{"id":"4755385c-b3bd-44fe-b21f-22f321919327","arxiv_id":"2506.20970","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A multi-UAV co-design algorithm jointly optimizes association, power, and positions to trade off LQR control cost and Fisher-information sensing accuracy under finite blocklength.","lead":"This paper proposes a joint optimization framework for multi-UAV networks that perform communication, sensing, and control simultaneously under finite-blocklength transmission. It jointly optimizes UAV-robot assignment, transmit power, and 3D UAV positions to balance control stability (LQR cost) against target-localization accuracy (Fisher information).","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The penalty-DC association update in Algorithm 1 is internally inconsistent: Eq. (44)'s linearized constraint has a left-hand side that can be negative and excludes the binary solution, so the AO convergence claim is unsupported.","rationale":"The reader's stated weakest assumption is the tightness of the rate-LQR bound in Eqs. (13)–(14), which affects Proposition 1. I agree that is a real modeling risk: taking the necessary condition at equality yields a proxy for the LQR cost rather than the true cost if the Kostina–Hassibi bound is not tight. However, the more decisive and internally checkable defect is in the association subproblem: Eq. (44) is not a correct linearization, the claim about its LHS is false, and the penalty in Eq. (45) does not correspond to the intended DC penalty. This is an internal inconsistency, not a questionable modeling choice, and it directly disables Algorithm 1 and therefore the AO convergence argument. The reader's rationale did mention this error, so I partially agree, but I place it as the single most load-bearing concern rather than the rate-LQR bound. A corrected version might rehabilitate the paper if it replaces Algorithm 1 with a valid DC or penalty method and re-runs the simulations; as written, the central claim that the proposed algorithm efficiently solves the joint SC2 problem is not supported.","tokens_in":20285,"tokens_out":3963,"duration_ms":46906,"concrete_test":"Run Algorithm 1 on the minimal instance M=1, K=1 with fixed p and q_m, starting from θ^(0)=0.5. First verify Eq. (44) at θ=0: the LHS is −0.25, disproving the claim that it cannot be negative. Then check whether the binary solution θ=1 satisfies Eq. (44): the LHS is 0.75 > 0, so the linearized constraint excludes the only feasible assignment. This shows the surrogate changes the feasible set. Also compute the penalty in Eq. (45) at θ=0.5 and compare with the intended penalty μΣ(θ−θ²): the values are 0.75μ and 0.25μ, respectively, so the objective is not a valid DC approximation. If Algorithm 1 still converges, it is not to a solution of problem (38).","verdict_should_be":"REJECT","load_bearing_attack":"Section 4.1, Eqs. (43)–(46), contains a load-bearing error that invalidates Algorithm 1 as a solver for the association subproblem. The intended DC constraint is sum_{m,k}(θ_{m,k} − θ_{m,k}^2) ≤ 0. The paper linearizes the concave term −Σθ² using a first-order Taylor expansion, but the resulting constraint (44), Σ[(θ^(t))² + 2θ^(t)(θ − θ^(t))] ≤ 0, is not a valid surrogate for the DC constraint. Its LHS can be negative: for M=K=1 with θ^(t)=0.5 and θ=0, the LHS equals −0.25, contradicting the paper's statement that the LHS cannot be smaller than 0. More seriously, at the binary solution θ=1 with θ^(t)=0.5, the LHS equals 0.75 > 0, so the desired binary point is infeasible for the linearized constraint. The penalty term φ(Θ) in (46) is then the same linearized quantity multiplied by μ, not the standard DC penalty μΣ(θ−θ²); it can be negative and does not drive variables to {0,1} while preserving the assignment constraints (38b)–(38c). Since Algorithm 1 is the first block of the AO loop, the monotonic-descent proof in Eqs. (56)–(59) assumes an exact or improved solution of subproblem (38), which this algorithm does not provide. The central claim of a near-optimal solution to problem (33) therefore rests on an invalid subroutine.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies co-design of sensing, communication, and control (SC2) in a multi-UAV low-altitude network with finite blocklength transmission. UAVs send observations to robots over ISAC links while also localizing a target. The paper formulates a weighted optimization problem (33) that jointly minimizes a sum of infinite-horizon LQR control costs and maximizes the determinant of the Fisher information matrix for the target, subject to association, power, collision-avoidance, and flight-boundary constraints. A closed-form expression for the LQR cost as a function of the remaining variables is derived in Proposition 1, and the non-convex problem is attacked by alternating optimization: penalty-based DC programming for UAV-robot association (Algorithm 1), projected gradient descent for power allocation (Algorithm 2), and SCA for UAV positions (Algorithm 3). The paper claims monotonic convergence of the AO loop and supports the method with simulations showing trade-offs between control and sensing.","tokens_in":20565,"tokens_out":13265,"duration_ms":142302,"significance":"The problem is timely and relevant: integrating control-loop requirements with ISAC resource allocation under finite blocklength is an important direction for 6G and UAV-enabled IoT. The closed-form LQR-cost derivation in Proposition 1 is algebraically clean, and the FIM-based localization metric follows standard estimation theory. However, the paper's central algorithmic contribution is invalidated by a fundamental error in the DC-programming association step, and the convergence proof relies on assumptions that the proposed algorithms do not guarantee. Because these issues affect the main claim of a near-optimal AO solution, the contribution as submitted cannot be considered sound.","major_comments":[{"comment":"The DC penalty method for the association subproblem is internally inconsistent. The intended DC constraint (43c) is Σ(θ_{m,k} - θ_{m,k}^2) ≤ 0. The correct first-order linearization of the concave term -Σθ^2 around θ^(t1) gives Σ[θ_{m,k} - (θ^(t1)_{m,k})^2 - 2θ^(t1)_{m,k}(θ_{m,k} - θ^(t1)_{m,k})] ≤ 0. Equation (44) instead writes Σ[(θ^(t1)_{m,k})^2 + 2θ^(t1)_{m,k}(θ_{m,k} - θ^(t1)_{m,k})] ≤ 0, which drops the necessary Σθ term and has the wrong sign. The statement that 'the LHS of (44) cannot be smaller than 0' is false: for M=K=1, θ^(t1)=0.5 and θ=0, the LHS equals -0.25. Moreover, at the binary point θ=1, the LHS equals 0.75, so the desired binary solution is infeasible for the linearized constraint. Consequently, the penalty term φ(Θ) in (46) is not the standard DC penalty μΣ(θ-θ^2); it can be negative and does not drive Θ to {0,1} while preserving the assignment constraints. Algorithm 1 therefore does not solve problem (38), and the monotonic-descent proof in Eqs. (56)-(59) is unsupported.","section":"4.1, Eqs. (43)-(46)"},{"comment":"The convergence inequality (57) requires that the power update strictly improves or preserves the objective value: δ1(p(t-1), Θ(t), q(t-1)) ≥ δ2(p(t), Θ(t), q(t-1)). The paper claims problem (47) is 'optimally solved' by projected gradient descent, but the objective ϕ(p) in (48) is non-convex and no convexity property is established. Projected gradient methods for non-convex objectives converge only to stationary points under suitable step-size conditions (e.g., sufficient decrease or Armijo backtracking); the ad-hoc update ρ ← ρ/‖∇ϕp‖ in Algorithm 2 does not guarantee objective decrease at each iteration. Thus the inequality (57), and hence the AO monotonic convergence claim, is not justified.","section":"4.2, Eq. (57) and Algorithm 2"},{"comment":"The SCA step for UAV positions also lacks a valid surrogate. Equation (54) defines ψ as a first-order Taylor expansion of ϕ({q_m}) at q^(t2)_m. For SCA to guarantee a non-increasing objective, the surrogate must be a global upper bound (or at least satisfy the standard SCA conditions of matching value and gradient and dominating the original function appropriately). For a general non-convex function like ϕ({q_m}), the first-order Taylor approximation is not a global upper bound, and the paper provides no argument that minimizing ψ decreases the original objective. Therefore the inequality (58) and the overall convergence proof are unsupported.","section":"4.3, Eq. (54) and Algorithm 3"},{"comment":"The rate-LQR bound from [27] is a necessary condition: to achieve a desired LQR cost b_k, the received data throughput must satisfy (13), with L_k given in (14). The paper takes this inequality at equality to obtain the closed-form b_k* in Eq. (34), effectively inverting the bound. Since the bound is only necessary and no achievability result is cited or proved, b_k* is a lower bound on the achievable LQR cost rather than an exact expression. The objective of problem (37) therefore optimizes a proxy, and the paper's repeated claims of minimizing the 'optimal LQR cost' should be qualified. This should be stated explicitly, or an achievability argument must be provided.","section":"3, Eqs. (13)-(14) and Proposition 1"}],"minor_comments":[{"comment":"There are several LaTeX spacing artifacts in the author block and running text, e.g., 'Y uan' instead of 'Yuan'.","section":"Throughout"},{"comment":"The x-axis label in Fig. 7 is 'Power constraint (W)', while the other figures use dBW; the units should be consistent and clarified.","section":"Fig. 7"},{"comment":"The normalization constants Ψc and Ψs are introduced as upper bounds of Σ b_k and det Φs, but their actual values (30 and 12 in simulations) appear to be arbitrary; the paper should explain how they are chosen or calibrated.","section":"Eqs. (33a), (37a)"},{"comment":"The step-size rule ρ ← ρ/‖∇ϕp‖ is unusual and not a standard line search; as written, it is dimensionally inconsistent and may not yield descent. A proper line search or a fixed step size with a Lipschitz condition would be preferable.","section":"Algorithm 2, step 5"},{"comment":"The proof assumes that Algorithm 1 returns the global optimum of problem (38). Since Algorithm 1 solves a penalized linearized problem, this assumption is not met even in principle; the inequality in (56) should be justified with respect to the actual output of Algorithm 1.","section":"Convergence proof, Eq. (56)"},{"comment":"The RMSE results in Fig. 7 are from a Monte Carlo simulation with 100 trials, but no error bars or statistical significance information is reported; adding them would improve the credibility of the comparison.","section":"Section 5"}],"recommendation":"reject","confidential_remarks":"The paper contains a clear algebraic error in the DC-programming step (Eqs. (44)-(46)) that invalidates Algorithm 1, and the convergence analysis assumes properties that the proposed algorithms do not provide. The rate-LQR bound is also treated as tight without an achievability justification. While the problem formulation and the closed-form LQR expression are promising, the manuscript would require a substantial redesign of the association algorithm, a rigorous convergence analysis for all three subproblems, and a clear statement of the proxy nature of the control objective before it could be considered acceptable. The paper also leans heavily on self-citations for simulation parameters, which is not problematic per se but should be scrutinized during a resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper has a good problem and a clean closed-form step, but the association subproblem is solved by a penalty-DC step that is wrong as written, and that error sits under the entire AO convergence claim.\n\nWhat is actually new: nobody has formulated joint sensing-communication-control for multi-UAV low-altitude networks under finite blocklength quite like this. The FIM expression, the LQR rate-cost inversion in Prop. 1, and the three-block AO decomposition are a legitimate new application. The simulations show the expected trade-offs and converge in a few iterations. The algebra in Prop. 1 is clean, and the derivation of the closed-form b* is straightforward once you accept the rate-LQR bound.\n\nThe soft spots: the central flaw is in Section 4.1. The DC constraint is Σ(θ-θ²) ≤ 0. The linearization of the concave part should put the linear term outside the squared term; Eq. (44) instead writes Σ[(θ^(t1))² + 2θ^(t1)(θ-θ^(t1))] ≤ 0, which is the linearization of Σθ², without the original θ term and with the wrong sign. The claimed property that the LHS cannot be smaller than 0 is false: at θ^(t1)=0.5 and θ=0, the LHS is -0.25, and at θ=1 it is +0.75, so the binary solution is excluded. Since the penalty term φ(Θ) in (46) is the same expression, it can be negative and will not push the variables to {0,1} while respecting the assignment constraints. Algorithm 1 is the first block of the AO loop, so the monotone-descent proof in (56)-(59) rests on a subroutine that does not actually optimize (38) as claimed.\n\nA second, softer concern is that the rate-LQR bound from [27] is treated as tight when deriving b* in Prop. 1. The bound is a lower bound on rate for a given cost; taking it at equality is an approximation that the paper does not justify. This is probably acceptable as a design heuristic, but it should be stated.\n\nThe SCA step in Section 4.3 also lacks a convergence argument, and the sensing-only benchmark is handicapped by giving it half the power budget. These are minor relative to the DC error.\n\nWho this is for: researchers working on UAV-ISAC resource allocation will get the formulation and the trade-off plots, but they should not rely on the algorithm as written. The paper deserves a serious referee because the problem is relevant and the error is fixable; with a corrected DC linearization and a proper convergence argument, it could be a solid contribution.\n\nRecommendation: send it out for review with the expectation of major revision, or desk-reject with an invitation to resubmit. The current version's central algorithm is not supported.","headline":"Clean formulation, flawed solver: the DC linearization in Algorithm 1 is wrong as written, and the AO convergence claim rests on it.","tokens_in":21187,"tokens_out":3402,"would_cite":false,"duration_ms":33955,"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":"The paper claims that the joint optimization of sensing, communication, and control for multi-UAV low-altitude networks can be reduced to a single weighted objective by deriving a closed-form expression for the optimal LQR control cost…","keywords":["low-altitude wireless networks","UAV networks","integrated sensing and communication","finite blocklength","LQR control cost","Fisher information matrix","target localization","alternating optimization"],"falsifier":"Simulate the full closed loop with the optimized associations, powers, and positions, apply the designed finite-blocklength rates to the robot controllers, and measure the empirical infinite-horizon LQR cost; if it exceeds the closed-form $b_k^*$ of Eq. (34) beyond numerical tolerance, the rate-LQR bound is only a necessary condition and the optimized solution is a proxy.","tokens_in":20011,"feed_emoji":"🚁","tokens_out":11174,"duration_ms":106332,"temperature":0.7,"pith_summary":"This paper works out a way to co-design sensing, communication, and control for a fleet of drones hovering over robots and a hidden target. Its central claim is that the control side of the problem can be collapsed into a closed-form expression: for fixed drone-robot assignments, transmit powers, and drone positions, the optimal linear-quadratic-regulator (LQR) control cost is $b_k^* = \\iota (\\det N_k M_k)^{1/\\iota}/(2^{f_k} - 1) + (b_k)_{\\min}$, where $f_k$ grows with the finite-blocklength data rate. With that closed form, the problem becomes a weighted trade-off between the LQR cost and the localization accuracy measured by the determinant of the Fisher information matrix, solved iteratively via alternating optimization. The simulations indicate that the resulting algorithm converges quickly and lets a single weighting factor shift drones between serving robots and surrounding the sensing target.","feed_headline":"One formula links drone control, sensing, and data rate","feed_subtitle":"A single algorithm tunes drone positions, power, and scheduling to stabilize robots while locating a target.","key_machinery":"The load-bearing object is the rate-LQR cost bound of [27], Eqs. (13)–(14): to keep robot $k$'s LQR cost at or below $b_k$, the received throughput must satisfy $B\\sum_m \\theta_{m,k}R_{m,k} \\ge g_k + \\frac{\\iota}{2}\\log\\!\\bigl(1 + \\frac{\\iota(\\det N_k M_k)^{1/\\iota}}{b_k - (b_k)_{\\min}}\\bigr)$. Because the right side is monotonically decreasing in $b_k$, the paper can invert the constraint at equality to obtain the closed-form optimal cost $b_k^*$ of Proposition 1, which then carries all control information through the optimization. Sensing enters through the determinant of the Fisher information matrix $\\det \\Phi_s$ built from the UAV-to-target geometry and power-scaled noise, and finite-blocklength transmission enters through the rate expression $R_{m,k} = \\log(1+\\Gamma_{m,k}) - \\sqrt{V_{m,k}/l_{m,k}}\\,Q^{-1}(\\epsilon)$ of [32].","core_discovery":"The paper's central claim is Proposition 1: given any UAV-robot associations $\\Theta$, transmit powers $\\mathbf{p}$, and UAV positions $\\{\\mathbf{q}_m\\}$, the optimal infinite-horizon LQR cost for robot $k$ is exactly $b_k^* = \\iota(\\det N_k M_k)^{1/\\iota}/(2^{f_k}-1) + (b_k)_{\\min}$, with $f_k = (2/\\iota)(B\\sum_m \\theta_{m,k} R_{m,k} - g_k)$. The expression is obtained by taking the rate-LQR cost constraint (33i) at equality, which is valid because the required rate $L_k$ decreases monotonically as $b_k$ rises. Substituting this closed form into the joint problem reduces the non-convex, mixed-integer program (33) to minimizing a weighted sum of the LQR cost and the inverse of the Fisher information determinant $\\det \\Phi_s$, and the paper claims the alternating-optimization algorithm — DC programming for association, projected gradient descent for power, and successive convex approximation for positions — converges to a near-optimal solution.","pith_inferences":["Treating blocklength as a fourth design variable is the paper's own flagged future direction; the closed form makes that extension immediate because $b_k^*$ is monotone in $R_{m,k}$, hence in $l_{m,k}$.","The inversion recipe generalizes: any control cost with a tight rate-cost bound could be substituted for the LQR cost in the same alternating-optimization framework, making the co-design approach a template for other cost functions.","The assumption that each robot is served by exactly one UAV could be relaxed: the closed form depends on the aggregate rate $\\sum_m \\theta_{m,k} R_{m,k}$, so cooperative multi-UAV transmission to a single robot fits the same formula with a generalized association constraint."],"forward_implications":["If the closed-form LQR cost is exact, then the joint SC2 problem (33) is equivalent to a weighted objective in $\\Theta$, $\\mathbf{p}$, and $\\{\\mathbf{q}_m\\}$ alone, and the alternating algorithm's monotone decrease in that objective is a genuine performance guarantee.","Longer blocklength $l_{m,k}$ improves throughput and therefore control cost, but the benefit saturates at the unconstrained minimum $(b_k)_{\\min}$, so the model predicts a regime where extra communication resources no longer help the control loop.","Varying the weighting factor $\\eta$ continuously repositions the UAVs between the robots and the sensing target, with the CRB for target localization changing more sharply than the LQR cost, an asymmetry visible in Fig. 8.","The closed form also lets the algorithm adapt to different power budgets and observation-noise levels: increasing power reduces LQR cost down to $(b_k)_{\\min}$, while worse observation noise raises the floor and cannot be fully compensated by communication power."],"supporting_citations":[{"why":"Provides the rate-LQR cost bound (13)–(14) that Proposition 1 inverts into the closed-form optimal control cost.","marker":"[27]"},{"why":"Supplies the finite-blocklength rate expression (7) used in the communication constraint and in $f_k$.","marker":"[32]"},{"why":"Gives the Fisher information and Cramér–Rao bound formulas used to build $\\det \\Phi_s$ for target localization.","marker":"[40]"},{"why":"Supplies the sensing-noise model $\\sigma_m^2$ and the constant $\\rho$ used in the FIM entries.","marker":"[20]"},{"why":"Provides the DC programming method used to solve the UAV-robot association subproblem.","marker":"[41]"},{"why":"Provides the projected gradient descent method used for the power allocation subproblem.","marker":"[43]"},{"why":"Provides the successive convex approximation framework used for the UAV position subproblem.","marker":"[44]"},{"why":"Establishes the control-oriented optimization setting and the assuredly stable throughput regime the paper adopts.","marker":"[28]"}],"fun_headline_variants":["Closed-form LQR cost unlocks joint drone SC2 design","Drone networks: one formula ties control, sensing, rate","UAV co-design: LQR closed form simplifies SC2 optimization","Closed-form control cost eases joint UAV SC2 design","A single formula reduces UAV SC2 co-design complexity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the rate-LQR cost bound (13)–(14) is tight enough that setting the rate constraint at equality in Proposition 1 yields the true optimal control cost, rather than merely a lower bound that real controllers cannot achieve.","fun_headline_variants_meta":{"raw":{"variants":["Closed-form LQR cost unlocks joint drone SC2 design","Drone networks: one formula ties control, sensing, rate","UAV co-design: LQR closed form simplifies SC2 optimization","Closed-form control cost eases joint UAV SC2 design","A single formula reduces UAV SC2 co-design complexity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000689,"raw_usage":{"total_tokens":3183,"prompt_tokens":1067,"completion_tokens":2116,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":2033}},"tokens_in":683,"tokens_out":2116,"duration_ms":19073,"temperature":1.0,"reasoning_tokens":2033,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:38:41.289203+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the full closed loop with the optimized associations, powers, and positions, apply the designed finite-blocklength rates to the robot controllers, and measure the empirical infinite-horizon LQR cost; if it exceeds the closed-form $b_k^*$ of Eq. (34) beyond numerical tolerance, the rate-LQR bound is only a necessary condition and the optimized solution is a proxy.","supporting_citations":[{"cited_title":"Rate-cost tradeoffs in cont rol,","cited_arxiv_id":null,"evidence_quote":"Provides the rate-LQR cost bound (13)–(14) that Proposition 1 inverts into the closed-form optimal control cost."},{"cited_title":"Channel coding rate in the finite blocklength regime,","cited_arxiv_id":null,"evidence_quote":"Supplies the finite-blocklength rate expression (7) used in the communication constraint and in $f_k$."},{"cited_title":"Fundamentals of statistical signal processi ng: Estima- tion theory ,","cited_arxiv_id":null,"evidence_quote":"Gives the Fisher information and Cramér–Rao bound formulas used to build $\\det \\Phi_s$ for target localization."},{"cited_title":"ISAC from the sk y: UA V trajectory design for joint communication and target local ization,","cited_arxiv_id":null,"evidence_quote":"Supplies the sensing-noise model $\\sigma_m^2$ and the constant $\\rho$ used in the FIM entries."},{"cited_title":"Cognitive U A V communication via joint maneuver and power control,","cited_arxiv_id":null,"evidence_quote":"Provides the successive convex approximation framework used for the UAV position subproblem."},{"cited_title":"Control-orien ted power allocation for integrated satellite-UA V networks,","cited_arxiv_id":null,"evidence_quote":"Establishes the control-oriented optimization setting and the assuredly stable throughput regime the paper adopts."}],"review_version":1}