{"id":"18bee82e-e7f9-4f81-b6ee-a2b8855145c9","arxiv_id":"2602.21167","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A closed-form solution minimizes total power in a horn-fed, relay-assisted pinching-antenna system by optimizing the pinching position, relay gain, and base-station power.","lead":"This paper designs a relay-fed pinching-antenna system where a base station with a horn antenna beams a signal to a full-duplex relay that injects it into a waveguide, and derives closed-form formulas for the antenna position, relay gain, and transmit power that minimize total power under a user signal-quality constraint. The interest is that it extends pinching-antenna coverage without a wired waveguide feed, using simpler hardware than previous array-based designs.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Title/abstract claim residual self-interference-aware optimization, but Eqs. (1)–(9) and the body abstract assume zero SI; the derived closed-form optima are therefore not SI-aware and the advertised contribution is unsupported.","rationale":"The reader's weakest_assumption exactly identifies this mismatch. The paper's internal abstract contradicts the arXiv metadata: the body says SI is eliminated by horn antennas, whereas the title/abstract promise residual SI modeling. Given that the full text contains no SI term, the mathematical results are correct for a zero-SI system, so the paper is not internally erroneous; rather, the advertised contribution is not implemented. A fair evaluation should condition acceptance on either including residual SI and re-deriving the optima or revising the title/abstract to remove the SI-aware claim. The benchmark comparison is also based on asymmetric channel models (NLoS array vs LoS horn), which may explain the power savings, but that is secondary to the SI discrepancy. Therefore I agree with the reader's CONDITIONAL verdict.","tokens_in":7017,"tokens_out":13823,"duration_ms":122088,"concrete_test":"Introduce a residual SI term into Eq. (8): replace σ_R^2 by σ_R^2 + β^2(P1|g1|^2+σ_R^2)|h_SI|^2, where h_SI is the residual SI channel. Re-solve the optimization (10) and compare the resulting P1* and β^2* with Eqs. (32)–(33). If they differ (they will for any |h_SI|>0), the no-SI expressions are not SI-aware.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper is advertised (arXiv title/abstract) as modeling residual self-interference and performing SI-aware optimization. However, the body abstract states horn antennas 'effectively eliminating self-interference,' and the signal model in Eqs. (1)–(9) contains no self-interference term: the relay received signal in Eq. (1) includes only AWGN, and the end-to-end SNR in Eq. (8) has only σ_R^2 and σ_UE^2. Consequently, Theorems 1 and 2 are derived for a zero-SI AF relay. If residual SI is actually present (as the title implies), the received signal at the relay should include a loop-interference component, e.g., an additive residual SI term with variance proportional to P2. This would alter the denominator of Eq. (8), making it depend on β^2 and P1, so the optimal relay gain and BS power in Theorem 2 would no longer take the closed forms in Eqs. (32)–(33). Thus the central 'SI-aware' claim is not supported by the model; the paper either has an incomplete model or an overstated claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a wireless-fed pinching-antenna system in which a full-duplex amplify-and-forward relay with horn antennas receives from a BS and feeds a dielectric waveguide; a movable pinching antenna radiates to a UE. The authors formulate a total-power minimization subject to a UE SNR constraint, jointly optimizing the pinching position x_Pin, relay gain β, and BS transmit power P1. Theorem 1 obtains the optimal position in closed form by maximizing |g2|^2; Theorem 2 derives closed-form P1* and β^2* using a univariate reduction. Numerical results compare the scheme with direct 64-antenna NLoS transmission and with fixed-antenna relaying. The derivations are internally consistent for the stated model, but the paper advertises residual self-interference awareness while Eqs. (1)–(9) omit any SI term.","tokens_in":7327,"tokens_out":7891,"duration_ms":64023,"significance":"Within the zero-SI model, the optimization is cleanly solved: the proofs are transparent, no fitted constants appear, and the separation of the position problem from the power/gain problem gives simple closed forms that could be useful for system-level design. The paper also positions horn antennas as a low-cost alternative to arrays at an FD relay, which is a plausible practical point. The advertised residual-SI-aware contribution, however, is not present: the signal model and optimization are SI-free. The numerical advantage over Benchmark 1 is also weakened by the asymmetric channel models. If these issues are corrected, the paper would be a solid, if incremental, contribution to the PAS literature.","major_comments":[{"comment":"The title/metadata claim residual self-interference is 'explicitly modeled,' but Eq. (1) contains no SI term and Eq. (8)'s denominator has only σ_R^2 and σ_UE^2. The problem (10) and Theorems 1–2 are derived for a zero-SI AF relay; the body abstract says horn antennas 'effectively eliminat[e] self-interference.' With residual SI, a loop term depending on β^2 and P1 would enter the SNR, changing P1* and β^2* in Eqs. (32)–(33). The advertised SI-aware claim is therefore unsupported. Please include a residual-SI term and re-derive, or explicitly state the zero-SI assumption and adjust the title/abstract.","section":"§II-A, Eqs. (1)–(8); §II-B"},{"comment":"Benchmark 1 models the direct BS–UE link as NLoS with path-loss exponent 4 and shadowing variance 11 dB, while the proposed architecture's links use free-space path loss (Eqs. (3), (9)). The comparisons in Figs. 1–2 therefore conflate architecture gains with channel-model differences. A LoS direct-transmission benchmark, or a justification for why NLoS is the correct comparison, is needed before claiming 'substantially outperforms.'","section":"§IV, Figs. 1–2, Benchmark 1"}],"minor_comments":[{"comment":"Typo: 'the proposed scheme outperforms Benchmark 2, which confirms the its superiority' should read 'confirms its superiority.'","section":"§IV"},{"comment":"The metadata title and abstract advertise residual-SI-aware optimization, while the body title is 'Wireless-Fed Pinching-Antenna Systems with Horn Antennas' and the body abstract states SI is effectively eliminated. These should be reconciled.","section":"Title/abstract"},{"comment":"Add parentheses to clarify the logical structure of the condition; as written, 'or x1 ≥ 0 and f(0) ≥ ...' is ambiguous.","section":"Eq. (13)"},{"comment":"Clarify whether the 0.1 W per-antenna RF-chain cost is included in P1 or treated as a fixed power offset; the text says total transmit power equals BS power, which is inconsistent if a per-element RF cost is added.","section":"§IV, Benchmark 1"},{"comment":"The proof states x1 is a local minimum and x2 a local maximum; when ∆=0 the two stationary points coalesce. The formula still works, but the degenerate case should be mentioned.","section":"Theorem 1 proof"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision. The main technical claims are sound under the zero-SI model, but the mismatch between the advertised title/abstract and the body is substantive, not cosmetic: it changes the optimization problem. The benchmark fairness issue should also be addressed. I saw no circularity or fabricated results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a minor but genuine variant of the authors' earlier wireless-fed pinching-antenna work: replace the arrays at the BS and relay with horn antennas, and derive closed-form optimal pinching position, relay gain, and BS power that minimize total power for a target SNR. The math in Theorems 1 and 2 is straightforward but correct for the stated model, and the position-optimization balancing waveguide attenuation against free-space path loss is cleanly done. That part deserves credit.\n\nThe problem is the title and abstract promise more than the model delivers. The arXiv abstract says residual self-interference is \"explicitly modeled\" and the design is \"SI-aware,\" but the signal model in Eqs. (1)-(9) contains no SI term at all: the relay received signal has only AWGN, and the end-to-end SNR in Eq. (8) has only two noise variances. The body abstract effectively admits this, saying horn antennas \"effectively eliminate self-interference.\" If that's the modeling claim, fine, but then the title/abstract are misleading. And if residual SI is actually present, the denominator of the SNR would depend on the relay gain and BS power, and the closed forms in Theorem 2 would no longer hold. So the central advertised contribution is unsupported as written. The authors need to either add a residual SI term and re-derive the optima, or drop the SI-aware language and present the contribution as a zero-SI horn-antenna design.\n\nThe numerical comparison has a second soft spot. Benchmark 1 is a 64-antenna BS doing direct NLoS transmission with path loss exponent 4 and 11 dB shadowing, while the proposed scheme uses free-space path loss on the BS-relay link plus the waveguide model. That's apples to oranges; the large power gap mostly reflects the channel model mismatch and the 0.1 W per RF chain, not the architecture. Benchmark 2 is more reasonable but should also be run with matched channel assumptions to substantiate the claimed savings.\n\nNothing circular here; self-citations supply the channel model, not the conclusion. The derivations are internally consistent for the zero-SI model.\n\nWho is this for? Researchers working on pinching-antenna systems and relay-assisted coverage extension will find the closed-form results handy, but they should read it as a zero-SI analysis. With revision, it could be a solid conference or short journal paper.\n\nI'd send it to peer review, but with the expectation that the authors either model SI honestly or drop the SI-aware claim, and that they fix the benchmark comparison.","headline":"Useful zero-SI optimization for a horn-fed pinching-antenna relay, but the SI-aware claim in the title/abstract is not in the equations and the benchmark comparison is unfair.","tokens_in":7761,"tokens_out":2328,"would_cite":false,"duration_ms":20836,"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 optimal pinching-antenna position, relay gain, and base-station power are derived in closed form, and the design uses less total power than direct 64-antenna transmission or fixed-antenna relaying.","keywords":["pinching antenna systems","wireless-fed relay","horn antenna","full-duplex amplify-and-forward","power minimization","closed-form optimization","waveguide attenuation","self-interference"],"falsifier":"Measure the end-to-end SNR of a horn-antenna full-duplex relay as the relay gain β is swept at fixed BS power P1. If the measured SNR saturates below the value predicted by Eq. (8) at high β—indicating a loop-interference term that grows with β²—then the model's optimal gain formula (33) is too optimistic and the closed-form power minimum does not hold for a real relay.","tokens_in":6958,"feed_emoji":"📡","tokens_out":11242,"duration_ms":93027,"temperature":0.7,"pith_summary":"An emerging approach to high-frequency coverage is the pinching-antenna system, where a signal travels down a dielectric waveguide and radiates from a position-adjustable antenna. This paper extends that idea by feeding the waveguide through a full-duplex amplify-and-forward relay equipped with horn antennas, avoiding the bulky RF chains of antenna arrays. It establishes that the optimal pinching-antenna position, relay amplification gain, and base-station transmit power can all be expressed in closed form, and that these settings minimize total power for a target SNR at the user. The design is shown numerically to consume less power than direct 64-antenna transmission or relay-assisted transmission with a fixed antenna.","feed_headline":"Closed-form formulas minimize horn-fed pinching-antenna relay power","feed_subtitle":"Optimal position, relay gain, and base-station power beat direct 64-antenna transmission and fixed-antenna relays.","key_machinery":"The load-bearing object is the end-to-end SNR, γ = P1β²|g1|²|g2|² / (σ_UE² + β²|g2|²σ_R²), whose denominator contains only the two AWGN noise terms. The pinching-antenna channel gain |g2|² = c² e^{-α_D x} / (16π² f² ||Φ_UE − Φ_Pin||²) couples waveguide attenuation with free-space distance, so the optimal position maximizes f(x) = e^{-α_D x} / ((x_UE − x)² + y_UE² + d²). The second piece of machinery is the affine substitution u = P1|g1|² − γ0σ_R², which turns the power-minimization problem into a univariate function whose stationarity condition yields the closed-form relay gain β²* and BS power P1* in Theorem 2.","core_discovery":"The central claim is that the end-to-end SNR of the proposed wireless-fed pinching-antenna system has a structure that decouples the placement problem from the power-allocation problem. For any fixed base-station power and relay gain, the SNR is monotonically increasing in the pinching antenna's channel gain, so the optimal position is found by maximizing |g2|² alone. Theorem 1 solves this maximization in closed form, balancing the exponential waveguide attenuation e^{-α_D x} against the free-space path loss to the user's location. With that position fixed, Theorem 2 reduces the remaining two-variable problem to a scalar convex optimization; substituting u = P1|g1|² − γ0 σ_R² yields closed-f","pith_inferences":["The paper's title and metadata abstract promise an 'explicitly modeled' residual self-interference, but the body equations contain no loop-interference term: Eq. (8) is SI-free. Adding a nonzero residual SI term to the denominator would change the optimal relay gain and BS power, so the formulas in Theorem 2 are a lower bound for a real full-duplex relay rather than an SI-aware design.","The horn antennas are the stated reason self-interference is 'effectively eliminated'; if a practical horn relay still has a small but nonzero loop component, the system will need either extra cancellation circuitry or a power back-off, both of which the closed-form optimum ignores.","The 64-antenna benchmark includes 0.1 W of RF circuit power per element, so part of the reported power saving comes from replacing the array with a single horn antenna rather than from the pinching-position optimization itself; a benchmark using an equivalently high-gain phased array would separate these effects.","The same position-then-power decomposition would likely carry over to multi-user or multi-waveguide scenarios, since the optimal position depends only on the single-user |g2|²; the relay-power balance would, however, need re-derivation when multiple users share the relay."],"forward_implications":["The optimal pinching-antenna position can be computed directly from the user's coordinates and the waveguide attenuation coefficient, eliminating the need for iterative search during deployment.","The relay gain and base-station power are given by simple algebraic formulas, so the system can adapt instantly to a new target SNR or noise floor without re-optimization.","At 28 GHz with the paper's parameters, the proposed scheme's total power is substantially below direct 64-antenna NLoS transmission and fixed-antenna relaying.","The decomposition of the SNR—placement first, power second—depends only on the monotonicity in |g2|², so the two-step method remains valid for other monotone channel-gain models.","The closed-form minimum total power explicitly separates the relay-noise, user-noise, and coupling contributions, making it possible to see which link dominates the power budget in a given geometry."],"fun_headline_variants":["Closed-form optimization for hybrid wireless-fed pinching antennas","Hybrid pinching-antenna relay cuts power with residual-SI-aware design","Optimal position and gain derived for horn-fed pinching-antenna system","Minimize total power in wireless-fed pinching-antenna full-duplex relay"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The full-duplex relay is assumed to have zero residual self-interference: the end-to-end SNR in Eq. (8) contains only the AWGN terms σ_UE² and σ_R², with no loop-interference component in the denominator. If residual self-interference is nonzero, the SNR expression changes and the closed-form relay gain and base-station power in Theorem 2 no longer minimize the true SNR-constrained total power.","fun_headline_variants_meta":{"raw":{"variants":["Closed-form optimization for hybrid wireless-fed pinching antennas","Hybrid pinching-antenna relay cuts power with residual-SI-aware design","Optimal position and gain derived for horn-fed pinching-antenna system","Minimize total power in wireless-fed pinching-antenna full-duplex relay"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000163,"raw_usage":{"total_tokens":1114,"prompt_tokens":814,"completion_tokens":300,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":558,"completion_tokens_details":{"reasoning_tokens":220}},"tokens_in":558,"tokens_out":300,"duration_ms":3211,"temperature":1.0,"reasoning_tokens":220,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T21:05:29.155939+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the end-to-end SNR of a horn-antenna full-duplex relay as the relay gain β is swept at fixed BS power P1. If the measured SNR saturates below the value predicted by Eq. (8) at high β—indicating a loop-interference term that grows with β²—then the model's optimal gain formula (33) is too optimistic and the closed-form power minimum does not hold for a real relay.","supporting_citations":[],"review_version":1}