{"id":"aaebc7b0-faaa-4a45-9b4b-cb06615b8c7e","arxiv_id":"2506.02828","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper derives approximate sensing coverage shapes and a dynamic ranging rate metric for mobile ISAC networks in disasters, but the key formula contradicts the paper's own qualitative claims.","lead":"This paper proposes a stochastic geometry model for a mobile integrated sensing and communication network in disaster zones, where base stations and disaster response vehicles are random points. It introduces a 'dynamic ranging rate' metric to measure sensing continuity, but the derived closed-form expression has an internal error that reverses the predicted effect of pulse interval.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (16) puts τ in the denominator, so the DRR in Eq. (17) increases with PRI, directly contradicting the paper's stated and simulated trend; the dwell-time probability also lacks derivation.","rationale":"The paper's central novelty is the DRR in Eq. (17). Its dependence on PRI is controlled entirely by Eq. (16), since ξr in Eq. (15) is independent of τ. The exponential in Eq. (16) has τ in the denominator, making P(κ ≥ τ) an increasing function of τ; therefore Eq. (17) cannot produce the 'DRR declines as τ increases' trend asserted in Sections IV and V. This is not a disagreement about modeling choices; it is an internal inconsistency in the claimed closed form. The lack of any derivation for Eq. (16) means the error cannot be traced from stated assumptions. The reader's weakest-assumption analysis identifies the same equation, and I agree. I also note that the Case-2 ellipse center depends on an unspecified expansion point (i,j), and the Monte Carlo validation is described only qualitatively, but these are secondary. Because the central claim fails as written, the REJECT verdict stands; the concrete test above would settle whether the fix is simply a typo in Eq. (16) or a deeper modeling error.","tokens_in":6521,"tokens_out":3740,"duration_ms":41459,"concrete_test":"Evaluate Eq. (17) with the Section IV defaults (λv = 2, λb = 1 node/km^2, W from the stated powers and gains, u = 1.4 m/s, E[Ts] = 0.5 s) at τ = 0.01, 0.1, and 1 s. If the analytic curve increases with τ, the formula cannot reproduce the claimed decreasing trend. Additionally, re-derive P(κ > τ) from the RWP dwell-time model: with chord length Lc and κ = Lc/u, P(κ > τ) = P(Lc > uτ), which is monotonically decreasing in τ; compare this with Eq. (16) to locate the sign or placement error.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is the dwell-time exceedance probability in Eq. (16). In Eq. (17) this appears as exp(-C/(u^2 τ^2)) with C = 4λb(1-W)^2/(π W) > 0. For fixed all other parameters, as τ increases, the exponent tends to 0 and P(κ ≥ τ) tends to 1; hence Eq. (17) predicts that the dynamic ranging rate increases monotonically with PRI. This directly contradicts the paper's own statement in Section IV and the Conclusion that DRR declines as τ increases, and it also contradicts the physical definition of P(κ > τ), which must decrease with τ. No derivation or citation is provided for Eq. (16), so this is not an omitted detail but a sign/structural error in the central claimed metric. Since the DRR formula is the main novelty, the validation claim is unsupported as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a stochastic-geometry model for disaster-specific ISAC networks in which base stations and mobile disaster response vehicles (DRVs) are modeled as independent Poisson point processes. It derives closed-form approximations for the DRV sensing area, introduces a new metric called the dynamic ranging rate (DRR) to quantify sensing service continuity, and claims Monte Carlo validation of the analytical expressions. The central result is Eq. (17), which expresses the DRR as a product of a dynamic ranging repetition rate and a dwell-time exceedance probability. The paper concludes that the DRR increases with DRV density and velocity and decreases with the pulse repetition interval.","tokens_in":6812,"tokens_out":5251,"duration_ms":53960,"significance":"The problem addressed is timely and practically relevant, and the use of stochastic geometry to obtain closed-form expressions for coverage and continuity in a mobile ISAC disaster scenario is a reasonable goal. The paper has the positive feature of attempting to quantify a service-continuity metric rather than only instantaneous coverage. However, the central claimed result, the closed-form DRR in Eq. (17), is not sound as written: the dwell-time probability in Eq. (16) has the wrong monotonicity in the pulse repetition interval, and no derivation is supplied for that expression. The Monte Carlo validation described in Section IV cannot support a formula whose behavior contradicts the paper's own stated trend. Since the DRR is the main novel contribution, the paper's central claim is not established.","major_comments":[{"comment":"The dwell-time exceedance probability is stated as P(κ ≥ τ) = exp(-4λb/π · (1-W)^2/(W u^2 τ^2)). For fixed W, λb, and u, this expression is an increasing function of τ and approaches 1 as τ → ∞. This violates the defining property of a survival function and directly contradicts the manuscript's claim in Section IV and the Conclusion that the DRR declines as τ increases. Since Eq. (17) multiplies the other factors by this term, the central DRR metric has the wrong monotonicity in the pulse repetition interval, and the claimed Monte Carlo validation in Figure 3 cannot hold for Eq. (17) as written.","section":"Section III, Eq. (16)"},{"comment":"No derivation or citation supports this expression. The phrase 'by leveraging the stochastic geometry properties of distance distributions in a PPP' is not a derivation: no dwell-time distribution, no coverage-crossing event, and no PPP distance probability density function are given. This matters because Eq. (16) is the load-bearing factor that converts a repetition rate into a continuity probability. A corrected version must be derived from a mobility and coverage model and must be nonincreasing in τ.","section":"Section III, Eq. (16)"},{"comment":"The second-order Taylor expansion of f(x,y) = (x^2+y^2)^αhat is taken at an unspecified point (i,j), and the resulting ellipse parameters in Eqs. (9)-(12) depend on that point. The manuscript never states how (i,j) is chosen, nor gives an error bound or sensitivity analysis. Consequently the Case-2 sensing area and any DRR values built on it are not uniquely determined by the model parameters.","section":"Section II-C, Eq. (8)"},{"comment":"The claimed MMSE solution β = d_v^{2(αhat-1)} is not the minimizer of the stated squared-error integral. Minimizing ∫_0^{d_v} (r^{2αhat} - β r^2)^2 dr gives β = 5 d_v^{2αhat-2}/(2αhat+3), not d_v^{2(αhat-1)}. The discrepancy affects the sensing radius R_c in Eq. (7) and hence the DRR. The derivation needs correction or a different approximation criterion.","section":"Section II-C, Eq. (6)"}],"minor_comments":[{"comment":"The symbol L(X_{k-1}, X_k) is first defined as the number of dynamic ranging events obtained by counting intersections, but in the same equation |L(X_{k-1}, X_k)| is treated as a transition length with expected value 1/(2√λv). Using the same notation for two different quantities makes the derivation difficult to follow.","section":"Section III, Eq. (14)"},{"comment":"The text states that analytical results closely match simulation outcomes, but the figure does not show simulation markers and no Monte Carlo procedure is described. The number of network realizations, the mobility sampling method, and the definition of simulated DRR are all absent.","section":"Section IV, Figure 3"},{"comment":"The parameter W is introduced without a clear dimensional or notational explanation; it appears in several different algebraic forms in later equations, and the manuscript would benefit from a consistent definition before first use.","section":"Section II-C, Eq. (4)"}],"recommendation":"reject","confidential_remarks":"The sign error in Eq. (16) is elementary and central: the purported survival probability increases with the PRI, contradicting the paper's own qualitative claims and making the validation claim impossible. A correction would require new derivation and new simulations, which is beyond a routine revision for this venue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The DRV/ISAC problem is worth thinking about, and the paper frames it cleanly: two independent PPPs for BSs and mobile disaster-response vehicles, a simple RSP-based sensing area, and a continuity metric. That application is new as far as I know, and the Case 1 coverage expression with the MMSE-scaled radius is a reasonable first-order approximation.\n\nBut the core contribution collapses on inspection. The dwell-time probability in Eq. (16) is simply asserted, and as written it makes the DRR in Eq. (17) increase monotonically with the pulse repetition interval τ. The text, the claimed simulations, and the conclusions all say the opposite. That is not a typo somewhere in the margin; it is the very mechanism the paper claims to capture. A probability of the form P(κ > τ) has to decrease in τ, and the exponent here has τ in the denominator, so the expression is structurally wrong. Without a correct derivation of this probability, the closed-form DRR is unsupported.\n\nThe problems do not stop there. The Case 2 ellipse depends on a Taylor expansion at an unspecified point (i,j), so calling it a closed form is generous. The Monte Carlo validation is described only in a sentence; no simulation steps, number of realizations, or confidence intervals are given, so the claimed close match cannot be checked. The reference list looks appropriate and relevant.\n\nSo the architecture is plausible and the directions are interesting, but the main result does not hold as written. The internal contradiction with the paper's own conclusion is a load-bearing flaw, not a cosmetic one. I would send this to a serious referee only because the topic is timely and the modeling framework could be corrected and revisited. If the editor asked me, I would recommend major revision at best, and honestly a reject is defensible until the DRR derivation is fixed and the simulations are properly documented.","headline":"The paper's central DRR formula has the wrong dependence on PRI, and it contradicts the manuscript's own conclusions.","tokens_in":7194,"tokens_out":3248,"would_cite":false,"duration_ms":33171,"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 derives a closed-form metric, the dynamic ranging rate, that quantifies how continuously a disaster ISAC network can re-acquire a target as mobile response vehicles move through the disaster zone.","keywords":["integrated sensing and communication","disaster response","stochastic geometry","Poisson point process","sensing coverage","dynamic ranging rate","sensing continuity","mobility model"],"falsifier":"A Monte Carlo simulation that directly counts, under the paper's Poisson point process and random-waypoint assumptions, the fraction of target-DRV encounters whose dwell time exceeds $\\tau$ would settle the metric: if the empirical probability falls as $\\tau$ rises while Eq. (16) rises, the DRR formula cannot be correct.","tokens_in":6355,"feed_emoji":"📡","tokens_out":9648,"duration_ms":87202,"temperature":0.7,"pith_summary":"Disaster zones are too dynamic for static sensing assumptions, so the paper adds a mobile layer of disaster-response vehicles (DRVs) over a sparse base-station layer in an integrated sensing and communication (ISAC) network. The paper's aim is to quantify sensing service continuity with a closed-form dynamic ranging rate (DRR), which counts how often a target that a base station already detected re-enters a DRV's sensing area and stays there longer than the radar pulse repetition interval. Closed-form sensing footprints for a DRV are derived by approximating the equal-received-power boundary as a circle or an ellipse depending on path-loss exponents, and Monte Carlo simulations are reported to match the analytical DRR curves. If the derivation holds, planners can choose DRV density, vehicle speed, and pulse timing to keep targets visible to the network during rescue operations.","feed_headline":"Sensing continuity in disasters now has a closed-form metric","feed_subtitle":"The new dynamic ranging rate turns rescue-vehicle density, speed, and radar timing into one score.","key_machinery":"The central object is the dynamic ranging rate (DRR), $\\xi$, defined in Eq. (13) as the product of the dynamic ranging repetition rate $\\xi_r$ and the probability $P(\\kappa > \\tau)$ that a target's dwell time inside a DRV sensing area exceeds the pulse repetition interval. It is carried by three pieces: the equal-received-power contour from Eq. (4), approximated as a circle when the path-loss exponents are equal and as an ellipse when they differ; an improved random waypoint mobility model that turns expected transition length and mean pause time into $\\xi_r$; and the exponential dwell-time exceedance probability in Eq. (16).","core_discovery":"On the paper's own terms, the central discovery is a closed-form dynamic ranging rate, Eq. (17): $$\\xi = \\frac{\\sqrt{W}}{1-W} \\cdot \\frac{\\lambda_v u}{\\sqrt{\\lambda_b} + 2\\sqrt{\\lambda_b \\lambda_v}\\, u\\, E[T_s]} \\cdot \\exp\\!\\left(-\\frac{4\\lambda_b}{\\pi}\\frac{(1-W)^2}{W $u^{2}$ \\$tau^{2}$}\\right).$$ The paper claims this metric quantifies sensing service continuity, increases with $\\lambda_v$ and $u$, decreases with $\\tau$, and matches Monte Carlo simulations.","pith_inferences":["One consequence the paper does not spell out: if Eq. (16) is corrected to be decreasing in $\\tau$, the closed-form DRR in Eq. (17) would change shape and the numerical PRI threshold near 0.1 s would need re-estimation.","The same coverage-contour and DRR construction could be lifted to any layered ISAC setting with static infrastructure plus mobile nodes, such as vehicular or UAV-assisted sensing, because the stochastic geometry is not disaster-specific.","The equal-received-power contour approximations connect sensing coverage to handoff-style analysis: the DRV sensing boundary plays the role of a cell edge, so handover metrics from heterogeneous networks could be re-derived for sensing continuity.","A direct experimental check of the dwell-time exceedance probability from field traces of DRV trajectories would separate the mobility-model contribution from the dwell-time probability contribution in the DRR."],"forward_implications":["If the DRR derivation is correct, increasing the density of DRVs raises sensing continuity, because more moving nodes create more chances to re-acquire a target.","If the DRR derivation is correct, increasing DRV speed raises the rate at which targets enter DRV sensing areas and therefore raises the DRR.","If the DRR derivation is correct, increasing the pulse repetition interval lowers the DRR, so PRI selection becomes a trade-off between detection range and continuity.","The reported simulations identify a PRI threshold near 0.1 s, beyond which DRR behavior becomes inconsistent and unreliable.","The circular and elliptical sensing-footprint approximations give closed-form coverage regions that can be evaluated without running a full spatial simulation."],"supporting_citations":[{"why":"Defines the dwell-time versus pulse-repetition-interval condition that is multiplied into the DRR as P(κ > τ).","marker":"[14]"},{"why":"Supplies the improved random-waypoint mobility model used to compute the expected transition length and mean pause time in ξr.","marker":"[10]"},{"why":"Gives the received-sensing-power expression and Swerling type-1 RCS model that define the DRV sensing boundary.","marker":"[7]"},{"why":"Motivates modeling BSs and DRVs as independent Poisson point processes in the disaster ISAC scenario.","marker":"[2]"},{"why":"Provides the path-loss exponent ranges that justify the two approximation cases for the DRV sensing area.","marker":"[12]"}],"fun_headline_variants":["Closed-form metric quantifies disaster sensing continuity","New equation rates sensing continuity in disaster zones","Dynamic ranging rate predicts sensing service continuity","Disaster ISAC sensing continuity now a single formula"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the un-derived exponential formula for the dwell-time probability $P(\\kappa\\ge\\tau)$ in Eq. (16), which has the pulse repetition interval $\\tau$ in the denominator and therefore approaches 1 as $\\tau$ grows, the opposite of the paper's stated claim that larger $\\tau$ degrades the dynamic ranging rate.","fun_headline_variants_meta":{"raw":{"variants":["Closed-form metric quantifies disaster sensing continuity","New equation rates sensing continuity in disaster zones","Dynamic ranging rate predicts sensing service continuity","Disaster ISAC sensing continuity now a single formula"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000511,"raw_usage":{"total_tokens":2394,"prompt_tokens":760,"completion_tokens":1634,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":376,"completion_tokens_details":{"reasoning_tokens":1578}},"tokens_in":376,"tokens_out":1634,"duration_ms":11494,"temperature":1.0,"reasoning_tokens":1578,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:16:15.964094+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A Monte Carlo simulation that directly counts, under the paper's Poisson point process and random-waypoint assumptions, the fraction of target-DRV encounters whose dwell time exceeds $\\tau$ would settle the metric: if the empirical probability falls as $\\tau$ rises while Eq. (16) rises, the DRR formula cannot be correct.","supporting_citations":[{"cited_title":"Tracking considerations in selection of radar waveform for range and range-rate measurements,","cited_arxiv_id":null,"evidence_quote":"Defines the dwell-time versus pulse-repetition-interval condition that is multiplied into the DRR as P(κ > τ)."},{"cited_title":"Mobility management in multi-tier lifi networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the improved random-waypoint mobility model used to compute the expected transition length and mean pause time in ξr."},{"cited_title":"On the performance trade- off of distributed integrated sensing and communication networks,","cited_arxiv_id":null,"evidence_quote":"Gives the received-sensing-power expression and Swerling type-1 RCS model that define the DRV sensing boundary."},{"cited_title":"Integrated Sensing and Commun. (ISAC); Use Cases and Deployment Scenarios,","cited_arxiv_id":null,"evidence_quote":"Motivates modeling BSs and DRVs as independent Poisson point processes in the disaster ISAC scenario."},{"cited_title":"On the expanded region of picocells in heterogeneous networks,","cited_arxiv_id":null,"evidence_quote":"Provides the path-loss exponent ranges that justify the two approximation cases for the DRV sensing area."}],"review_version":1}