{"id":"37a9e961-4c1e-405f-8e35-2687c86133d0","arxiv_id":"2501.01012","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A delay-augmented reconfigurable refractive surface, optimized with an alternating SDR/SCA/barrier algorithm, mitigates beam split in wideband near-field multi-user communications.","lead":"This paper designs a beamforming method for a new type of antenna called a reconfigurable refractive surface (RRS) that works in wideband, near-field, multi-user settings. It adds small time-delay units to the surface to stop different frequencies from splitting apart, and shows by simulation that the method improves the weakest user's data rate.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Delayed-RRS claim rests on an unstated frequency-response model; every reported gain may be an artifact of the private ψ(θ_c,f) used in simulation, so the central result is not independently testable.","rationale":"The reader's weakest-assumption analysis identifies exactly the same load-bearing concern that I find: the frequency-selective transmission coefficient ψ_{m,i}=ψ(θ_i^c,f_m) in Eq. (1) is never given an explicit functional form, even though every quantitative result in Section VII is computed from it. I agree that this is the most important gap. The paper has real strengths: the system model is clearly laid out, the problem decomposition into digital, analog, and delay subproblems is natural, and the simulations demonstrate qualitative consistency with the authors' narrative. However, because the central quantitative claims are not reproducible without the undisclosed model, the results must be treated as conditional. I do not see a more fundamental internal inconsistency: the SCA-based digital beamforming step is a standard relaxation, and the delay-compensation structure is physically plausible. The convergence argument for the barrier-method subproblems is informal, but that alone would not change the verdict. The Appendix A derivation of Proposition 1 has a suspicious step in the variable transformation, but Proposition 1 is a side result about feed-RRS distance, not the core beamforming claim, so it is secondary. The controlling uncertainty remains the RRS frequency-response model. Since the reader's CONDITIONAL verdict already reflects this concern, no adjustment is needed; the appropriate next step is to ask the authors for the explicit model and code, or for a robustness check against an independent model.","tokens_in":18379,"tokens_out":5907,"duration_ms":55876,"concrete_test":"Require the authors to release the exact functional forms of the two 'constructed functions' in Section VII.A (the magnitude and phase of ψ(θ_c,f) as explicit functions of f and θ_c, including the k_p dependence) together with the simulation code. Independently re-run the Fig. 5 comparison ('Our proposed' versus 'Without TD') with (a) the disclosed model and (b) an alternative physics-based frequency response, such as the Lorentzian element-response model used in [15], fitted to the same operating points. If in case (b) the rate gap between 'Our proposed' and 'Without TD' at P = 10 dB shrinks below, say, 0.5 bps/Hz or changes sign, the central claim that Delayed-RRS robustly mitigates beam split under RRS frequency selectivity is not established; if the gap persists in both models, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central evidence is the simulation campaign in Figs. 5-9, and every one of those curves is generated from a frequency-selective RRS model that is never written down. Equation (1) defines ψ_{m,i}=ψ(θ_i^c,f_m) only abstractly; Section VII.A says 'we construct two functions' with reference to [8] and introduces a sensitivity knob k_p, but it gives no formulas for either the amplitude-frequency or phase-frequency response, no parameter values beyond k_p, and no code. The qualitative conclusion in Fig. 2(c) that edge-subcarrier beams 'lose focus' is a direct consequence of the phase errors produced by this specific ψ; a different, equally plausible frequency response could produce a different beam-split pattern or even different relative gains. More importantly, the feasibility of the optimization in P1 depends on the coupling structure of ψ across subcarriers: the joint optimization of θ_i^c and τ_i is only meaningful if the modeled amplitude and phase are simultaneously realizable at all subcarriers. Without the explicit model, an independent reader cannot reproduce Figs. 5-9, cannot test sensitivity to k_p beyond the reported points, and cannot tell whether the Delayed-RRS gain over 'Without TD' is a robust physical effect or a property of the chosen constructed functions. This missing specification is load-bearing because the paper's headline claim is exactly that the proposed scheme mitigates beam split under RRS frequency selectivity; if the underlying ψ is private, the comparison to baselines is not falsifiable by a third party. A secondary concern is that the Appendix A derivation of Proposition 1 appears to contain an algebraic slip in the sine/cosine conversion between Eqs. (39) and (41), but that result is not the core of the paper; the primary issue is the undisclosed RRS response model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers a wideband (OFDM) multi-user downlink in which a reconfigurable refractive surface (RRS) serves as the transmit antenna of a base station. The authors model the RRS as frequency selective, couple that selectivity with the near-field spherical-wave channel, and argue that the two effects jointly worsen the beam-split phenomenon. To mitigate this, they propose a 'Delayed-RRS' architecture in which each RRS element is augmented with an ideal time-delay unit, and they formulate a max-min rate problem over the digital beamformer, the RRS phase configuration, and the time delays. The problem is decomposed into three subproblems: digital beamforming via SDR/SCA, analog beamforming via an exponential-barrier gradient method, and time-delay compensation via a similar gradient method. Convergence and complexity claims are given, an optimal feed-RRS distance is derived in Appendix A, and simulations in Figs. 5-9 compare the proposed scheme against baselines.","tokens_in":18670,"tokens_out":9922,"duration_ms":90822,"significance":"The problem addressed is timely: wideband near-field operation is central to 6G extreme-aperture systems, and most prior work treats near-field beam split and metasurface frequency selectivity separately. The Delayed-RRS structure is a plausible and practically motivated extension of delay-phase architectures to RRS hardware, and the alternating-optimization framework is a reasonable approach to a difficult nonconvex problem. If the numerical results are reproducible and the RRS model is physically representative, the paper would provide a useful design guideline and a fair baseline comparison. However, the central quantitative claims currently rest on an unspecified frequency-response model, and the Appendix A derivation contains an internal inconsistency. The significance is therefore conditional: the paper's contribution is real but cannot be fully assessed until those gaps are closed.","major_comments":[{"comment":"The frequency-selective RRS response ψ(θ_c^i, f_m) is never given an explicit functional form. Eq. (1) only defines it abstractly, and Section VII.A states that 'we construct two functions' with a sensitivity knob k_p, but the actual amplitude-frequency and phase-frequency formulas, all parameter values except k_p, and the mapping from k_p to the response are omitted. Every simulation curve in Figs. 5-9 and the beam-focus claim in Fig. 2(c) are generated from this private model. Because the analog and delay subproblems (P3) and (P4) require gradients of the rate with respect to ψ, the implemented algorithm is also underspecified without this model. This is a load-bearing omission for the paper's headline claim that the proposed Delayed-RRS scheme mitigates beam split under RRS frequency selectivity. Please provide the exact functions (or the explicit equation from the reference used, with all constants), the parameter values, and the definition of k_p; ideally include the simulation code or a detailed setup so that an independent reader can reproduce Figs. 5-9.","section":"Section VII.A and Eq. (1)"},{"comment":"The two expressions for the ideal amplitude gain A in Eq. (41) are not equal. In the first expression, the bracketed term is (h^2/(a^2+h^2))^{(α_t+α_r-2)/4}, which equals cos^{(α_t+α_r-2)/2} θ_0 because h^2/(a^2+h^2)=cos^2 θ_0. In the second expression, the bracketed term is (sin θ_0)^{(α_t+α_r-2)/2}. Replacing cos^{(α_t+α_r-2)/2} by sin^{(α_t+α_r-2)/2} changes the stationary condition. Eq. (42) follows from differentiating the cos-based expression (A ∝ cot θ_0 [1 - cos^β θ_0] with β=(α_t+α_r-2)/2), not from the sin-based expression. Please correct the typo, re-derive the condition, and verify the claimed unique solution. This matters because Proposition 1 and its validation in Fig. 6 depend on this derivation.","section":"Appendix A, Eqs. (41)-(42)"},{"comment":"The time-delay architecture is introduced as an ideal component e^{-j2π f_m τ_i} with no discussion of delay resolution, bandwidth limitations, insertion loss, or power cost. Since the Delayed-RRS is a hardware-oriented proposal, this idealization should be stated explicitly as an assumption and its impact on the reported gains should at least be discussed. In addition, the maximum delay is given as τ_max=1/f_c in Section V.C but as τ_max=1/(2 f_c) in Table I; this inconsistency changes the maximum phase range from about 2π to about π and should be resolved.","section":"Section V.C and Table I"}],"minor_comments":[{"comment":"There are many typographical and grammatical errors (e.g., 'imporve', 'an new', 'coefficeints', 'cofiguring', 'deeployed', 'iteratitively') that should be corrected in a revision.","section":"Throughout"},{"comment":"The notation in Eqs. (12)-(13) should be clarified: ψ_m is a vector of transmission coefficients, while h(f_m,r) is a column vector from Eq. (2); the dot product and the normalization factor a_m need a precise definition so that the array gain is unambiguous.","section":"Section III.A, Eq. (12)-(13)"},{"comment":"The text says the objective is to 'maximize the sum rate' but the problem in Eq. (16) maximizes the minimum rate. Please use consistent terminology.","section":"Section IV.A and Eq. (16)"},{"comment":"Figure 4 and the surrounding text do not state what is plotted on the axes or specify the 'two functions' beyond saying they are constructed following [8]. At minimum, define the amplitude and phase response axes and give the exact expressions.","section":"Section VII.A, Fig. 4"},{"comment":"The text describes the NLoS case as 'Rayleigh' and a 'Rayleigh channel model', but later refers to 'pure los and Rician conditions'; unify the terminology and clarify the channel model used in Fig. 9.","section":"Section VII.B, Fig. 9"},{"comment":"The convergence discussion would be more convincing if a numerical convergence plot or a stopping criterion were provided; Algorithm 2 runs for a fixed 'iter = 3' iterations, which seems small for an alternating algorithm.","section":"Section VI.A and Algorithm 2"},{"comment":"The barrier function is an exponential penalty, not a standard interior-point barrier that diverges at the constraint boundary. The text should state this explicitly and explain why the penalty formulation is preferred.","section":"Section V.B, Eq. (29)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely problem and the proposed Delayed-RRS scheme is interesting, but the missing frequency-response model is a serious reproducibility gap because all quantitative claims are supported only by simulation. This is fixable in revision by adding the explicit model, parameters, and ideally code. The Appendix A inconsistency is also fixable. I do not see a fundamental flaw that would require rejection, provided the authors supply the missing model and correct the derivation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi,\n\nThe thing to know about this one: the core idea is good—add true time-delay units to each RRS element so the wideband near-field beam split can be compensated in the analog domain, and then do alternating optimization of digital beamformer, RRS phase shifts, and delays to maximize the worst-user rate. That combination is new as far as the citations go; prior work treats near-field beamsplit and metasurface frequency selectivity separately. The algorithm is standard but competent: SDR/SCA for the digital part, barrier-method gradient descent for the analog part, and the complexity analysis is honest. I also give them credit for the Without-TD baseline; the gap between that and their full scheme is the actual measure of the delay unit's value, and it's meaningful (about 2 dB equivalent). So this is a legitimate step forward in the RRS beamforming subfield.\n\nThe soft spot is exactly where the reader put it: the frequency-selective RRS model. Equation (1) defines ψ(θc_i, f_m) abstractly, and Section VII.A says only that they 'construct two functions' based on [8] with a sensitivity knob kp, but no formulas, no amplitude/phase parameter values, nothing. Every curve in Figs. 5-9 comes from that private model. The beam-split behavior in Fig 2(c)—edge subcarriers losing focus—is a direct consequence of the chosen ψ, and the whole Delayed-RRS gain story depends on that choice. Another ψ, equally plausible, could change the relative gains or even wipe them out. The stress-test note hits this correctly: the comparisons are not falsifiable by a third party. I'd call this a serious but fixable flaw.\n\nSecondary issues: the Appendix A derivation for the optimal feed-RRS distance has a sign/cosine slip between (39) and (41), and (42) doesn't follow cleanly; that result is a side claim, though, not the main engine of the paper. No code or data either, which makes the missing ψ harder to excuse.\n\nNet: the paper is worth a referee, not a desk reject. A good referee should force them to write down the exact ψ model, correct the appendix, and share code. If that happens, I'd be reasonably confident in the result. If they can't or won't share the model, the simulation results should be treated as conditional on private choices.","headline":"Good idea, well-executed optimization, but the simulations rest on an unstated frequency-response model—so the headline gains are not independently checkable yet.","tokens_in":19283,"tokens_out":4145,"would_cite":false,"duration_ms":32924,"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 paper proposes that adding a controllable true time delay to each element of a reconfigurable refractive surface can compensate the frequency-dependent phase errors that, together with the near-field spherical wavefront, split…","keywords":["beam split","near-field communications","reconfigurable refractive surfaces","frequency selectivity","wideband beamforming","time-delay units","max-min fairness","OFDM"],"falsifier":"Measure the complex transmission coefficient of a real RRS element across the 1 GHz band, for example with free-space or waveguide S-parameter measurements at several bias voltages, then insert the measured $\\psi(\\theta_i^c, f_m)$ into the paper's simulator and compare the Delayed-RRS against the no-delay baseline; the central claim fails if the delay gain shrinks below the reported level or the edge-subcarrier focus loss persists despite optimized delays.","tokens_in":18112,"feed_emoji":"📡","tokens_out":7948,"duration_ms":66545,"temperature":0.7,"pith_summary":"The paper studies a wideband downlink in which a reconfigurable refractive surface (RRS) serves as the base-station antenna and users lie in its near field. It argues that two effects jointly worsen the beam-split problem: the near-field spherical wavefront makes different subcarriers focus at different locations, and the RRS's frequency-selective transmission coefficients add phase errors that make edge subcarriers lose focus entirely. To fix this, the authors introduce a Delayed-RRS element that appends a true time delay, and they design an alternating optimization that tunes the digital beamformer, the RRS phase shifts, and the delays to maximize the minimum user rate. If the scheme works as claimed, wideband near-field RRS systems could recover much of the data-rate loss that would otherwise confine usable communication to frequencies near the center carrier.","feed_headline":"Adding time delays fixes wideband beam split for refractive surfaces","feed_subtitle":"Jointly tuning beamformer, phase shifts, and delays lifts the worst user rate as much as a 2 dB power boost.","key_machinery":"The load-bearing object is the Delayed-RRS element: a conventional RRS element with response $\\psi(\\theta_i^c, f_m)$ at center-phase setting $\\theta_i^c$ and subcarrier frequency $f_m$, cascaded with a time-delay unit whose transfer function is $e^{-j2\\pi f_m \\tau_i}$, giving $\\psi_{m,i} = e^{-j2\\pi f_m \\tau_i} \\psi(\\theta_i^c, f_m)$. The delay is the mechanism that can align phases across the whole band because its phase varies linearly with frequency, which matches how the near-field propagation phase $e^{-j2\\pi f_m r_{i,k}/c}$ and the RRS response both vary. The optimization carries the argument: the max-min rate problem is split into digital beamforming (solved by semidefinite relaxation plus successive convex approximation), analog phase-shift design (barrier-function gradient ascent), and time-delay compensation (the same barrier method). The appendix adds a closed-form analysis showing that a single-feed RRS has an optimal feed-RRS distance that grows with the size of the RRS.","core_discovery":"The central claim is that the beam split in an RRS-based wideband near-field multiuser system is not merely a near-field phenomenon: the frequency selectivity of the RRS itself breaks phase alignment between elements on edge subcarriers, so beams that would simply shift focus in a frequency-flat near-field array instead spread and lose gain. The paper models each element's transmission coefficient as $\\psi_{m,i} = \\psi(\\theta_i^c, f_m)$ and proposes the delayed-RRS modification $\\psi_{m,i} = e^{-j2\\pi f_m \\tau_i} \\psi(\\theta_i^c, f_m)$, where $\\tau_i$ is a tunable time delay that adds a frequency-linear phase usable to compensate both the spherical near-field phase and the RRS's frequency-dependent response. On this basis it formulates a max-min rate problem and solves it by alternating semidefinite relaxation with successive convex approximation for the digital precoder, a barrier-function gradient method for the phase shifts, and a similar gradient method for the delays. Simulations show that the delay compensation is worth roughly 2 dB of transmit power and that ignoring either the near-field condition or the frequency selectivity costs noticeable rate, with the relative importance of the two depending on user distance.","pith_inferences":["Editorial inference: The quantitative gains are tied to the borrowed but unspecified transmission-coefficient model $\\psi(\\theta_i^c, f_m)$; with a different practical response, such as a Lorentzian amplitude-phase coupling, the size of the delay benefit could change even if the qualitative mechanism survives.","Editorial inference: The delay-compensation idea transfers to other frequency-selective surfaces and to wideband near-field sensing or localization, where beam split similarly corrupts focusing across the band.","Editorial inference: A direct extension would be to replace the assumed model with measured element responses and re-run the same optimizer; the paper's claim predicts the Delayed-RRS would still outperform the no-delay baseline on edge subcarriers."],"forward_implications":["In the simulated regime, adding optimized time delays improves the worst-user rate by an amount comparable to raising transmit power by about 2 dB.","Ignoring either the near-field spherical-wave channel or the RRS frequency selectivity causes measurable rate loss, and the loss grows with transmit power because it appears as inter-user interference.","There exists an optimal feed-to-RRS distance for a single-feed RRS, and the optimal distance increases with the number of RRS elements; the simulation matches the derived formula.","A small number of phase-quantization bits is sufficient to approach the continuous-phase rate bound, and under coarse quantization ignoring frequency selectivity can even behave better.","The alternating optimization converges because each subproblem drives the minimum rate monotonically upward, up to a controlled error in the barrier-method steps."],"supporting_citations":[{"why":"Supplies the practical frequency-selective RIS response model that underlies Eq. (1) and the two frequency-response functions used in simulation.","marker":"[8]"},{"why":"Provides the equivalent-circuit reasoning that makes the RRS element frequency selective over wide bandwidths.","marker":"[7]"},{"why":"Offers a Lorentzian element-response model and wideband RIS sum-rate baseline that the paper contrasts with its joint near-field and frequency-selective treatment.","marker":"[15]"},{"why":"Introduces adjustable-delay RIS elements for OFDM, the hardware concept that the Delayed-RRS time-delay units adopt.","marker":"[27]"},{"why":"Represents prior near-field-only wideband beamforming work whose approach the paper positions against its joint optimization.","marker":"[9]"},{"why":"Shows delay-adjustable metasurfaces for near-field wideband systems, the closest prior architecture that the proposed scheme extends.","marker":"[10]"},{"why":"Establishes delay-phase precoding for wideband massive MIMO, the conceptual source of frequency-linear phase compensation for beam split.","marker":"[28]"},{"why":"Analyzes near-field wideband beamforming for extremely large arrays, supporting the claim that near-field beam split focuses subcarriers at different locations.","marker":"[29]"}],"fun_headline_variants":["Time delays tame beam split in wideband refractive surfaces","Delayed-RRS beamforming lifts worst user rate by 2 dB","Beam split in near-field RRS fixed by tunable delays","Delay-compensated beamforming rivals 2 dB power boost for RRS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire quantitative argument rests on the assumption that the RRS transmission coefficient really is $\\psi(\\theta_i^c, f_m)$ with the smooth amplitude and phase frequency response constructed from the cited practical model; the paper never gives this function explicitly, so if a real RRS responds differently the reported rate gains and beam-split visuals may not carry over.","fun_headline_variants_meta":{"raw":{"variants":["Time delays tame beam split in wideband refractive surfaces","Delayed-RRS beamforming lifts worst user rate by 2 dB","Beam split in near-field RRS fixed by tunable delays","Delay-compensated beamforming rivals 2 dB power boost for RRS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000217,"raw_usage":{"total_tokens":1508,"prompt_tokens":1089,"completion_tokens":419,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":705,"completion_tokens_details":{"reasoning_tokens":344}},"tokens_in":705,"tokens_out":419,"duration_ms":4336,"temperature":1.0,"reasoning_tokens":344,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:38:08.912591+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the complex transmission coefficient of a real RRS element across the 1 GHz band, for example with free-space or waveguide S-parameter measurements at several bias voltages, then insert the measured $\\psi(\\theta_i^c, f_m)$ into the paper's simulator and compare the Delayed-RRS against the no-delay baseline; the central claim fails if the delay gain shrinks below the reported level or the edge-subcarrier focus loss persists despite optimized delays.","supporting_citations":[{"cited_title":"Intelligent Reflecting Surface Enhanced Wideband MIMO-OFDM Communications: From Practical Model to Reflection Optimization,","cited_arxiv_id":null,"evidence_quote":"Supplies the practical frequency-selective RIS response model that underlies Eq. (1) and the two frequency-response functions used in simulation."},{"cited_title":"Analysis of a Waveguide-Fed Metasurface Antenna,","cited_arxiv_id":null,"evidence_quote":"Provides the equivalent-circuit reasoning that makes the RRS element frequency selective over wide bandwidths."},{"cited_title":"Wideband Multi-User MIMO Communications with Frequency Selec- tive RISs: Element Response Modeling and Sum-Rate Maximization,","cited_arxiv_id":null,"evidence_quote":"Offers a Lorentzian element-response model and wideband RIS sum-rate baseline that the paper contrasts with its joint near-field and frequency-selective treatment."},{"cited_title":"Adjustable- Delay RIS Is Capable of Improving OFDM Systems,","cited_arxiv_id":null,"evidence_quote":"Introduces adjustable-delay RIS elements for OFDM, the hardware concept that the Delayed-RRS time-delay units adopt."},{"cited_title":"Wideband Beamforming for RIS Assisted Near-Field Communications","cited_arxiv_id":"2401.11141","evidence_quote":"Represents prior near-field-only wideband beamforming work whose approach the paper positions against its joint optimization."},{"cited_title":"Near-Field Wideband Extremely Large-Scale MIMO Transmissions With Holographic Metasurface-Based Antenna Arrays,","cited_arxiv_id":null,"evidence_quote":"Shows delay-adjustable metasurfaces for near-field wideband systems, the closest prior architecture that the proposed scheme extends."},{"cited_title":"Delay-Phase Precoding for Wideband THz Massive MIMO,","cited_arxiv_id":null,"evidence_quote":"Establishes delay-phase precoding for wideband massive MIMO, the conceptual source of frequency-linear phase compensation for beam split."},{"cited_title":"Near-Field Wideband Beamforming for Extremely Large Antenna Arrays,","cited_arxiv_id":null,"evidence_quote":"Analyzes near-field wideband beamforming for extremely large arrays, supporting the claim that near-field beam split focuses subcarriers at different locations."}],"review_version":1}