{"id":"2e7528be-9609-4f02-ad60-811f2ba1abc4","arxiv_id":"2508.04331","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A frequency-aware LC-RIS phase-shift design raises simulated worst-case secrecy rate to about 2 bits/symbol over 8 GHz at 60 GHz versus benchmarks that ignore the LC frequency response.","lead":"Liquid-crystal smart surfaces can steer reflected wireless signals; this paper designs their phase settings to keep signals strong for legitimate users and weak for eavesdroppers across a wide 8 GHz band. It matters for future low-power 6G links, though the result is simulation-only and rests on assumptions that need scrutiny.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Hadamard power S_c^{∘β_k} for non-integer β_k is not a well-defined function of general PSD S_c; Lemma 2 only holds for rank-one S_c, so the relaxed P5/P7 and Algorithm 1 are ill-posed.","rationale":"The paper addresses a relevant and timely problem: frequency-dependent LC-RIS phase shifts in wideband secure illumination. The system model and the original problem P1 are clearly stated, and the simulation setup is reasonably detailed. However, the mathematical reformulation that leads to the SDP contains a fundamental flaw. The step from P3 to P4 relies on Sk = S_c^{∘β_k}, which is only valid when each S_k is the outer product of the elementwise β_k-th power of a phase vector. For a general PSD variable S_c that is not rank-one, the non-integer Hadamard power is not uniquely defined, and Lemma 2's proof only works under the rank-one assumption it is meant to establish. Therefore P5 is not equivalent to P4, and Algorithm 1's line 8 computes an undefined quantity whenever the SDP returns a non-rank-one matrix. The penalty method encourages low rank but does not guarantee rank-one at every iteration. This is an internal inconsistency, not merely a deviation from current consensus. The proposed concrete test would expose the ambiguity in a simple 2×2 case. Until the Hadamard-power operation is rigorously defined—for example, by restricting to rank-one iterates and using phase-domain variables, or by proving a generalized property for a specific branch—the secrecy-rate results are not well-defined. This supports the reader's rejection, though we identify the Hadamard-power issue as the primary load-bearing concern rather than the physical LC model.","tokens_in":11976,"tokens_out":9597,"duration_ms":105352,"concrete_test":"Take N=2, β_k=0.5, and S_c = [[1, 0.5+0.5j],[0.5−0.5j,1]], which is PSD. Compute S_c^{∘0.5} using two branches for the off-diagonal square root (principal angle and angle+2π), yielding off-diagonal entries w and −w. Pick any fixed A_k with nonzero off-diagonal entries and evaluate tr(A_k S_c^{∘0.5}) for both branches. If the two values differ, the constraint cC1 in P4/P5 is not a single-valued function of S_c, confirming that the relaxed problem P7 and Algorithm 1's step 8 are ill-posed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To obtain P4, the authors set S_k = S_c^{∘β_k} for β_k = 1+β(f_k/f_c−1), which is non-integer for most subcarriers. For a general Hermitian matrix S_c, the off-diagonal phases are known only modulo 2π. Raising a complex number to a non-integer power is multi-valued: e.g., if [S_c]_{ij}=e^{jθ}, then (e^{jθ})^{β_k} can be e^{jβ_k θ} or e^{jβ_k(θ+2π)}, which differ for non-integer β_k. Thus S_c^{∘β_k} is not a well-defined matrix function. Lemma 2 attempts to prove that positivity/rank/diagonal constraints hold at all subcarriers if they hold at the center frequency, but its proof uses the rank-one decomposition S_c = s_c s_c^H and replaces S_k with s_c^{∘β_k}(s_c^{∘β_k})^H, thereby assuming the rank-one property it is supposed to establish. Since P5/P7 optimize over PSD matrices that are not guaranteed to be rank-one, and Algorithm 1 line 8 computes S_k = (S_c^{(I_max)})^{∘β_k}, the optimization steps and the final secrecy-rate evaluation are undefined for non-rank-one iterates. This is an internal inconsistency in the derivation of the claimed achievable secrecy rate, independent of the physical LC model.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper addresses phase-shift design for an LC-based RIS in a wideband OFDM secure downlink with location-uncertain legitimate users and an eavesdropper. It models the LC phase response as scaling linearly with frequency via ω(f_k) = ω_c(1+β(f_k/f_c−1)), formulates a worst-case secrecy-rate maximization over user and eavesdropper regions, and proposes an alternating optimization with semidefinite programming. A key step maps the frequency-coupling constraint into the Hadamard power S_k = S_c^{∘β_k} and uses Lemma 2 to reduce all subcarrier constraints to a single center-frequency matrix. Simulations report about 2 bits/symbol over an 8 GHz bandwidth and claim improved ensured secrecy rate relative to three benchmarks.","tokens_in":12343,"tokens_out":7568,"duration_ms":94317,"significance":"The topic is timely and practically motivated: LC-RIS hardware exhibits frequency-dependent phase shifts, and secure illumination with only approximate location information is a relevant problem. However, the paper's central algorithmic contribution rests on an ill-posed matrix operation. The Hadamard power of a general Hermitian matrix to a non-integer exponent is not well defined, and Lemma 2 proves the needed propagation only under a rank-one assumption. Since the proposed algorithm solves a relaxed problem over non-rank-one matrices and then applies this undefined operation, the optimization and the reported secrecy-rate results are not mathematically grounded. The paper does not provide machine-checked proofs or reproducible code, and the numerical evidence is therefore not sufficient to establish the claimed performance gain.","major_comments":[{"comment":"The transformation S_k = S_c^{∘β_k} is not a well-defined matrix function for non-integer β_k on a general Hermitian matrix. For an entry e^{jθ}, the complex power has multiple branches: (e^{jθ})^{β_k} = e^{jβ_k(θ+2πm)}, and these differ when β_k is not an integer. Lemma 2 proves that C2–C4 propagate to all subcarriers only by writing Sc = s_c s_c^H, which assumes the rank-one property that P5/P7 are meant to relax. Since P7 optimizes over all PSD matrices without the rank constraint, Algorithm 1 line 8 applies the Hadamard power to a non-rank-one iterate. Consequently cC1, the algorithmic update, and the final secrecy-rate evaluation are undefined. This is an internal inconsistency independent of the physical LC model.","section":"III-C, P4/P5/Lemma 2, Eq. (15)"},{"comment":"The first-order Taylor expansion S_c^{∘β_k} ≈ (S_c^{(i)})^{∘β_k} + β_k (S_c^{(i)})^{∘(β_k−1)} ⊙ (S_c − S_c^{(i)}) requires differentiability of the entrywise power map at complex/Hermitian matrices. For non-integer β_k, z↦z^β is not analytic on the complex plane and has branch cuts; the expression (S_c^{(i)})^{∘(β_k−1)} is itself undefined for general Hermitian entries. Thus cC1 is not a valid convex approximation, and the convex program solved in lines 4–7 of Algorithm 1 is not a surrogate of P3. This is a load-bearing flaw because the entire algorithm is built on this approximation.","section":"III-C.2, Eq. (19)"},{"comment":"Constraint (9d) is written as an equality on unwrapped phases: [ω(f_k)]_n = [ω_c]_n β_k. Since [ω_c]_n ∈ [0,2π) and β_k can exceed 1, the right-hand side can exceed 2π, whereas the physical phase shift is defined modulo 2π. The subsequent reformulation S_k = S_c^{∘β_k} additionally requires a branch choice for off-diagonal phase differences of the relaxed matrix; different branch choices produce different matrices. The feasible set of the optimization is therefore not the physical set of LC phase configurations. This model-level ambiguity compounds the algebraic issue in P4/P5.","section":"II-B, Eq. (5) and P1 constraint (9d)"}],"minor_comments":[{"comment":"In the second bullet, 'The size, |Pe|, can be adjusted ...' appears to be a typo; it should refer to |Pu|, the size of the legitimate-user area.","section":"II-C"},{"comment":"The transmitted signal is written as x(f_k) = q s(f_k) with s(f_k) ∈ C^{N_s}, but the users and eavesdropper are single-antenna. Either s(f_k) should be a scalar (N_s=1) or N_s should be defined and the signaling model clarified.","section":"II-A, Eq. (1)"},{"comment":"The term 'λ_max(S_c^{(i)}), × λ_max^H(S_c^{(i)})' contains a typographical artifact; the product of the eigenvector and its Hermitian should be written cleanly. The labels cC2, cC3 are also confusingly introduced.","section":"Eq. (18a)"},{"comment":"The x-axis spans 50–66 GHz while the text states an 8 GHz bandwidth. The 'interested frequency band' is not defined, so the reader cannot reconcile the figure with the stated bandwidth.","section":"Fig. 4"}],"recommendation":"reject","confidential_remarks":"The ill-posed Hadamard-power operation is not a local fix; the optimization problem would need to be reformulated, e.g., in the phase domain or with a valid rank-one-preserving parameterization, and all simulations would need to be rerun. Given that the paper's central claim depends on this step, I do not see a path to acceptance within the current scope. There is also a scope-fit concern: the 'near-field' aspect is not central to the derivation, and the CSI-free illumination setup is closer to a coverage-optimization problem than to a near-field-specific contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing you should know first: the paper's practical motivation is sound and fairly original. Modeling the LC-RIS phase shift as linearly scaling with frequency, and building an illumination design that respects that constraint, is a legitimate problem that the wideband RIS literature mostly ignores. The authors cite experimental evidence and the secure-illumination setup (uncertain user/eve locations) is a sensible use case. The simulation shows a meaningful secrecy-rate gain over the frequency-agnostic benchmarks. That said, the central optimization machinery has a load-bearing mathematical gap. The reformulation S_k = S_c^{∘β_k} for non-integer β_k is not a well-defined function of a general Hermitian matrix: raising a complex entry to a non-integer power is multi-valued, and for a sum of exponentials (any non-rank-one S_c) there is no natural choice. Lemma 2's proof simply assumes S_c = s_c s_c^H to verify the rank-one property, which is circular for the purpose of allowing a rank relaxation. The relaxed P5/P7 and Algorithm 1's line 8 all compute S_c^{∘β_k} for iterates that are not guaranteed rank-one. The Taylor expansion in (19) also presumes smoothness of z^β, which fails on a branch cut. As a result, the algorithm as stated is not a well-defined optimization; the claimed achievable secrecy rate is not rigorously grounded. A second, smaller issue: the beam-squinting justification is inconsistent with the simulation, which uses a 256-element BS UPA. Their own Fig. 3b shows significant squint loss for arrays beyond about 60 elements. The claim that the BS beamformer can be designed only at the center frequency does not sit well with their own plot. The rest is more standard. The simulation is a single geometry, the LC model is a uniform linear scaling from one experimental characterization, and no code or data are provided. Those are minor-to-moderate concerns given the paper's focus on a new constraint. Overall: the problem is worth working on, and the frequency-scaling idea is a real contribution. But the current formulation cannot be trusted as a valid algorithm. A rewrite that parameterizes the RIS phases directly (e.g., optimizing ω_c and computing ω_k = β_k ω_c) would avoid the Hadamard-power ambiguity entirely. I'd send it to peer review because the issue is specific and fixable, but the authors should be told that the rank-relaxation path, as written, is not sound.","headline":"The LC frequency-scaling model is a real and useful contribution, but the core relaxation uses an undefined Hadamard power for non-rank-one matrices; the algorithm as written is not well-defined.","tokens_in":12834,"tokens_out":6364,"would_cite":false,"duration_ms":67623,"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 establishes that explicitly modeling the frequency-dependent phase response of LC-RIS elements in wideband OFDM secure illumination improves worst-case secrecy rate, achieving about 2 bits/symbol across an 8 GHz band at 60 GHz.","keywords":["liquid crystal RIS","frequency-dependent phase shift","wideband OFDM","physical layer security","near-field beamforming","secrecy rate","semidefinite programming","reconfigurable intelligent surface"],"falsifier":"Measure each LC cell's phase shift versus frequency across the 56–64 GHz band in a 100-element array. If the measured $[\\omega(f_k)]_n$ deviates from $[\\omega_c]_n(1 + \\beta(f_k/f_c - 1))$ beyond a small fraction of the cell's tuning range, then constraint (9d) is mis-specified and the 2 bits/symbol claim is not guaranteed. Alternatively, rerun the algorithm with per-element $\\beta$ values drawn from a realistic distribution and compare the resulting worst-case secrecy rate with the uniform-$\\beta$ result.","tokens_in":11889,"feed_emoji":"🔒","tokens_out":7854,"duration_ms":81828,"temperature":0.7,"pith_summary":"Liquid-crystal reconfigurable intelligent surfaces (LC-RISs) are cheap and scalable, but their phase shifts drift with frequency, and the paper argues that ignoring this drift leaks information in wideband secure links. The paper's central proposal is to treat the drift as a structured constraint: each LC cell's phase at every OFDM subcarrier is the center-frequency phase multiplied by a known factor, so the whole wideband design collapses to an optimization at one frequency. Under this model, a semidefinite-programming algorithm maximizes the worst-case secrecy rate over all possible user and eavesdropper positions in two approximate regions, without needing full channel state information. Simulations show the frequency-aware design holds a secrecy rate near 2 bits/symbol over an 8 GHz band centered at 60 GHz, above three benchmarks that neglect the LC frequency response. If true, this turns a hardware limitation into a design handle for secure wideband coverage.","feed_headline":"LC-RIS design keeps 2 bits/symbol secrecy over 8 GHz","feed_subtitle":"Accounting for liquid-crystal frequency drift in RIS phase shifts secures wideband links without full channel knowledge.","key_machinery":"The load-bearing object is Eq. (5), the per-cell linear frequency-scaling law $[\\omega(f_k)]_n = [\\omega_c]_n \\beta_k$ with $\\beta_k = 1 + \\beta(f_k/f_c - 1)$, where $\\beta = 2.4$ comes from a single experimental LC characterization. Its matrix-level consequence, $S_k = S_c^{\\circ \\beta_k}$ (elementwise/Hadamard power), lets Lemma 2 transfer feasibility constraints from the center frequency to every subcarrier, so the optimizer only handles one matrix $S_c$. The solution machinery combines a nuclear-norm penalty for the rank-one constraint, a first-order Taylor linearization of the Hadamard-power constraint, and alternating optimization over $\\gamma$ (the secrecy-rate threshold) and $S_c$, w","core_discovery":"The paper claims that the frequency-dependent phase response of LC-RIS elements is not merely a degradation but a controllable, structured relationship. Specifically, the phase of element $n$ at subcarrier $k$ is modeled as $[\\omega(f_k)]_n = [\\omega_c]_n \\beta_k$, with $\\beta_k = 1 + \\beta(f_k/f_c - 1)$ and $\\beta = 2.4$ taken from experimental characterization. This yields $S_k = S_c^{\\circ \\beta_k}$, the Hadamard (elementwise) power of the center-frequency covariance matrix, and Lemma 2 shows that rank-one, positive-semidefinite, and unit-modulus constraints at the center frequency imply the same for every subcarrier. The paper then formulates the secure illumination problem as maximizing","pith_inferences":["The uniform $\\beta = 2.4$ scaling is the fragile link: measuring per-element $\\beta$ distributions and feeding them into the same optimizer would show whether the 2 bits/symbol claim holds or is optimistic.","The Hadamard-power reduction is not specific to secrecy; the same center-frequency feasibility transfer could simplify wideband RIS designs for coverage extension, energy harvesting, or localization.","Because the design requires only region-level location knowledge, it pairs naturally with mobility and location-estimation error: one configured state can serve a user until the user leaves the designed region, reducing reconfiguration overhead beyond what the paper quantifies."],"forward_implications":["A worst-case secrecy rate of about 2 bits/symbol is maintained across the full 8 GHz band at 60 GHz center frequency.","Accounting for the LC frequency response in the RIS phase design yields a higher ensured secrecy rate on every subcarrier than frequency-blind benchmarks.","Secure illumination is possible with only approximate location regions for users and eavesdroppers, avoiding full CSI acquisition and frequent RIS reconfiguration.","Only the center-frequency phase vector needs to be optimized; all subcarrier phase settings follow deterministically from the scaling law.","The non-convex wideband design is reduced to a sequence of convex semidefinite programs with a closed-form update for the secrecy threshold."],"supporting_citations":[{"why":"Supplies the experimental liquid-crystal phase-shift versus frequency data and the $\\beta=2.4$ factor that grounds the linear frequency-scaling law (5).","marker":"[4]"},{"why":"Provides the piece-wise linear voltage-to-phase model for $h(v)$ used to connect applied voltage to reference phase at the center frequency.","marker":"[8]"},{"why":"Supplies the secrecy-rate definition and the Lemma 1 optimal beamformer proof that the paper reuses for the fixed-RIS beamforming subproblem.","marker":"[9]"},{"why":"Supports the beam-squinting analysis that justifies optimizing the BS beamformer only at the center frequency for moderate antenna counts.","marker":"[18]"},{"why":"Provides the near-field steering-vector model used for the LC-RIS array response in the line-of-sight channel.","marker":"[19]"},{"why":"Supplies the nuclear-norm penalty method used to relax the rank-one constraint on the center-frequency covariance matrix.","marker":"[20]"}],"fun_headline_variants":["LC-RIS hits 2 bits/symbol secrecy over 8 GHz without CSI","Frequency-aware phase design secures wideband LC-RIS links","Wideband secure illumination via frequency-dependent LC-RIS","Liquid crystal RIS thwarts eavesdroppers across 8 GHz"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The design rests on the assumption that every LC cell's phase shift scales linearly and identically with frequency according to one measured factor; if real cells deviate from this rule, the optimized phase settings are not actually achievable and the claimed secrecy-rate gain is not defined.","fun_headline_variants_meta":{"raw":{"variants":["LC-RIS hits 2 bits/symbol secrecy over 8 GHz without CSI","Frequency-aware phase design secures wideband LC-RIS links","Wideband secure illumination via frequency-dependent LC-RIS","Liquid crystal RIS thwarts eavesdroppers across 8 GHz"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000333,"raw_usage":{"total_tokens":1675,"prompt_tokens":717,"completion_tokens":958,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":461,"completion_tokens_details":{"reasoning_tokens":883}},"tokens_in":461,"tokens_out":958,"duration_ms":10750,"temperature":1.0,"reasoning_tokens":883,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:44:10.020444+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure each LC cell's phase shift versus frequency across the 56–64 GHz band in a 100-element array. If the measured $[\\omega(f_k)]_n$ deviates from $[\\omega_c]_n(1 + \\beta(f_k/f_c - 1))$ beyond a small fraction of the cell's tuning range, then constraint (9d) is mis-specified and the 2 bits/symbol claim is not guaranteed. Alternatively, rerun the algorithm with per-element $\\beta$ values drawn from a realistic distribution and compare the resulting worst-case secrecy rate with the uniform-$\\beta$ result.","supporting_citations":[{"cited_title":"Architecture for sub-100 ms liquid crystal reconfigurable intelligent surface based on defected delay lines,","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental liquid-crystal phase-shift versus frequency data and the $\\beta=2.4$ factor that grounds the linear frequency-scaling law (5)."},{"cited_title":"Fast transition-aware reconfiguration of liquid crystal- based RISs,","cited_arxiv_id":null,"evidence_quote":"Provides the piece-wise linear voltage-to-phase model for $h(v)$ used to connect applied voltage to reference phase at the center frequency."},{"cited_title":"A tutorial on wideband XL-MIMO: Challenges, opportunities, and future trends,","cited_arxiv_id":null,"evidence_quote":"Supports the beam-squinting analysis that justifies optimizing the BS beamformer only at the center frequency for moderate antenna counts."}],"review_version":1}