems,","cited_arxiv_id":null,"evidence_quote":"Offers a multi-UAV ISAC trajectory, association, and beamforming design used as a Benchmark 3 baseline."},{"cited_title":"Trajectory design and resource allocation for multi-UA V-assisted sensing, communication, and edge computing integration,","cited_arxiv_id":null,"evidence_quote":"Establishes the joint trajectory-and-offloading formulation for multi-UAV ISCC systems that this paper extends with secrecy constraints."},{"cited_title":"Secure rate maximization for ISAC-UA V assisted communication amidst multiple eavesdroppers,","cited_arxiv_id":null,"evidence_quote":"Provides the secure UAV-ISAC secrecy-rate formulation and multiple-eavesdropper benchmark for secure trajectory design."},{"cited_title":"Secure offloading in NOMA-aided aerial MEC systems based on deep reinforcement learning,","cited_arxiv_id":null,"evidence_quote":"Supplies the partial-offloading model and UAV mobile-edge-computing setup for user tasks."},{"cited_title":"Secure intelligent reflecting surface-aided integrated sensing and communica- tion,","cited_arxiv_id":null,"evidence_quote":"Provides the imperfect-eavesdropper-location uncertainty model used for worst-case secrecy constraints."},{"cited_title":"Deep reinforcement learning for online computation offloading in wireless powered mobile-edge computing networks,","cited_arxiv_id":null,"evidence_quote":"Defines the sensing threshold constraint that the beampattern gain must satisfy."},{"cited_title":"Energy minimization for wireless communication with rotary-wing UA V ,","cited_arxiv_id":null,"evidence_quote":"Gives the rotary-wing UAV propulsion power model used for the drone energy constraint."}],"review_version":1}