{"id":"b2112ece-072a-4745-b7ce-5b93df7d3165","arxiv_id":"2502.03904","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A Gaussian-sinc pulse shaping filter for Zak-OTFS combines sinc nulls with Gaussian sidelobe suppression and is reported to improve BER by 4 to 6 dB in simulations.","lead":"This paper introduces a new pulse shaping filter for Zak-OTFS modulation that multiplies a sinc pulse with a Gaussian pulse, aiming for both clean detection zeros and low interference. In simulations, it reports 4 to 6 dB SNR gains over standard filters in a Veh-A channel.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'no time/bandwidth expansion' claim for the GS filter is defined only at 99% energy containment; under stricter occupied-bandwidth thresholds the GS filter expands more than RRC, and the BER comparison is not tested at matched bandwidth.","rationale":"Reading the paper in good faith, the proposed GS filter is simple and the reported BER gains are plausible; the closed-form I/O relation and noise covariance derivations are substantial, and the mechanism of combining sinc zeros with Gaussian sidelobe suppression is sound. The reader's verdict of CONDITIONAL is appropriate. The single most load-bearing weakness is the definitional status of 'no expansion.' The paper adopts the 99% energy-containment convention from the Gaussian-filter literature, so internally the claim is consistent. However, the novelty claim is explicitly contrasted with RRC, which is strictly bandlimited at the cost of 5-10% expansion. The GS spectrum is not bandlimited, and its occupied bandwidth at thresholds stricter than 99% grows with the Gaussian edge transition. The paper provides no computation at other thresholds and no BER comparison under matched occupied bandwidth, so the claimed advantage over RRC is not robustly established. A single numerical check can settle this: compute the 99.9% energy bandwidth and rerun the key simulation with RRC at that matched bandwidth. If the GS gain persists, the central claim holds; if not, the contribution should be reframed as a tradeoff rather than a free lunch. This is exactly the concern the reader identified as the weakest assumption, so I agree with the reader's assessment and see no reason to change the CONDITIONAL verdict.","tokens_in":49618,"tokens_out":16464,"duration_ms":171923,"concrete_test":"Compute the exact energy-containment bandwidth B_eps and time duration T_eps of the GS filter (Eq. 23) for eps = 0.99, 0.999, and 0.9999, using the Fourier-transform expressions in Appendices A and B or direct numerical integration, and compare with RRC at beta_tau = 0.05 and beta_nu = 0.1. If B_0.999/B > 1.05 or T_0.999/T > 1.1, the no-expansion claim fails under a stricter criterion. Then rerun the 8-QAM embedded-pilot simulations of Figs. 11-12 with RRC roll-offs chosen so that the RRC 99.9% energy bandwidth matches the GS filter's 99.9% energy bandwidth; if the GS SNR gain at 10^-2 drops materially below 4 dB, the headline advantage is not robust to the bandwidth definition.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the GS filter 'does not incur time or bandwidth expansion' (Sec. IV-B) rests on the 99% energy-containment definition of B' and T' used in Appendix A. The GS pulse in Eq. (23) is the product of a bandlimited sinc and a Gaussian, so its spectrum is the convolution of the sinc's rectangular mask with a Gaussian of width sigma_f = B sqrt(alpha/(2*pi^2)) ~ 0.047B for alpha = 0.044. The filter is therefore not bandlimited; it has small but strictly infinite spectral tails. The paper asserts alpha = 0.044 achieves 99% energy within B and T, but it does not report how the occupied bandwidth grows as the energy threshold is tightened. For a 99.9% or -40 dB occupied-bandwidth criterion, the Gaussian edge transition adds on the order of a few sigma_f of width, which is roughly 10-30% of B. This is larger than the 5% (beta_tau = 0.05) and 10% (beta_nu = 0.1) expansion already allowed for RRC in Section V. Thus the advertised advantage, 'RRC-like side-lobe reduction without expansion,' is criterion-dependent. Since the 4 dB and 6 dB BER gains are claimed for the alpha = 0.044 filter without comparing against RRC at matched occupied bandwidth, the headline comparison may partly be an artifact of the 99% definition rather than a robust property of the filter.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a separable delay-Doppler pulse shaping filter for Zak-OTFS, the Gaussian-sinc (GS) filter, defined as the product of a sinc and a Gaussian in each axis (Eq. (23)). The authors derive closed-form expressions for the effective channel (Theorem 1, Eq. (25)) and the noise covariance (Theorem 2, Eq. (27)) under matched filtering. They evaluate MSE and BER for model-free I/O relation estimation with exclusive and embedded pilot frames over a Veh-A channel, reporting, for example, about 4 dB SNR gain at 10^-2 uncoded BER and more than 6 dB at 10^-4 coded BER with 8-QAM compared to Gaussian and sinc filters (Figs. 11-12). The paper argues that the GS filter inherits the sinc filter's nulls at information grid points and the Gaussian filter's low side lobes without incurring time or bandwidth expansion under a 99% energy-containment definition.","tokens_in":50003,"tokens_out":7801,"duration_ms":82298,"significance":"If the claims hold, the GS filter is a simple and attractive option for Zak-OTFS: it has no parameters fitted to BER data (alpha = 0.044 is fixed by a 99% energy-containment criterion), the separable construction is easy to state, and the closed-form I/O and noise-covariance expressions could be useful for analysis and faster simulation. The paper's strengths include self-contained derivations in the appendices, evaluation under both exclusive and embedded pilot schemes, and results for both uncoded and coded BER. The performance advantage is, however, less clean than advertised: the 'no expansion' property is tied to the 99% energy-containment definition and is not compared against RRC at equal occupied bandwidth, the closed forms are not numerically verified against direct simulation, and Theorem 1 contains a typo. These issues are fixable, so the contribution warrants revision rather than rejection.","major_comments":[{"comment":"The theorem statement repeats C^(2)_{i,1}(tau,nu) in both Doppler indicator branches, but the Appendix B derivation (Eqs. (43)-(44) and the subsequent combination) uses C^(2)_{i,2}(tau,nu) for the case nu = nu_i. As written, Theorem 1 is incorrect. Please correct the second branch and verify that the simulation code uses the corrected expression.","section":"§IV-C, Eq. (25)"},{"comment":"The 'no time or bandwidth expansion' claim is made only with respect to the 99% energy-containment criterion. The GS filter in Eq. (23) is the product of a bandlimited sinc and a Gaussian, so its spectrum is the convolution of a rectangular mask with a Gaussian of standard deviation B sqrt(alpha/(2*pi^2)) ≈ 0.047B at alpha = 0.044. Under a stricter occupied-bandwidth threshold (e.g., 99.9% or -40 dB), the occupied bandwidth grows by several times this width, which is comparable to or larger than the 5% and 10% expansion allowed for the RRC filter in Section V. The paper should quantify occupied bandwidth as a function of the energy threshold and, ideally, provide a BER comparison against RRC at matched occupied bandwidth; otherwise the advertised advantage over RRC is criterion-dependent.","section":"§IV-B and Appendix A"},{"comment":"The closed-form expressions for the effective channel and noise covariance are not validated against direct simulation (e.g., numerical Zak transform or time-domain I/O) on any of the reported MSE/BER plots. Given the algebraic complexity of Appendices B-C and the typo in Theorem 1, the reader cannot tell whether the simulated curves actually use the claimed closed forms or whether those forms are correct. Please include at least one validation figure or table comparing closed-form and direct-simulation effective-channel coefficients, MSE, or BER curves.","section":"§IV-C and §V"},{"comment":"The replica indices a and b in Eq. (10) are truncated to -1, 0, 1 with the statement that this 'is found to ensure an adequate support set.' This truncation is load-bearing for the model-free channel-matrix construction, especially for the high side lobes of the sinc filter and the infinite tails of the GS filter. Please justify the truncation numerically, for example by showing MSE or BER sensitivity to the truncation range for the filters and channel parameters considered.","section":"§V, paragraph after Eq. (10)"}],"minor_comments":[{"comment":"The phrase 'does not incur time or bandwidth expansion' should be qualified as 'under the 99% energy-containment definition' in the abstract and introduction to avoid overstatement.","section":"Abstract and Introduction"},{"comment":"The coded BER results use a rate-1/2 convolutional code with constraint length 7, but the generator polynomials are not given; please provide them for reproducibility.","section":"§V-B"},{"comment":"No Monte Carlo run counts or confidence intervals are reported for the BER/MSE curves; at least the number of channel realizations and frames should be stated.","section":"§V"},{"comment":"The figure caption does not specify the roll-off factors for RRC, the alpha parameters for Gaussian and GS, or the normalization used; please state these values in the caption.","section":"Fig. 3 and §IV-A"}],"recommendation":"major_revision","confidential_remarks":"This is a well-scoped engineering paper from a group with an extensive Zak-OTFS track record. The main risk is that the headline no-expansion claim is a definitional artifact of the 99% energy-containment criterion, and the closed-form derivations contain at least one typo and are not independently validated. If the authors add sensitivity analysis for occupied bandwidth and validation of the closed forms, the paper could be acceptable. The self-citation pattern is heavy but not inappropriate given the paper's direct continuity with prior Zak-OTFS work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper proposes a Gaussian-sinc (GS) pulse shaping filter for Zak-OTFS—simply the product of sinc and Gaussian in delay and Doppler—and derives closed-form expressions for the effective channel and noise covariance. The closed-form derivation is the substantive contribution, and it appears correct in structure. The BER simulations show the expected gains: about 4 dB over Gaussian and sinc at 10^-2 uncoded BER, and over 6 dB at 10^-4 coded BER with 8-QAM under embedded-pilot model-free estimation.\n\nWhat is genuinely new is the filter itself and the analytical expressions; the cited literature covers sinc, RRC, and Gaussian filters but not their product. The paper is self-contained, the appendices are thorough, and the intuition (sinc gives nulls for detection, Gaussian suppresses side lobes for estimation) is clearly laid out and matched by the simulations.\n\nThe soft spots, in order. First, the 'no time/bandwidth expansion' claim relies on a 99% energy-containment criterion. The GS pulse is not bandlimited—the Gaussian factor leaves infinite spectral tails—so at a stricter occupied-bandwidth threshold the filter will need expansion. The RRC filter is assigned explicit 5% and 10% expansion in the comparisons, so the headline gain is not tested at matched occupied bandwidth. This is a genuine caveat, not a fatal flaw, but it should be studied and qualified.\n\nSecond, the closed-form expressions are not verified against direct numerical evaluation. A plot comparing Theorem 1 to a brute-force integral would catch errors, especially since the appendices are algebra-heavy.\n\nThird, there is a likely typo in Theorem 1: the second indicator uses the same C^(2)_{i,1} for both Doppler cases; it should presumably be C^(2)_{i,2}. Also, the BER figures have no error bars or run counts, which makes the magnitude of the gains less certain.\n\nThis is a solid incremental paper. It deserves a serious referee, but it needs revision. I would send it to review with a request for a matched-bandwidth comparison, a verification of the closed-form I/O, and a fix of the typos and simulation statistics. Readers working on Zak-OTFS waveform design will find the filter and the closed forms useful.","headline":"A solid incremental Zak-OTFS pulse-shaping paper with substantial closed-form derivations, but the headline 'no expansion' claim is criterion-dependent and needs matched-bandwidth comparison.","tokens_in":50466,"tokens_out":3157,"would_cite":false,"duration_ms":31905,"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 a Gaussian-sinc pulse shaping filter for Zak-OTFS that keeps the sinc filter's nulls while cutting side lobes, and reports about 4 dB SNR gain at 10^-2 uncoded BER and more than 6 dB at 10^-4 coded BER over Gaussian and…","keywords":["Zak-OTFS","delay-Doppler domain","pulse shaping filter","Gaussian-sinc filter","I/O relation estimation","noise covariance","equalization and detection","embedded pilot"],"falsifier":"Reproduce the paper's setup (M=32, N=48, Veh-A fractional channel, embedded pilot at 0 dB PDR, 8-QAM, MMSE detection) and compare GS to sinc and Gaussian: the central claim predicts about 4 dB SNR gap at $10^{-2}$ uncoded BER and more than 6 dB at $10^{-4}$ coded BER, so a materially smaller gap would falsify the practical claim; separately, computing the 99.9% energy-containment time-bandwidth product of the GS filter and comparing it with RRC's expanded product would test how far the no-expansion advantage extends beyond the 99% convention.","tokens_in":49452,"feed_emoji":"📡","tokens_out":10256,"duration_ms":89300,"temperature":0.7,"pith_summary":"The paper sets out to establish that a new delay-Doppler pulse shape, the Gaussian-sinc (GS) filter, gives Zak-OTFS the best of both existing filters: the sinc filter's nulls at information grid points, which help equalization and detection, and the Gaussian filter's low side lobes, which help model-free input-output (I/O) relation estimation. It claims this combination is achieved without the time and bandwidth expansion that root-raised-cosine filters require for side-lobe reduction. The paper derives closed-form expressions for the effective channel and noise covariance of GS-filtered Zak-OTFS, and supports the claim with simulations on a fractional delay-Doppler Veh-A channel using exclusive and embedded pilots. If the claim holds, replacing the pulse shape alone improves Zak-OTFS reliability by the reported margins while keeping spectral efficiency unchanged.","feed_headline":"Sinc plus Gaussian pulse gains 4 dB for Zak-OTFS","feed_subtitle":"Keeps the sinc nulls for detection while cutting side lobes for channel estimation, with no time or bandwidth expansion.","key_machinery":"The load-bearing object is the Gaussian-sinc (GS) filter, a separable delay-Doppler pulse built as $g_{tx}(\\tau,\\nu)=g_1(\\tau)g_2(\\nu)$ with $g_1(\\tau)=\\Omega_\\tau\\sqrt{B}\\,\\mathrm{sinc}(B\\tau)e^{-\\alpha_\\tau B^2\\tau^2}$ and $g_2(\\nu)=\\Omega_\\nu\\sqrt{T}\\,\\mathrm{sinc}(T\\nu)e^{-\\alpha_\\nu T^2\\nu^2}$. The sinc factor provides nulls at the Nyquist sampling points on the information lattice, which the paper identifies as the property that makes sinc good for equalization and detection, while the Gaussian factor provides fast decay and low side lobes, the property that makes Gaussian good for I/O relation estimation; the energy constants $\\Omega_\\tau,\\Omega_\\nu$ normalize each factor to unit energy, and at $\\alpha_\\tau=\\alpha_\\nu=0.044$ the 99% energy-containment duration and bandwidth equal the unexpanded $T$ and $B$. With the matched receiver $g_{rx}(\\tau,\\nu)=g_{tx}^*(-\\tau,-\\nu)e^{j2\\pi\\nu\\tau}$, Theorem 1 reduces the effective channel to a sum over physical channel paths of closed-form integrals of the filter's delay and Doppler components, with indicator-function cases separating zero and nonzero delay and Doppler offsets, and Theorem 2 gives the noise covariance as a double sum over quasi-periodic replicas with closed-form erf-based integral terms; these expressions constitute the paper's analytic basis for evaluating GS-filtered Zak-OTFS performance.","core_discovery":"The central claim is that the Gaussian-sinc (GS) filter, defined as a separable product of sinc and Gaussian pulses in delay and Doppler, inherits the complementary strengths of its two parents. For the delay variable it takes $g_1(\\tau)=\\Omega_\\tau\\sqrt{B}\\,\\mathrm{sinc}(B\\tau)e^{-\\alpha_\\tau B^2\\tau^2}$, with the analogous form $g_2(\\nu)$ for Doppler, so the transmitted pulse is $g_{tx}(\\tau,\\nu)=\\Omega_\\tau\\Omega_\\nu\\sqrt{BT}\\,\\mathrm{sinc}(B\\tau)\\mathrm{sinc}(T\\nu)e^{-\\alpha_\\tau B^2\\tau^2}e^{-\\alpha_\\nu T^2\\nu^2}$. The paper shows that with $\\alpha_\\tau=\\alpha_\\nu=0.044$ the filter keeps 99% of its energy within the unexpanded frame bandwidth $B$ and duration $T$, and that its delay/Doppler magnitude profile retains the sinc nulls while lowering side lobes. It then derives closed-form expressions (Theorems 1 and 2) for the matched-filter effective channel and the noise covariance, and reports that in Veh-A channels with model-free I/O estimation using an embedded pilot and 8-QAM, GS achieves about 4 dB SNR gain over both Gaussian and sinc filters at $10^{-2}$ uncoded BER and more than 6 dB at $10^{-4}$ coded BER with rate-1/2 coding.","pith_inferences":["One could apply the same product construction to other pulse shapes or to the time-frequency windowing of windowed Zak-OTFS, since the conflict between main-lobe nulls and side-lobe leakage is not specific to the separable sinc and Gaussian pair.","The single operating point $\\alpha_\\tau=\\alpha_\\nu=0.044$ is one choice on a continuous family interpolating between sinc ($\\alpha=0$) and increasingly Gaussian shapes; the closed forms in the paper make it possible to search this family per channel profile, a step the paper does not take.","The crossover between Gaussian and sinc BER curves suggests an adaptive rule: use more Gaussian-like shaping when estimation noise dominates and more sinc-like shaping when detection dominates; the GS filter is a fixed compromise that could be outperformed by a channel-aware switch.","The paper's own future-work note points to superimposed or spread pilots; a testable extension is to check whether the GS advantage persists when pilot and guard regions are removed and throughput is higher."],"forward_implications":["If the claim holds, Zak-OTFS can be made more reliable at no spectral-efficiency cost: the GS filter uses the same time and bandwidth as sinc or Gaussian while reporting lower BER in the simulated Veh-A channel.","The closed-form effective channel and noise covariance remove the need to compute full twisted convolutions for GS-filtered Zak-OTFS, making analysis and optimization of the filter parameters $\\alpha_\\tau,\\alpha_\\nu$ feasible.","Because the GS filter keeps the sinc nulls, its detection performance with perfect channel knowledge stays close to sinc's; because it cuts side lobes, its I/O estimation MSE stays close to Gaussian's, so the two receiver functions no longer force opposite filter choices.","The reported gains appear in both exclusive and embedded pilot setups, with the embedded pilot case showing the larger improvement, meaning the filter is compatible with the practical pilot-and-guard frame structure.","The U-shaped BER-versus-PDR behavior in embedded-pilot frames is shallower for GS than for non-Gaussian filters, indicating less sensitivity to strong pilot power."],"supporting_citations":[{"why":"supplies the Zak-OTFS system model, the model-free I/O relation estimation approach, and the crystallization condition under which the pilot read-off is valid.","marker":"[10]"},{"why":"introduces the Gaussian pulse, the embedded pilot frame, and the time and bandwidth expansion versus predictability tradeoff that the proposed GS filter targets.","marker":"[14]"},{"why":"gives the general matched-filter expressions for the effective channel and noise covariance that Theorems 1 and 2 specialize to closed form for the GS filter.","marker":"[15]"},{"why":"establishes the Zak-OTFS mathematical framework and the twisted-convolution formulation of the input-output relation.","marker":"[9]"},{"why":"provides the Zak-OTFS theory reference supporting the system model and receiver processing.","marker":"[11]"},{"why":"defines the Veh-A channel model with fractional delays used as the simulation testbed for the BER and MSE results.","marker":"[20]"}],"fun_headline_variants":["New filter merges sinc and Gaussian for 4 dB OTFS gain","Gaussian-sinc pulse achieves 4 dB gain for Zak-OTFS","Hybrid pulse cuts side lobes, keeps nulls, gains 4 dB"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that 'no time or bandwidth expansion' is measured by the 99% energy-containment convention, so an infinitely supported GS filter counts as unexpanded only under that threshold, and that the effective channel spreads stay within the delay and Doppler periods (the crystallization condition) so model-free estimation can read a single local response.","fun_headline_variants_meta":{"raw":{"variants":["New filter merges sinc and Gaussian for 4 dB OTFS gain","Gaussian-sinc pulse achieves 4 dB gain for Zak-OTFS","Hybrid pulse cuts side lobes, keeps nulls, gains 4 dB"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000558,"raw_usage":{"total_tokens":2744,"prompt_tokens":1128,"completion_tokens":1616,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":744,"completion_tokens_details":{"reasoning_tokens":1552}},"tokens_in":744,"tokens_out":1616,"duration_ms":13516,"temperature":1.0,"reasoning_tokens":1552,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T00:16:16.969782+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reproduce the paper's setup (M=32, N=48, Veh-A fractional channel, embedded pilot at 0 dB PDR, 8-QAM, MMSE detection) and compare GS to sinc and Gaussian: the central claim predicts about 4 dB SNR gap at $10^{-2}$ uncoded BER and more than 6 dB at $10^{-4}$ coded BER, so a materially smaller gap would falsify the practical claim; separately, computing the 99.9% energy-containment time-bandwidth product of the GS filter and comparing it with RRC's expanded product would test how far the no-expansion advantage extends beyond the 99% convention.","supporting_citations":[{"cited_title":"OTFS — predictability in the delay-Doppler domain and its v alue to communication and radar sensing,","cited_arxiv_id":null,"evidence_quote":"supplies the Zak-OTFS system model, the model-free I/O relation estimation approach, and the crystallization condition under which the pilot read-off is valid."},{"cited_title":"Optimal Zak-OTFS receiver and its relation to the radar matched filte r,","cited_arxiv_id":null,"evidence_quote":"gives the general matched-filter expressions for the effective channel and noise covariance that Theorems 1 and 2 specialize to closed form for the GS filter."},{"cited_title":"OTFS — a mathematical foundation for communication and rad ar sensing in the delay-Doppler domain,","cited_arxiv_id":null,"evidence_quote":"establishes the Zak-OTFS mathematical framework and the twisted-convolution formulation of the input-output relation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the Zak-OTFS theory reference supporting the system model and receiver processing."}],"review_version":1}