{"id":"da71b13b-c824-4402-88e7-183bfbbd57ec","arxiv_id":"2505.05160","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A temperature-constrained phase-shift optimization for multi-user LC-RIS downlinks improves max-min SINR over temperature-neglecting designs in simulation.","lead":"This paper designs phase shifts for a liquid-crystal reconfigurable intelligent surface (LC-RIS) that stay effective when ambient temperature shrinks the achievable phase range. Simulations show that a temperature-aware phase-shift optimization keeps the worst user's signal quality much higher than designs that ignore temperature.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The printed SCA linearization of the SINR constraint (Eqs. 23–24) is algebraically inconsistent and lacks a trust region, so the reported max-min SINR gains may not correspond to true achievable SINR.","rationale":"The reader's weakest assumption correctly identifies the linearized constraint cC3 as the load-bearing step. My independent check of Eqs. (14)–(24) confirms that the printed linearization is not the first-order Taylor expansion of Eq. (15): the sign of the noise term is wrong in Eq. (23), the interference sum over j is missing from both Eqs. (23) and (24), and the claimed δθ_n ≪ 1 justification is not enforced by any algorithmic mechanism. This is more than a typo: without a faithful surrogate, the SCA iterates are not guaranteed to produce phase vectors satisfying the actual SINR constraints, so the reported max-min SINR improvement may be an artifact of the unconservative approximation. The paper does have independent support: the temperature-dependent phase-range model in Eq. (9) is derived from published LC refractive-index formulas, and the physics of LC-RIS is externally grounded. However, the algorithmic derivation is not machine-checked, and no code or averaging statistics are provided, so the simulation claim cannot yet be verified. Since the flaw is in principle fixable and the underlying idea is sound, a conditional accept remains appropriate; the authors must correct the linearization and demonstrate that the algorithm's returned κ is achievable. Therefore I do not move the reader's verdict.","tokens_in":9706,"tokens_out":5321,"duration_ms":53439,"concrete_test":"Implement Algorithm 1 with the minimal algebraic correction to Eqs. (23)–(24): replace the cC3 expression by the full first-order expansion of Eq. (15), including the sum over j≠k and the correct sign of σ_k^2, and run the Table I parameters at T = 55 °C. After each AO iteration, compute the true SINR_k from Eq. (11) using the returned W and θ, and compare min_k SINR_k with the κ returned by P3. If at any iteration min_k SINR_k lies more than ε below κ, or if the corrected algorithm no longer clearly outperforms benchmark 1, then the printed linearization—not temperature resilience—is the source of the claimed improvement.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that Algorithm 1 achieves significantly higher max-min SINR than the temperature-neglecting baseline under temperature-limited LC-RIS phases. That claim depends on the constraint cC3 in Eq. (23) being a faithful linearized surrogate of the actual SINR constraint (14). The printed derivation is not faithful. Starting from Eq. (15), the correct first-order expansion is: |s_k^{(t-1)}|^2 - κ Σ_{j≠k} |s_{k,j}^{(t-1)}|^2 - κ σ_k^2 + 2Σ_n Re{s_k^{(t-1)*} i e^{iθ_n^{(t-1)}} a_n^{(k)} δθ_n} - 2κ Σ_{j≠k} Σ_n Re{s_{k,j}^{(t-1)*} i e^{iθ_n^{(t-1)}} a_n^{(k,j)} δθ_n} ≥ 0. Eq. (23) instead contains '-σ_k^2' inside the κ term (wrong sign, turning -κσ_k^2 into +κσ_k^2) and only a single sum Σ_n c_n^{(k,j)}, with no sum over the interfering users j≠k. Eq. (24) defines c_n^{(k,j)} as if j were fixed and omits the double summation required by the interference term. Moreover, the expansion drops |δs_k|^2 and |δs_{k,j}|^2 on the grounds that δθ_n ≪ 1, but P3 imposes no trust region, step-size rule, or penalty to keep δθ_n small; a feasibility solve over the linear constraint can return large updates. If the implementation follows the printed equations, the returned θ may violate the true SINR constraints, so the reported κ is not an achievable max-min SINR. If the implementation follows an unprinted corrected version, the paper is not reproducible from the derivation as given. Either way, the simulation evidence for the headline improvement is not currently backed by a valid, verifiable algorithmic derivation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers an LC-RIS-assisted multi-user MISO downlink system and studies the impact of ambient temperature on the achievable phase-shift range of the RIS elements. The authors formulate a max-min SINR optimization problem with a temperature-dependent phase constraint and propose an alternating optimization algorithm: the BS precoder is optimized via SDR with bisection, and the RIS phase shifts are optimized via successive convex approximation (SCA) based on a first-order Taylor expansion of the SINR constraints. Simulation results are presented showing that the proposed temperature-resilient design outperforms a temperature-neglecting baseline, a random-phase baseline, and a no-RIS baseline across different RIS sizes, temperatures, and transmit powers. The claimed contribution is a scalable O(N) phase-shift optimization that accounts for temperature-induced phase-range shrinkage.","tokens_in":10126,"tokens_out":4438,"duration_ms":46715,"significance":"If the proposed method is correct, it addresses a practical and under-studied problem: the thermal sensitivity of LC-RIS phase shifters. The temperature model itself is a strength: it is externally grounded in the LC physics literature (Eqs. (3)-(5) from [15,16]) and the paper re-derives the temperature-dependent maximum phase shift in Eq. (9) rather than introducing an ad-hoc model. The idea of handling the reduced phase range via a constraint is natural, and the SCA approach is, in principle, more scalable than the O(N^3) SDR used in the prior single-user work [13]. However, the central derivation of the linearized SINR constraint contains algebraic inconsistencies and the algorithm lacks a mechanism to keep the linearization valid, so the simulation evidence for the headline improvement is not currently backed by a valid optimization formulation.","major_comments":[{"comment":"The printed linearized constraint cC3 is algebraically inconsistent with the first-order expansion of the SINR constraint (14)-(15). In Eq. (15), the noise term appears as -κ σ_k^2, but Eq. (23) contains -κ(Σ_{j≠k}|s_{k,j}|^2 - σ_k^2), which flips the sign to +κ σ_k^2. Moreover, Eq. (23) has only a single sum Σ_n c_n^{(k,j)} with no sum over the interfering users j≠k, even though the interference term in Eq. (15) is a sum over j. Equation (24) defines c_n^{(k,j)} for one fixed j and therefore omits the required double summation over j and n. The desired-signal term 2Re{s_k^{(t-1)*} i e^{iθ_n^{(t-1)}} a_n^{(k)} δθ_n} and the interference term should appear as separate sums; folding them into one coefficient indexed by (k,j) is not a faithful linearization. As written, the constraint cannot be used to reproduce the expansion of Eq. (14).","section":"§III-C, Eqs. (23)-(24)"},{"comment":"The second-order terms |δs_k|^2 and |δs_{k,j}|^2 are dropped on the grounds that δθ_n ≪ 1, but problem P3 in Eq. (25) imposes no trust region, step-size bound, or penalty to keep δθ_n small. Constraint C2 only restricts the absolute value of each θ_n, not the change per iteration. A feasibility solve over the linearized constraint can therefore return large updates that violate the assumption underlying the Taylor expansion, so the iterates may not converge to a point satisfying the true SINR constraint. The authors should add a trust region (e.g., ||θ - θ^{(t-1)}||∞ ≤ Δ) or a backtracking line search to enforce validity of the linearization, and should state the resulting convergence properties.","section":"§III-C, just after Eq. (22)"},{"comment":"Because of the issues with Eqs. (23)-(24), the reported max-min SINR gains are not verifiable from the manuscript. If the implementation followed the printed equations, the final θ may violate the true SINR constraints and the reported κ would not be an achievable SINR. If the implementation used a corrected but unprinted linearization, the paper is not reproducible from the derivation. The authors need to provide either a corrected derivation of the linearized constraint, a detailed statement of the actual constraint used in the simulations, or release the code; without this, the simulation evidence for the headline claim is inconclusive.","section":"§IV, Figs. 3-4"},{"comment":"The claim that the phase-shifter subproblem is solved in O(N) complexity is not supported. Even a linear feasibility problem with N variables and one constraint solved via a general-purpose interior-point solver like CVX typically has complexity O(N^3) or higher, not O(N). The total complexity expression O(Imax((KM)^3.5 + N)) therefore understates the actual cost. This does not invalidate the temperature-resilient design, but it weakens the scalability comparison with the O(N^3) SDR of [13] and should be corrected or justified with a specific solver and iteration count.","section":"§III-C, Complexity Analysis"}],"minor_comments":[{"comment":"Constraint C1 is written as Σ_{k=1}^K ||w_k||^2 ≤ P, ∀k, but the '∀k' is inappropriate; the constraint is a single global power budget, not a per-user constraint.","section":"§II, Eq. (12b)"},{"comment":"Equation (24) uses δθ_n without the iteration superscript (t), and the expression ends with a stray '·' after the bracket. Please make the notation consistent with Eq. (18).","section":"§III-C, Eq. (24)"},{"comment":"The temperature T is given as 55°C while Tr and Tc are in Kelvin. Since Eq. (9) requires absolute temperature, the conversion from Celsius to Kelvin should be stated explicitly in the text and figure axes should be labeled consistently.","section":"§IV-A, Table I"},{"comment":"There are typos in the references: 'beamforing' should be 'beamforming', and 'V eh.' should be 'Ve h.' in [18]; reference [20] has an inconsistent version/access date format.","section":"References [18] and [20]"},{"comment":"The naming 'cC3' is confusing; please use a more descriptive name such as C3_linear or C̄3, and ensure the notation for the constraint matches between Eqs. (23) and (25).","section":"§III-C, Eq. (23)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a relevant and timely problem, and the temperature modeling is a genuine strength. However, the central linearization step is not mathematically sound as printed, and the simulations cannot be trusted until the derivation is corrected and the algorithm is augmented with a trust region or equivalent safeguard. The complexity claim also needs revision. I believe the core idea is salvageable, so major revision is appropriate rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this paper asks a worthwhile question—how to keep multi-user SINR fairness when the LC-RIS phase range shrinks with temperature—and the max-min formulation is a sensible way to frame it. But the printed derivation of the linearized SINR constraint is wrong. Equations (23)–(24) do not match the first-order Taylor expansion of (15). The noise term appears with the wrong sign, and the interference linearization is missing the sum over users j. As written, the algorithm in Algorithm 1 is not solving the stated optimization problem, so the reported gains over the baseline are not backed by a valid derivation.\n\nWhat is genuinely good: the temperature model in (9) is grounded in standard LC physics and properly attributed to the authors' earlier work [13]. The extension to a fairness objective with AO/SDR/SCA is natural, and the O(N) complexity per iteration for the phase subproblem is a nice selling point. The simulations compare against the obvious baselines, and the qualitative behavior (more elements and power help; high temperature hurts the naive design) is plausible.\n\nThe soft spots are proportional. The linearization error is load-bearing—it is the core of the phase-shift subproblem. The paper also drops the second-order terms |δs|^2 with the justification that δθ is small, but there is no trust region or step-size rule to enforce that. The table omits the LC parameter α (only a range is given in the text), and there are no confidence intervals or averaging details for the Monte Carlo runs. No code is provided, so the results cannot be checked.\n\nWho is this for? Researchers working on LC-RIS hardware-aware design will find the problem statement useful. The paper deserves a serious referee—the idea is relevant and the flaw looks repairable—but it should not be accepted in this form. I would ask the authors to fix the linearization, add a trust region, and share code or at least detailed simulation settings.","headline":"Temperature-aware LC-RIS fairness is a real problem, but the printed SCA linearization of the SINR constraint is algebraically inconsistent and the simulation gains are therefore not yet credible.","tokens_in":10691,"tokens_out":4068,"would_cite":false,"duration_ms":35960,"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 a temperature-aware phase-shift design for liquid-crystal RISs preserves multi-user fairness when heat shrinks the available phase range.","keywords":["liquid crystal RIS","reconfigurable intelligent surface","temperature-resilient phase design","max-min SINR fairness","mmWave multi-user MISO","alternating optimization","successive convex approximation","phase shifter range shrinkage"],"falsifier":"On a small instance (for example $N=16$, $K=2$, $\\theta_{\\max}=\\pi$), run the proposed algorithm and then evaluate the true SINR at the returned phase vector; if the achieved minimum SINR falls below the $\\kappa$ value produced by the linearized constraint, the Taylor surrogate is not faithful. A second check is algebraic: substituting the expansions into the original SINR inequality should reproduce the linearized constraint term by term, so a symbolic or numeric expansion can settle whether that constraint actually represents the original SINR bound.","tokens_in":9477,"feed_emoji":"🌡️","tokens_out":7825,"duration_ms":73427,"temperature":0.7,"pith_summary":"The paper argues that liquid-crystal reconfigurable intelligent surfaces (LC-RISs) lose usable phase range when the ambient temperature rises, and that a phase-shift design which treats this shrinkage as a hard constraint keeps the weakest user's signal-to-interference-plus-noise ratio (SINR) high. It formulates the fairness goal as a max-min SINR problem with a temperature-dependent upper bound on every phase, then solves it by alternating a semidefinite-relaxation precoder step with a successive-convex-approximation phase step. The reported simulations show the proposed scheme beating a temperature-blind design, a random-phase design, and a no-RIS baseline across surface sizes, temperatures, and transmit powers. If the result holds, LC-RIS deployments in warm climates should re-optimize their phases within the shrunken range rather than trusting settings computed at a reference temperature.","feed_headline":"Heat shrinks LC-RIS phase range; new design restores fairness","feed_subtitle":"In hot conditions LC-RIS phases lose range; optimizing inside the shrunken range beats temperature-blind baselines.","key_machinery":"The load-bearing object is the temperature-dependent maximum phase shift $\\theta_{\\max}(T)=2\\pi\\left(\\frac{T_c-T}{T_c-T_r}\\right)^{\\alpha}$, which converts ambient temperature into a per-element upper bound on the phase variables. The second mechanism is the successive convex approximation of the phase subproblem: expanding $e^{i\\theta_n}$ to first order around the previous iterate turns the non-convex SINR inequalities into the linear constraint $\\widetilde{C3}$, while the precoder subproblem is handled by semidefinite relaxation with bisection. Together these form the alternating optimization loop that the paper calls Algorithm 1.","core_discovery":"The paper's central claim is that temperature is not a nuisance to be calibrated away but a first-class constraint on the RIS optimization: when the ambient temperature $T$ exceeds the reference temperature $T_r$, each LC element can only provide phases in $[0,\\theta_{\\max}(T)]$ with $\\theta_{\\max}(T)=2\\pi\\left(\\frac{T_c-T}{T_c-T_r}\\right)^{\\alpha}$, and a design that respects this bound preserves multi-user fairness. The authors derive this bound from the birefringence model of nematic liquid crystals, embed it in a max-min SINR program, and solve the phase subproblem by a first-order Taylor expansion of $e^{i\\theta_n}$ that renders the SINR constraints linear. Their simulations indicate that the temperature-aware design maintains a substantially higher minimum SINR than a design that ignores the temperature effect, with only $O(N)$ complexity per phase update.","pith_inferences":["The hardware model suggests a material-level design lever the paper does not optimize: a liquid crystal with a higher clearing temperature $T_c$, or a cell gap chosen to leave margin at the reference temperature, would delay the phase-range shrinkage and could be combined with the proposed algorithm.","A trust-region or step-size control that enforces tiny phase updates would make the Taylor surrogate internally consistent; without it, the algorithm's achieved SINR should be checked directly against the true constraint at the returned phases.","Because the phase bound applies element-wise, the same formulation carries over to the paper's stated future scenarios of inhomogeneous temperature across the surface and multiple LC-RISs, using per-element temperature maps.","The max-min SINR objective could be replaced by sum-rate or energy-efficiency objectives under the same temperature bound; the linearization would need to be re-derived for those metrics."],"forward_implications":["Operators deploying LC-RIS in hot environments should treat the surface's phase range as a known function of current temperature and re-solve the phase configuration when the temperature changes.","The $O(N)$ phase-update complexity makes the approach practical for large LC-RIS panels, where a competing semidefinite-relaxation approach would scale as $O(N^3)$.","Temperature-blind phase designs lose most of the RIS beamforming gain once $T$ exceeds $T_r$; the paper's numbers show that simply raising transmit power does not recover that loss efficiently.","The same temperature constraint can be ported to any LC-based phase shifter network, including reflectarrays and transmit arrays, not only RISs."],"supporting_citations":[{"why":"This reference supplies the temperature-dependent phase-range model $\\theta_{\\max}(T)$ and the pathloss parameterization used in the simulations.","marker":"[13]"},{"why":"This reference gives the maximum phase shift relation $\\theta_{\\max}(T)=2\\pi d/\\lambda\\cdot\\Delta n(T)$ and the full-range design condition at the reference temperature.","marker":"[15]"},{"why":"This reference provides the four-parameter model for the extraordinary and ordinary refractive indices that underlies the birefringence formula.","marker":"[16]"},{"why":"This reference supplies the RIS channel representation used to write the received signal and the SINR expression.","marker":"[1]"},{"why":"This reference supplies the semidefinite-relaxation with bisection approach used for the precoder subproblem.","marker":"[18]"},{"why":"This reference justifies the unit-amplitude passive reflection assumption $|\\beta_n|=1$ for the LC-RIS elements.","marker":"[12]"}],"fun_headline_variants":["Heat-proofing LC-RIS phase shifts preserves multi-user fairness","Temperature-aware LC-RIS design beats baseline by respecting phase bounds","Optimizing inside shrunken LC-RIS phase range restores SINR fairness","New algorithm keeps LC-RIS fair when heat shrinks phase range","Design that respects LC temperature limits lifts downlink SINR"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The phase-update step depends on the assumption that at every iteration each phase changes only a tiny amount, so that the squared terms dropped from the Taylor expansion really are negligible; the algorithm has no mechanism that forces such tiny changes.","fun_headline_variants_meta":{"raw":{"variants":["Heat-proofing LC-RIS phase shifts preserves multi-user fairness","Temperature-aware LC-RIS design beats baseline by respecting phase bounds","Optimizing inside shrunken LC-RIS phase range restores SINR fairness","New algorithm keeps LC-RIS fair when heat shrinks phase range","Design that respects LC temperature limits lifts downlink SINR"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000649,"raw_usage":{"total_tokens":2999,"prompt_tokens":989,"completion_tokens":2010,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":1920}},"tokens_in":605,"tokens_out":2010,"duration_ms":12474,"temperature":1.0,"reasoning_tokens":1920,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:11:19.938857+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a small instance (for example $N=16$, $K=2$, $\\theta_{\\max}=\\pi$), run the proposed algorithm and then evaluate the true SINR at the returned phase vector; if the achieved minimum SINR falls below the $\\kappa$ value produced by the linearized constraint, the Taylor surrogate is not faithful. A second check is algebraic: substituting the expansions into the original SINR inequality should reproduce the linearized constraint term by term, so a symbolic or numeric expansion can settle whether that constraint actually represents the original SINR bound.","supporting_citations":[{"cited_title":"Studies of liquid crystal response time,","cited_arxiv_id":null,"evidence_quote":"This reference gives the maximum phase shift relation $\\theta_{\\max}(T)=2\\pi d/\\lambda\\cdot\\Delta n(T)$ and the full-range design condition at the reference temperature."},{"cited_title":"Temperature effect on liquid crystal refractive indices,","cited_arxiv_id":null,"evidence_quote":"This reference provides the four-parameter model for the extraordinary and ordinary refractive indices that underlies the birefringence formula."},{"cited_title":"Max- Min fair beamforing design for a RIS-assisted system with SWIPT,","cited_arxiv_id":null,"evidence_quote":"This reference supplies the semidefinite-relaxation with bisection approach used for the precoder subproblem."},{"cited_title":"Fast transition-aware reconfiguration of liquid crystal-based RISs,","cited_arxiv_id":null,"evidence_quote":"This reference justifies the unit-amplitude passive reflection assumption $|\\beta_n|=1$ for the LC-RIS elements."}],"review_version":1}