{"id":"611d3900-f2eb-411d-803e-d6f57e1f3391","arxiv_id":"2509.03836","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"For three waveguide layouts, the paper gives analytical averages for pinching-antenna SWIPT energy and rate, but the energy expressions omit the path-loss coefficient mu from the signal model.","lead":"This preprint derives closed-form formulas for average harvested energy and achievable rate in a wireless power-and-information system using a movable pinching antenna placed along three waveguide routes. A smart generalist would read it to see whether a speculative 6G antenna concept can support simultaneous charging and data transfer, though the energy formulas currently miss a key path-loss factor.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Energy results omit the path-loss coefficient μ defined in Eq. (1), making the central harvested-energy formulas dimensionally wrong and numerically too large by roughly six orders of magnitude.","rationale":"The reader's strongest claim and rationale identify exactly the same load-bearing flaw: the harvested-energy expressions drop the path-loss coefficient mu that is defined in Eq. (1) and used in the SNR and rate analysis. This is a decisive internal inconsistency. Because the LM energy formulas, the NLM input power, and the NLM upper-bound expressions all omit mu, the central contribution — analytical closed forms for average harvested energy under the three deployment schemes — is not supported by the paper's own equations. The numerical validation cannot repair this, since Eq. (14) and Eq. (16) are the formulas being compared to simulation. The rate analysis appears internally consistent and is not implicated, but the energy half is central to the claimed energy-rate trade-off. I do not agree fully with the reader's stated weakest assumption: the weakest point is not merely the physical realism of the free-space point-source model, but the paper's failure to carry its own path-loss coefficient through the energy derivation. Still, the reader's conclusion (REJECT) is correct, and the error is fixable in principle: reinsert mu everywhere and repeat the numerical study. Until then, the paper's headline energy results are dimensionally inconsistent with Eq. (1).","tokens_in":8422,"tokens_out":5406,"duration_ms":57754,"concrete_test":"Re-derive Lemma 3 from Eq. (2) after inserting the mu factor that Eq. (1) requires: replace E[1/L^2] with E[mu/L^2]. The corrected closed form should be (αβημϖ)/(h D_y) arctan(D_y/(ϖ h)). Compare this corrected expression with Eq. (14) and with the Monte Carlo curves in Fig. 2 at Pt = 0.3 W, σ^2 = -90 dBm, Dx = Dy = 8 m, h = 3 m. If the simulation curves match Eq. (14) as printed, then the simulations must be using a transmit power of Pt/mu (≈ 1.4e6 times larger than stated) or the channel model in the simulator differs from Eq. (1). If the simulation curves instead match the corrected expression, Eq. (14) is wrong by exactly the factor mu.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim requires accurate closed-form average harvested energy for the LM and NLM. That claim fails under the paper's own signal model. Eq. (1) defines the received signal amplitude as sqrt(mu Pt)/||ψp-ψu||, so the received power is mu Pt / ||ψp-ψu||^2. However, Eq. (2) defines the average LM harvested energy as E[αβηPt/L^2], dropping the factor mu, and Eq. (4) defines Pin = βPt/L^2 rather than βμPt/L^2. Consequently, Lemmas 3 and 4, Eq. (16), Lemma 5, and all NLM energy results omit the squared free-space path-loss factor mu = c^2/(16π^2 f_c^2). At fc = 28 GHz, mu ≈ 7.3e-7 m^2, so the reported energy values are about 1.4 million times too large unless Pt is implicitly reinterpreted as Pt/mu, which contradicts the stated transmit-power values and the SNR/rate expressions in Eqs. (5)-(6), where mu is correctly retained. This is not a modeling approximation or a consensus disagreement; it is an internal inconsistency between Eq. (1) and the energy analysis. The rate half of the paper appears unaffected because Lemmas 6-7 include mu inside the logarithmic SNR terms.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies a single-user SWIPT system in which a pinching antenna is moved along a rectangular waveguide to minimize the distance to a uniformly located UE. Three waveguide placements are considered (edge, center, diagonal), together with a hybrid TS/PS protocol. For each placement the authors derive closed forms for the average harvested energy under a linear model and an upper bound under a non-linear logistic model, as well as closed forms for the average achievable rate, based on the distribution of the optimized antenna-UE distance. Monte-Carlo simulations are reported to validate the expressions and to exhibit an energy-rate trade-off.","tokens_in":8727,"tokens_out":13607,"duration_ms":142212,"significance":"If the derivations were correct, this would be a useful first analytical framework for pinching-antenna SWIPT, providing directly computable averages for deployment planning and insight into the energy-rate trade-off. The paper's distance-distribution approach (Lemmas 1-2) is transparent, and the rate integrals in Lemmas 6-7 are algebraically detailed and include the free-space path-loss factor consistently. The main strength is that the closed forms are explicit enough to be checked. However, the energy half of the framework is not valid as written because the path-loss coefficient defined in Eq. (1) is omitted from Eq. (2), Eq. (4), and Lemmas 3-5, and the so-called NLM upper bound depends on an unproved concavity assumption. These issues affect the central claim—prediction of harvested energy and the energy-rate region—and require correction before the contribution can be assessed.","major_comments":[{"comment":"Eq. (1) defines the received amplitude with factor sqrt(mu), so the received power is mu Pt / ||psi_p - psi_u||^2. Yet Eq. (2) defines the average LM harvested energy as E[alpha beta eta Pt / L^2] and Eq. (4) defines Pin = beta Pt / L^2; the factor mu is absent. Consequently Lemma 3 (14), Lemma 4 (16), and Lemma 5 (19) are missing mu everywhere and are dimensionally wrong (Pt/L^2 has units W/m^2 rather than W). At fc = 28 GHz, mu ~ 7.3e-7 m^2, so the reported energy values are too large by about 1.4 million. The rate analysis in Lemmas 6-7 correctly includes mu inside the SNR, so this is an internal inconsistency, not merely a modeling convention. Fix by inserting mu in (2), (4), and all energy/Pin expressions, and rerun the energy simulations and figures.","section":"Eqs. (1)-(4), Lemmas 3-5"},{"comment":"The NLM upper bound applies Jensen's inequality E[Phi(Pin)] <= Phi(E[Pin]). This requires Phi to be concave on the support of Pin. The logistic model (3) is a sigmoid: it is convex for Pin < b and concave for Pin > b. With the stated parameters (b = 2.9 microW) and typical received powers, the operating range is not guaranteed to be concave, so the claimed inequality direction is not established and may even be reversed. The paper needs to prove concavity over the relevant range, restrict the parameter regime, or replace the \"upper bound\" by a valid bound. As written, the NLM energy results are not supported.","section":"Lemma 5 and Eq. (18)"},{"comment":"Fig. 2 reports agreement between simulation and analysis for harvested energy. If the Monte-Carlo code uses the same definition Pin = beta Pt / L^2 as Eq. (4), the agreement validates only the algebra of the internally inconsistent energy model, not the physical model of Eq. (1). After correcting the missing mu, the numerical curves and any conclusions about absolute harvested energy and the energy-rate trade-off must be regenerated. The qualitative ranking of the three deployment schemes may survive because mu is a common multiplicative factor in the LM case, but the NLM numerical values and saturation behavior may change.","section":"Fig. 2 and numerical validation"}],"minor_comments":[{"comment":"Eq. (7) writes L3 = ||psi_p,3 - psi_u|| but the right-hand side is the squared distance; a square root is missing. The same convention recurs in Lemmas 1-3, where the support of the PDF is [h^2, h^2 + (...)^2], indicating that l is L^2 rather than L. Please define the squared distance as a separate random variable, e.g., X = L^2, and use it consistently in (9)-(10), (12)-(13), and the proofs of Lemmas 3-4.","section":"Eq. (7) and Lemmas 1-3"},{"comment":"The abstract contains grammatical errors, e.g., \"we studies the performance\" and \"the pinching-antenna.\" The paper should be carefully proofread throughout.","section":"Abstract and grammar"},{"comment":"The parameters 'a = 100 / microW' and 'b = 2.9 microW' imply that Pin is expressed in microW, but Eq. (4) defines Pin as beta Pt / ||...||^2, which has units W/m^2 (and should be W after adding mu). State the unit conventions used in the Monte-Carlo implementation, otherwise the NLM numerical evaluation is ambiguous.","section":"Simulation parameters in Section IV"},{"comment":"The labels S1/S2 and C1/C2 are defined only in the body text; please define them in the captions for readability.","section":"Captions of Figs. 2-3"},{"comment":"The one-line Jensen argument is omitted; please include it and state explicitly the assumed regularity conditions, given the concavity issue raised above.","section":"Lemma 5 proof"}],"recommendation":"major_revision","confidential_remarks":"The missing mu is pervasive and makes the energy results numerically wrong by roughly six orders of magnitude, but the error is mechanical: inserting mu into (2), (4), and the derived Pin/energy expressions fixes the dimensional inconsistency, and the rate half appears sound. The Jensen-bound issue for the sigmoid NLM is also fixable in revision by proving concavity over the operating range or by changing the claimed bound. I therefore do not recommend outright rejection; the manuscript may become acceptable after a serious revision and a full rerun of the numerical results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core issue is exactly what the stress-test note says: Eq. (2) and Eq. (4) define average harvested energy and incident power without the μ from Eq. (1). Since received power is μPt/d², Lemmas 3–5 and the NLM bounds are dimensionally inconsistent with the paper's own signal model. At 28 GHz this is a factor of ~1.4 million, so the numerical energy results are meaningless as reported. The Monte-Carlo curves match the formulas, but they simulate the same wrong model, so they don't rescue anything.\n\nThe genuinely new part is the application of pinching antennas to SWIPT with three waveguide deployment schemes (edge, center, diagonal). The distance CDFs in Lemmas 1–2 are correct, and the DDS derivation in Appendix A is a nice geometric argument. I checked the rate integrals in Lemmas 6–7; they retain μ inside the log and the algebra appears sound. So the rate side of the paper holds up.\n\nTwo additional soft spots, both minor compared with the μ omission. The Jensen upper bound in Eq. (18) is called an upper bound, but the logistic function Φ(Pin) is not concave over the whole domain—it's convex for Pin below the inflection point. So the claimed bound is not guaranteed. Also, for the diagonal scheme, the paper asserts the projection always lies on the waveguide segment; it does, but only because their coordinate scaling forces x* to remain in [0,Dx]. Worth stating explicitly.\n\nWho gets value from this? Researchers working on pinching-antennas or SWIPT who want analytical benchmarks for deployment choices. The rate formulas and the distance distributions will be useful even after the energy expressions are fixed. The error is embarrassing but mechanical: reinsert μ into Pin and the energy integrals, and the framework becomes coherent. The paper deserves a serious referee, not a desk reject, because the core setup is new and the rate analysis is solid.\n\nMy recommendation: send it to review, but with a clear note that the energy derivations must be corrected before acceptance. If the authors fix the μ omission and either prove concavity or relabel the Jensen result as an approximation, the paper would be a reasonable contribution to a narrow subfield.","headline":"The energy half of this pinching-antenna SWIPT paper drops the path-loss coefficient μ from Eq. (1), making the harvested-energy formulas off by roughly six orders of magnitude; the rate half is sound and the application is new.","tokens_in":9204,"tokens_out":2964,"would_cite":false,"duration_ms":27952,"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":"Closed forms predict energy-rate trade-off for pinching-antenna SWIPT systems under three waveguide placements.","keywords":["pinching antenna","SWIPT","average harvested energy","average achievable rate","energy-rate trade-off","time switching","power splitting","closed-form analysis"],"falsifier":"A direct experiment would mount a pinching antenna on a waveguide at known height h over a rectangular area, reposition the antenna to the optimal point for each receiver location, and compare measured received power against μPt E[1/L^2]. A systematic distance dependence different from 1/L^2, or a mismatch beyond measurement noise at any receiver position, would falsify the channel model behind Lemmas 3 to 7.","tokens_in":8341,"feed_emoji":"📡","tokens_out":5893,"duration_ms":61085,"temperature":0.7,"pith_summary":"This paper claims that a pinching-antenna—an antenna element clipped onto a dielectric waveguide—can support simultaneous wireless information and power transfer whose average performance is predictable by elementary closed forms. A base station with one pinching antenna serves a user uniformly located in a rectangle, and the paper proposes three waveguide deployments: along an edge, through the center, or along the diagonal. For each deployment the antenna slides to the point on the waveguide closest to the user, and the paper derives the distribution of that optimal distance. From the distance distribution it obtains exact integrals for average harvested energy under linear and nonlinear energy-harvesting models, a Jensen upper bound for the nonlinear model, and exact average achievable rate. A sympathetic reader would care because this turns a deployment-design problem into a comparison of simple formulas, letting the energy-rate trade-off be chosen without exhaustive simulation.","feed_headline":"Closed forms predict energy and rate for pinching-antenna SWIPT","feed_subtitle":"Three waveguide placements yield analytic energy-rate curves, so deployment can be chosen without simulation.","key_machinery":"The load-bearing object is the distribution of L*_ν, the distance from the optimally repositioned pinching antenna to a uniformly random user, characterized in Lemmas 1 and 2. The optimal position is the orthogonal projection of the user onto the waveguide: the y-coordinate is 0 or Dy/2 for the edge and center schemes, and the projection onto the diagonal with slope k = Dy/Dx for the diagonal scheme. The closed forms come from integrating three functions of this distance—1/L*^2 for linear harvested energy, the logistic saturation function of 1/L*^2 for nonlinear harvested energy, and log2(1 + μγ̄/L*^2) for achievable rate—against the one-dimensional distance density. Arctangent and logarithm","core_discovery":"The central claim is that, under the free-space point-source channel of Eq. (1), the random distance between the optimally positioned pinching antenna and a uniformly located user has a tractable distribution for all three deployments: for the edge and center schemes the squared distance follows a shifted uniform-root law, and for the diagonal scheme it follows a piecewise square-root density. Integrating against these densities yields closed forms (Lemmas 3, 4, 6, and 7) for average harvested energy and average achievable rate, and a Jensen bound (Lemma 5) for the nonlinear energy-harvesting model. The paper positions this as the first analytical performance model for pinching-antenna-enabl","pith_inferences":["Editorial check: the printed energy formulas (14), (16), and (19) omit the path-loss prefactor μ = c^2/(16π^2 f_c^2) that appears in Eq. (1); if that constant is intended, the linear-energy formulas simply scale by μ, but the nonlinear Jensen bound is not linear in μ, so the printed NLM curves would shift non-uniformly.","The same distance-distribution machinery should extend to multiple pinching antennas on one waveguide or to a user moving along a known trajectory, with the distance density becoming a mixture over time.","Because the diagonal-deployment projection has a particularly clean CDF, curved or segmented waveguides with invertible projection-distance CDFs may admit analogous closed forms.","A direct comparison of these ideal-channel predictions with measurements using a real directive pinching antenna would quantify the combined loss due to antenna pattern, waveguide leakage, and repositioning latency."],"forward_implications":["The energy-rate trade-off can be optimized over the time-switching factor α and power-splitting factor β without Monte Carlo simulation, because both objectives are explicit functions of these parameters.","Under the nonlinear energy-harvesting model, the Jensen upper bound replaces simulation with a one-line evaluation; at high transmit power the bound reflects the saturation behavior of the rectifier.","Deployment choice is geometry-dependent: the paper's simulations find the diagonal scheme best in a square room, while the center scheme can overtake it in an elongated room—the closed forms make this comparison immediate.","The diagonal projection reduces a two-dimensional positioning problem to a one-dimensional quadratic minimization, so the distance probability density remains one-dimensional and analytically integrable.","The same distance distribution underlies both energy and rate expressions, so the three Lemmas form a shared toolbox for any future SWIPT protocol that depends only on the chosen antenna position."],"supporting_citations":[{"why":"Introduces the pinching-antenna concept and the physical mechanism of controlled radiation along a dielectric waveguide that the paper builds on.","marker":"[5]"},{"why":"Provides the prior analytical study of pinching-antenna systems that this work extends to SWIPT.","marker":"[7]"},{"why":"Supplies the unified analytical framework for outage probability and average rate of pinching-antenna systems that motivates the closed-form analysis here.","marker":"[10]"},{"why":"The integral table used to evaluate the arctangent and logarithm integrals in Lemmas 3 through 7.","marker":"[11]"}],"fun_headline_variants":["Closed forms for pinching-antenna SWIPT energy and rate","Analytic energy-rate curves for three pinching-antenna placements","Pinching-antenna SWIPT: closed-form performance without simulation","Tractable distance laws enable closed-form SWIPT metrics","Pinching antennas: closed-form energy and rate for three deployments"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The results rest on the free-space point-source model of Eq. (1): the pinching antenna radiates isotropically with no waveguide attenuation, no antenna pattern, no small-scale fading or interference, and it can be moved instantly to the exact projection point on the waveguide—if any of these fail, the derived distance distributions and closed forms no longer describe the system.","fun_headline_variants_meta":{"raw":{"variants":["Closed forms for pinching-antenna SWIPT energy and rate","Analytic energy-rate curves for three pinching-antenna placements","Pinching-antenna SWIPT: closed-form performance without simulation","Tractable distance laws enable closed-form SWIPT metrics","Pinching antennas: closed-form energy and rate for three deployments"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000754,"raw_usage":{"total_tokens":3156,"prompt_tokens":678,"completion_tokens":2478,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":422,"completion_tokens_details":{"reasoning_tokens":2391}},"tokens_in":422,"tokens_out":2478,"duration_ms":19958,"temperature":1.0,"reasoning_tokens":2391,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T10:39:02.481083+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct experiment would mount a pinching antenna on a waveguide at known height h over a rectangular area, reposition the antenna to the optimal point for each receiver location, and compare measured received power against μPt E[1/L^2]. A systematic distance dependence different from 1/L^2, or a mismatch beyond measurement noise at any receiver position, would falsify the channel model behind Lemmas 3 to 7.","supporting_citations":[{"cited_title":"Pinching antenna-using a dielectric waveguide as an antenna,","cited_arxiv_id":null,"evidence_quote":"Introduces the pinching-antenna concept and the physical mechanism of controlled radiation along a dielectric waveguide that the paper builds on."},{"cited_title":"Flexible-antenna systems: A pinching-antenna perspective,","cited_arxiv_id":null,"evidence_quote":"Provides the prior analytical study of pinching-antenna systems that this work extends to SWIPT."},{"cited_title":"Performance analysis of pinching- antenna systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the unified analytical framework for outage probability and average rate of pinching-antenna systems that motivates the closed-form analysis here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The integral table used to evaluate the arctangent and logarithm integrals in Lemmas 3 through 7."}],"review_version":1}