Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination

Alejandro Jim\'enez-S\'aez; Mohamadreza Delbari; Qikai Zhou; Robin Neuder; Vahid Jamali

REVIEW 3 major objections 4 minor 22 references

Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2508.04331 v1 pith:LMQZP4MD submitted 2025-08-06 eess.SP

Mohamadreza Delbari , Qikai Zhou , Robin Neuder , Alejandro Jiménez-Sáez , Vahid Jamali This is my paper · ORCID

classification eess.SP

keywords liquidcrystalRISfrequency-dependentphaseshiftwidebandOFDMphysicallayersecuritynear-fieldbeamformingsecrecyratesemidefiniteprogrammingreconfigurableintelligentsurface

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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

What would settle it

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.

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Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

Referee Report

3 major / 4 minor

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.

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 (3)

[III-C, P4/P5/Lemma 2, Eq. (15)] 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.
[III-C.2, Eq. (19)] 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.
[II-B, Eq. (5) and P1 constraint (9d)] 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.

minor comments (4)

[II-C] 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.
[II-A, Eq. (1)] 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.
[Eq. (18a)] 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.
[Fig. 4] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LC frequency-scaling model is an external input, not fitted to the simulated secrecy rate.

full rationale

The derivation chain does not reduce to its own inputs. The frequency-dependent phase constraint (5), [ω(f_k)]_n = [ω_c]_n β_k with β=2.4, is imported from the experimental characterization in [4] (Fig. 3e) and prior modeling in [8]; it is a stated system model, not a parameter fitted to reproduce the reported ≈2 bits/symbol secrecy rate. Algorithm 1 then optimizes RIS phases under this model and evaluates secrecy rate in simulation, so the headline number is a computed consequence of the model rather than a refit. Lemma 1 (optimal BS beamformer q = √P_t a_BS(p_RIS, f_c)) is deferred to the authors' prior [9, Lemma 1], but this is a standard LOS steering-vector result and is not the central LC-RIS secrecy claim; it is not an unverified uniqueness theorem or an ansatz smuggled in by citation. Lemma 2's reduction of per-subcarrier PSD/rank/diagonal constraints to center-frequency constraints is technically questionable for non-rank-one matrices because the non-integer Hadamard power S_c^{∘β_k} is ill-defined for general PSD matrices, and Algorithm 1 applies it to relaxed non-rank-one iterates; however this is an internal mathematical/correctness flaw, not a circular equivalence between the claimed prediction and an input. The benchmarks that ignore frequency-dependent phase shifts are deliberately weaker baselines, and comparing against them is the intended evaluation, not circularity.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim rests on the LC phase-frequency scaling model, the blocked-direct-channel and LOS-dominance assumptions, an unproved beamforming lemma deferred to a self-cited reference, and the unstated discretization of continuous worst-case regions. beta = 2.4 is an experimentally fitted material parameter from prior work, and the algorithm hyperparameters are manually chosen.

free parameters (2)

beta (LC frequency-scaling coefficient) = 2.4 [4]
Controls the linear scaling of phase shift with frequency in Eq. (5); taken from the experimental LC-RIS characterization in [4]. The wideband gain claim depends on this value and on its assumed uniformity across all unit cells.
Algorithm hyperparameters (eta^(0), I_max, J_max) = 0.01, 9, 2
Penalty initial value and iteration counts in Algorithm 1 are chosen by hand with no sensitivity study; the reported secrecy rate may depend on these choices.

assumptions (7)

domain assumption Direct BS-to-user and BS-to-eavesdropper channels are severely blocked (h_d,g = 0) for all users and the eavesdropper.
Section II-A; motivates the RIS-only link and is necessary for the effective channel to be solely the RIS-reflected path.
domain assumption All links are LOS-dominated with high Rician K-factor, enabling channel matrices to be approximated by steering vectors.
Section II-A and III-B; used to set q = sqrt(Pt) a_BS(p_RIS, f_c) and to express H_t(f_c) as an outer product of steering vectors.
domain assumption Reflection amplitude of every LC unit cell is unity across all subcarriers: [Omega]_n = 1.
Section II-A, based on [4]; simplifies Gamma(f) to a phase-only diagonal matrix.
domain assumption LC phase shift at subcarrier f_k equals the center phase scaled by beta_k = 1 + beta(f_k/f_c - 1) with a single beta = 2.4 (Eq. 5).
Section II-B, Eqs. (4)-(5); this is the load-bearing model that makes the frequency-aware design well-posed. It is extrapolated from experimental data in [4] and assumed uniform across elements.
domain assumption The optimal BS beamformer for P2 is q = sqrt(Pt) a_BS(p_RIS, f_c) (Lemma 1).
Section III-B; proof omitted and deferred to [9, Lemma 1], a self-cited prior work. The assertion that the BS is in the beam-squinting acceptable regime is not backed by a theorem and appears inconsistent with Fig. 3b.
domain assumption Near-field steering vector and pathloss models from [19] accurately represent the physical channel for the large RIS.
Section III-B and IV-A; adopted from [19] with no independent validation in this paper.
domain assumption The continuous worst-case constraints over p_u in P_u and p_e in P_e can be enforced by a finite set of sample points, though the discretization is not described.
Section III-C, constraint C1 says 'for all (p_u,p_e)', but Algorithm 1 and simulations do not specify how the continuous area constraints are sampled; this is an unstated approximation.

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Cite this review

Pith. "Pith review of Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination." pith.science (2026). https://pith.science/paper/LMQZP4MD

@misc{pith2026250804331,
  author       = {Pith},
  title        = {Pith review of: Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMQZP4MD}},
  note         = {Machine review of arXiv:2508.04331}
}

read the original abstract

Liquid crystal (LC) technology provides a low-power and scalable approach to implement a reconfigurable intelligent surface (RIS). However, the LC-based RIS's phase-shift response is inherently frequency-dependent, which can lead to performance degradation if not properly addressed. This issue becomes especially critical in secure communication systems, where such variations may result in considerable information leakage. To avoid the need for full channel state information (CSI) acquisition and frequent RIS reconfiguration, we design RIS for a wideband orthogonal frequency division multiplexing (OFDM) system to illuminate a desired area containing legitimate users while avoiding leakage to regions where potential eavesdroppers may be located. Our simulation results demonstrate that the proposed algorithm improves the secrecy rate compared to methods that neglect frequency-dependent effects. In the considered setup, the proposed method achieves a secrecy rate of about 2 bits/symbol over an 8 GHz bandwidth when the center frequency is 60 GHz.

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Reference graph

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Reviewed August 6, 2026 · model on record in the stance chip above.

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