{"id":"9a712e4a-6c48-46a0-9230-5f3548f167ec","arxiv_id":"2504.13723","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A joint antenna-position and power-allocation design for two-user downlink pinching-antenna NOMA, with a claimed closed-form optimum for the single-pinching-antenna case that is internally inconsistent.","lead":"This paper designs how 'pinching antennas', movable radiating spots along a waveguide, can serve two users at once with non-orthogonal multiple access while protecting one user's quality of service. It proposes an iterative optimization for multiple antennas and a claimed exact formula for one antenna, with simulations showing gains over fixed-antenna baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (48) of Lemma 4 omits the joint-feasibility condition that Eqs. (49) and (50) share a common x; in the symmetric case it gives beta_p = beta_s = 0, so Eq. (54) contradicts Remark 1 and returns an infeasible position.","rationale":"I read the paper in good faith. The multi-antenna BCD-SCA algorithm, the initialization scheme, and the simulation comparisons with fixed-position antennas are plausible, and the paper explicitly acknowledges the in-waveguide attenuation simplification with supporting numerical evidence in Fig. 11. The single-antenna closed-form result in Section IV, however, is the paper's headline analytic contribution, and it contains an internal feasibility error. Lemma 4's proof replaces the two coupled equality constraints from Lemma 3 by an optimization over alpha_p alone, silently dropping the requirement that Eqs. (49) and (50) have a common solution x. At the claimed optimum, the boundary choice in Eq. (48) forces one of R_p or R_s to be zero; in the fully symmetric case both are zero, so Eq. (54) returns x = xp or x = xs while Remark 1 claims the midpoint. A concrete numerical instance confirms that the proposed solution violates a QoS constraint, whereas a slightly larger alpha_p with x at the midpoint is feasible. This is an internal inconsistency in the proof, not a disagreement with community consensus or a mere modeling choice. The reader's rationale already identifies the same Lemma 4 omission, although the formal weakest-assumption field emphasizes the channel model; my independent check supports the Lemma 4 concern. Because this error invalidates the claimed global optimality of the closed-form solution, the REJECT verdict remains appropriate; no verdict adjustment is needed, though the multi-antenna heuristic parts could be revised and resubmitted.","tokens_in":21014,"tokens_out":13692,"duration_ms":121393,"concrete_test":"Run the symmetric feasibility check. Fix xp = 0, xs = 1, Cp = Cs = 9, sigma_p^2 = sigma_s^2 = 1, gamma_p = 1, and P*eta = 20. Evaluate the paper's closed form: Eq. (48) gives alpha_p* = 0.725, then beta_p = beta_s = 0 and Eq. (54) returns x = 0 or x = 1. Check feasibility: at x = 0, constraint (42c) has LHS = (P*eta + P*eta*gamma_p)*alpha_p* - (x - xs)^2*sigma_s^2*gamma_p = 28, while RHS = P*eta*gamma_p + Cs*sigma_s^2*gamma_p = 29, so the SIC constraint is violated; the symmetric violation occurs at x = 1 for constraint (42b). Independently compute the jointly feasible optimum: alpha_p = (P*eta*gamma_p + C*sigma^2*gamma_p + (xs - xp)^2*sigma^2*gamma_p/4)/(P*eta*(1+gamma_p)) = 0.73125, with x = (xp + xs)/2 = 0.5, which satisfies both equalities and yields a positive secondary rate. This direct calculation falsifies Eq. (48) and Eq. (54).","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV's closed-form solution is internally invalid. Lemma 3 requires both constraints (42b) and (42c) to hold with equality. For xp <= xs and x between the users, the two equalities (49) and (50) must be satisfied by the same x, i.e. xp + sqrt(R_p(alpha_p)) = xs - sqrt(R_s(alpha_p)), where R_m(alpha_p) denotes the right-hand side of Eq. (49)/(50). This joint condition is never imposed in Lemma 4; the proof optimizes f(alpha_p) in Eq. (51) over the box B <= alpha_p <= 1 alone. In the symmetric case sigma_p = sigma_s and Cp = Cs, Eq. (48) returns alpha_p* = (P*eta*gamma_p + C*sigma^2*gamma_p)/(P*eta*(1+gamma_p)), for which R_p = R_s = 0 and hence beta_p = beta_s = 0. Eq. (54) then gives x = xp or x = xs, contradicting Remark 1's midpoint claim; no position simultaneously satisfies the two equalities. The claimed alpha_p* is also infeasible, not merely suboptimal: with xp = 0, xs = 1, Cp = Cs = 9, sigma_p^2 = sigma_s^2 = 1, gamma_p = 1, and P*eta = 20, Eq. (48) gives alpha_p* = 0.725; at x = 0, constraint (42c) has LHS = 28 but RHS = 29, and at x = 1, constraint (42b) likewise fails. The feasible optimum for that instance is alpha_p = 0.73125 and x = 0.5, exactly the midpoint of Remark 1. Thus Lemma 2's condition is only necessary; the missing interval-overlap condition makes the headline global-optimality claim false. The BCD-SCA multi-antenna heuristic may remain salvageable, but the claimed single-antenna closed-form optimum is not correct as stated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a two-user cognitive-radio-inspired NOMA downlink in which N pinching antennas are placed on a single dielectric waveguide. It formulates the problem of maximizing the secondary user's rate subject to the primary user's SINR target, jointly over antenna positions and power-splitting coefficients, and proposes a BCD-SCA algorithm for the general multi-antenna case. For the special case of a single pinching antenna (N=1), it claims to derive a closed-form global optimum (Lemma 4, Eqs. (48)-(55)) and several design insights, including a midpoint placement rule for symmetric users (Remark 1). Numerical results compare the proposed schemes with fixed-position antenna systems and exhaustive-search benchmarks.","tokens_in":21452,"tokens_out":6281,"duration_ms":52407,"significance":"If the closed-form solution in Section IV were correct, the paper would offer a simple and useful design rule for pinching-antenna placement in NOMA systems, and the BCD-SCA algorithm with its initialization scheme would be a valuable low-complexity alternative to exhaustive search. The channel model is not fitted to data, and the paper does not claim parameter-free universal validity, so the work is not circular. However, the central analytical claim of a global closed-form optimum is invalid as stated, which undermines the paper's main contribution and the interpretation of the single-antenna simulation results.","major_comments":[{"comment":"The derivation of alpha_p^* misses the joint-feasibility condition that constraints (42b) and (42c) must be satisfied by the same position x. After substituting (49) and (50) into the objective, the reformulated problem (51) is optimized over the box B <= alpha_p <= 1 alone, but the two interval constraints for x must also overlap. In the symmetric case sigma_p = sigma_s, C_p = C_s, with x_p = 0, x_s = 1, gamma_p = 1, and P*eta = 20, Eq. (48) gives alpha_p^* = 0.725, which yields beta_p = beta_s = 0 in Eq. (54); no position x then satisfies both equality constraints, and the claimed solution is infeasible (at x = 0, constraint (42c) gives LHS = 28 while the RHS equals 29). The true optimum for this instance is alpha_p = 0.73125 and x = 0.5, exactly the midpoint of Remark 1. Because the closed-form optimum is the advertised headline result and is used to produce Figure 12, this is a load-bearing error.","section":"Section IV, Lemma 4 and Eqs. (48)-(55)"},{"comment":"The feasibility condition P*eta >= max{C_p*sigma_p^2*gamma_p, C_s*sigma_s^2*gamma_p} is stated as necessary and sufficient, but it is only necessary. It ignores that constraints (42b) and (42c) define two intervals for x that must intersect at a common value. For example, with x_p = 0, x_s = 100, C_p = C_s = 1, sigma_p^2 = sigma_s^2 = 1, gamma_p = 1, and P*eta = 1, the inequality (44) holds, yet the only position satisfying (42b) with alpha_p = 1 is x = 0 and the only position satisfying (42c) is x = 100, so the problem is infeasible. The subsequent case analysis following Lemma 2 relies on the false sufficiency claim.","section":"Section IV, Lemma 2 and Eq. (44)"},{"comment":"The proof of Lemma 3, which asserts that both constraints (42b) and (42c) hold with equality at the optimum, is not a rigorous argument. It describes an iterative perturbation of x and alpha_p without showing convergence or proving that the procedure terminates at a point satisfying both equalities, and it does not account for the requirement that the two constraints be consistent with a single x. The numerical counterexample above shows that the equality conditions (49)-(50) and the position formula (54) are mutually inconsistent for the alpha_p^* claimed in Eq. (48), so Lemma 3 cannot support the closed-form result as written.","section":"Section IV, Lemma 3 and Appendix B"}],"minor_comments":[{"comment":"In the proof of Lemma 1, the text refers twice to 'constraints (42b) and (42b)'; these should read '(42b) and (42c)'.","section":"Appendix A"},{"comment":"The first sentence contains a duplicated phrase 'i.e., i.e.,'.","section":"Remark 1"},{"comment":"The term \\|g_s^k\\|^\\top appears to be a typo: \\|g_s^k\\| is a scalar, so the linearization should use (g_s^k)^\\top (or the elementwise notation of the preceding paragraph).","section":"Eq. (27)"},{"comment":"The statement that g(x_1) is unimodal is justified only by numerical observation; the convergence of Newton's method to the global maximum of problem (35) is therefore not established.","section":"Section III-B1"},{"comment":"The use of 'or' in Eq. (54) suggests two alternative candidate positions, but the two expressions must coincide for a feasible solution; this wording obscures the missing interval-overlap condition that is necessary for the closed-form result.","section":"Eq. (54)"}],"recommendation":"reject","confidential_remarks":"The technical flaw is in the core of the paper, not in a peripheral detail. The authors are established researchers in the area, so the manuscript is likely to draw attention, but the closed-form global-optimality claim in Section IV is incorrect as stated and cannot be repaired by a local correction; it would require a re-derivation of the solution with the missing interval-overlap condition. The BCD-SCA algorithm for multiple antennas may be salvageable, but the paper's advertised analytical contribution and the single-antenna simulation insights would need substantial revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: read this for the multi-antenna algorithm, not for the closed-form. The BCD-SCA design for NOMA over pinching antennas is a legitimate engineering contribution and the simulations are solid, but the single-antenna global-optimal solution in Section IV is wrong as stated.\n\nWhat is actually new: the CR-NOMA QoS formulation for pinching antennas (maximize secondary rate subject to primary QoS and SIC) is not in the cited [20]-[23]. The BCD-SCA treatment of the multi-antenna problem is standard but competently done; the initialization via Newton's method on a path-loss-only surrogate is sensible, and the numerical comparisons against exhaustive search and fixed-position antennas give the paper real empirical content. The in-waveguide attenuation check in Fig. 11 is a good-faith robustness test. The citation pattern is fine; the self-citations to [9],[11] are for the channel model and the path-loss-first insight, and those inputs are clearly stated.\n\nThe soft spot is Section IV, and it is load-bearing. Lemma 2's feasibility condition is necessary but not sufficient: it checks each constraint's right-hand side separately but never requires the two allowed intervals for x to overlap. As a result, the boundary cases in Lemma 2 can be infeasible when the users are far apart. Lemma 4 inherits the same problem and makes it worse. Lemma 3 requires both constraints tight, and Lemma 4 then substitutes those equalities into the objective and optimizes over alpha_p alone, without checking that the same x satisfies both. In the symmetric case, Eq. (48) returns alpha_p* = B where B is the lower bound, which gives beta_p=beta_s=0; Eq. (54) then forces x=xp or x=xs, contradicting Remark 1's midpoint claim. No position satisfies both constraints unless the two users are at the same x. A concrete instance: xp=0, xs=1, Cp=Cs=9, sigma^2=1, gamma_p=1, P*eta=20 gives alpha_p*=0.725 from (48), and no x is feasible; the true optimum is around alpha_p=0.73125 at x=0.5. This is not a minor typo; the abstract and Section IV claim a closed-form global optimum, and that claim is false.\n\nThe multi-antenna algorithm may be salvageable, and the simulations suggest it works. But Section IV needs to be re-derived with the interval-overlap condition included, or removed entirely. As it stands, the paper is not publishable without major revision.\n\nWho this is for: researchers working on pinching-antenna NOMA or flexible-antenna optimization. The BCD-SCA part is a useful data point; the closed-form section is a cautionary example of a missed feasibility condition.\n\nI would send it to peer review rather than desk-reject, because the multi-antenna contribution is real and the flaw, while serious, is localized and fixable. A good referee will catch the same issue.","headline":"Multi-antenna NOMA design is a reasonable, well-simulated contribution, but the paper's headline single-antenna closed-form is internally inconsistent and needs major revision before it can be accepted.","tokens_in":22038,"tokens_out":12022,"would_cite":false,"duration_ms":107821,"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":"The paper claims that for a single pinching antenna, the joint optimization of antenna position and NOMA power split has a closed-form global optimum, and that for multiple antennas a BCD-SCA algorithm achieves near-optimal performance…","keywords":["pinching antennas","non-orthogonal multiple access","cognitive radio-inspired NOMA","antenna position optimization","power allocation","block coordinate descent","successive convex approximation","closed-form solution"],"falsifier":"Measure the received field at a user as a single pinching antenna is moved along a dielectric waveguide and compare the complex amplitude against $\\eta^{1/2}e^{-j(2\\pi d/\\lambda + 2\\pi(x-x_0)/\\lambda_g)}/d$. If the measured phase-magnitude pairs depart from this model by more than the simulation noise level, or if the experimentally optimal position found by sweeping $x$ differs from Eqs. (54)-(55) by more than a discretization step, the paper's central claim is refuted.","tokens_in":20755,"feed_emoji":"📡","tokens_out":7027,"duration_ms":57142,"temperature":0.7,"pith_summary":"The paper studies a two-user downlink in which pinching antennas placed along a dielectric waveguide serve a primary user with a strict SINR target and a secondary user whose rate is maximized. It claims that for a single pinching antenna the joint placement-and-power problem has a closed-form global optimum: the antenna is placed between the two users at a position given by Eqs. (54)-(55), and the power split is given by Eq. (48). For multiple antennas, it claims that a block coordinate descent and successive convex approximation (BCD-SCA) algorithm reaches near-optimal performance with far lower complexity than exhaustive search. The result matters because pinching antennas can be repositioned to reduce large-scale path loss, and the paper provides design rules and an algorithm to exploit that flexibility under NOMA.","feed_headline":"Pinching-antenna placement boosts NOMA rates past fixed arrays","feed_subtitle":"Closed-form optimal antenna position for one pinching antenna; near-optimal BCD-SCA for many.","key_machinery":"The load-bearing object is the effective channel gain $\\tilde h_m = \\sum_{n=1}^{N} \\frac{\\eta^{1/2} e^{-j\\left(\\frac{2\\pi}{\\lambda}\\|\\psi_m-\\tilde\\psi_n^{\\rm Pin}\\| + \\frac{2\\pi}{\\lambda_g}\\|\\psi_0^{\\rm Pin}-\\tilde\\psi_n^{\\rm Pin}\\|\\right)}}{\\|\\psi_m-\\tilde\\psi_n^{\\rm Pin}\\|}$, which combines free-space spherical-wave path loss and phase with in-waveguide phase accumulation. It converts the antenna positions into complex channel coefficients, and the objective and constraints in problem (12) are all expressed through it. For $N=1$, its squared magnitude collapses to $\\eta/((x-x_p)^2+C_p)$ and $\\eta/((x-x_s)^2+C_s)$, which is what makes the closed-form solution possible. For $N>1$, the paper approximates the nonconvex terms involving this gain by first-order Taylor expansions inside a BCD loop.","core_discovery":"The central discovery is that the nonconvex joint optimization of pinching-antenna locations and NOMA power coefficients can be solved exactly in the single-antenna case. The proof rests on three structural facts: the optimal antenna position lies between the two users' x-coordinates; at the optimum both QoS constraints bind; and the objective is monotonically decreasing in $\\alpha_p$ over the feasible set. These yield $\\alpha_p^* = \\max\\left\\{\\frac{P\\eta\\gamma_p + C_p\\sigma_p^2\\gamma_p}{P\\eta(1+\\gamma_p)}, \\frac{P\\eta\\gamma_p + C_s\\sigma_s^2\\gamma_p}{P\\eta(1+\\gamma_p)}\\right\\}$ and the closed-form positions in Eqs. (54)-(55). For multiple antennas, the paper decomposes the problem into a power-allocation step that is optimal for fixed positions and an SCA-based position update that converges to a stationary point, and shows numerically that the resulting rates match exhaustive search.","pith_inferences":["A testable extension beyond the paper: use the closed-form single-antenna rule as an initialization for each antenna in the multi-antenna case, placing the first antenna at the computed optimal point and spacing the rest by $\\Delta$; the paper only tests a Newton-method initialization aimed at path loss, not this direct rule.","If the coherent-sum model remains valid, a corollary the paper does not emphasize is that for fixed antenna positions the optimal power allocation is always the smallest $\\alpha_p$ satisfying both QoS constraints, so the secondary user's rate is governed by the tighter of the two constraints.","The closed-form derivation depends on the two-user structure: Lemma 1 uses the interval between the two users, and Lemma 3 uses both constraints binding. We infer that extending the proof to more than two users would require a different argument, since the number of constraints would exceed the available degrees of freedom.","The paper's own numerical check of in-waveguide attenuation at 0.08 dB/m shows negligible loss; we infer that the design rule would need re-calibration at higher attenuation or longer waveguides, where the optimal antenna position would shift toward the feed point to reduce accumulated loss."],"forward_implications":["For a single pinching antenna, a base station can compute the optimal antenna position and power split in closed form, eliminating iterative search in that configuration.","When both users have equal noise power and equal distance to the waveguide, the optimal antenna sits exactly at the midpoint between the two users on the waveguide.","The BCD-SCA algorithm achieves secondary-user data rates close to those of exhaustive search while reducing execution time from hundreds or thousands of seconds to a few seconds, even as the number of antennas grows to 12.","Across the tested transmit powers, SINR targets, and carrier frequencies, the pinching-antenna system outperforms fixed-position antenna arrays, and the gap widens as transmit power increases."],"supporting_citations":[{"why":"Supplies the pinching-antenna channel model and the argument that pinching antennas create strong LoS links and mitigate large-scale path loss, which motivates the whole system.","marker":"[9]"},{"why":"Provides the rate-maximization algorithm for single-user pinching-antenna placement that the OMA case and the initialization in problem (34) build on.","marker":"[11]"},{"why":"Supports the no-in-waveguide-attenuation modeling choice by reporting negligible performance loss for bounded communication areas.","marker":"[19]"},{"why":"One of the CR-NOMA references that defines the primary-user and secondary-user SIC decoding structure used in the problem formulation.","marker":"[24]"},{"why":"Supplies the in-waveguide propagation phase-shift model $\\theta_n = 2\\pi\\|\\psi_0^{\\rm Pin}-\\tilde\\psi_n^{\\rm Pin}\\|/\\lambda_g$ used in the signal model (3).","marker":"[27]"},{"why":"Establishes that the SCA-based inner loop converges to a stationary point of the position subproblem.","marker":"[28]"},{"why":"Provides the semidefinite relaxation baseline used to optimally solve the fixed-position antenna benchmark in the comparisons.","marker":"[31]"}],"fun_headline_variants":["Pinching-antenna NOMA: closed-form location and power for QoS","Exact pinching-antenna placement solves NOMA QoS problem","Pinching antennas beat fixed arrays with optimal NOMA placement","Pinching-antenna NOMA: optimal QoS placement found in closed form","Closed-form pinching-antenna positions boost NOMA QoS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the channel model in Eqs. (1)-(3): each pinching antenna radiates a spherical wave with amplitude $\\eta^{1/2}/d$ and phase $2\\pi d/\\lambda + 2\\pi(x_n-x_0)/\\lambda_g$, with no in-waveguide attenuation and all antennas fed the same phase-shifted signal at equal power $P/N$; if the waveguide introduces position-dependent loss or reflecting phase terms, the closed-form optimality conditions and the BCD-SCA objective no longer describe the physical system.","fun_headline_variants_meta":{"raw":{"variants":["Pinching-antenna NOMA: closed-form location and power for QoS","Exact pinching-antenna placement solves NOMA QoS problem","Pinching antennas beat fixed arrays with optimal NOMA placement","Pinching-antenna NOMA: optimal QoS placement found in closed form","Closed-form pinching-antenna positions boost NOMA QoS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000449,"raw_usage":{"total_tokens":2307,"prompt_tokens":1031,"completion_tokens":1276,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":647,"completion_tokens_details":{"reasoning_tokens":1184}},"tokens_in":647,"tokens_out":1276,"duration_ms":8569,"temperature":1.0,"reasoning_tokens":1184,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:02:42.799831+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the received field at a user as a single pinching antenna is moved along a dielectric waveguide and compare the complex amplitude against $\\eta^{1/2}e^{-j(2\\pi d/\\lambda + 2\\pi(x-x_0)/\\lambda_g)}/d$. If the measured phase-magnitude pairs depart from this model by more than the simulation noise level, or if the experimentally optimal position found by sweeping $x$ differs from Eqs. (54)-(55) by more than a discretization step, the paper's central claim is refuted.","supporting_citations":[{"cited_title":"Rate maximization for downlink pinching-antenna systems,","cited_arxiv_id":null,"evidence_quote":"Provides the rate-maximization algorithm for single-user pinching-antenna placement that the OMA case and the initialization in problem (34) build on."},{"cited_title":"No-pain no-gain: DRL assisted optimization in energy-constrained CR-NOMA networks,","cited_arxiv_id":null,"evidence_quote":"One of the CR-NOMA references that defines the primary-user and secondary-user SIC decoding structure used in the problem formulation."},{"cited_title":"Coordinated beam- forming for multiuser MISO interference channel under rate outage constraints,","cited_arxiv_id":null,"evidence_quote":"Establishes that the SCA-based inner loop converges to a stationary point of the position subproblem."},{"cited_title":"Joint beamforming and power-splitting control in downlink cooperative SWIPT NOMA systems,","cited_arxiv_id":null,"evidence_quote":"Provides the semidefinite relaxation baseline used to optimally solve the fixed-position antenna benchmark in the comparisons."}],"review_version":1}