{"id":"2416a678-d86c-4ecf-8d40-57181d1d4350","arxiv_id":"2512.16496","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"An OFDM receiver with delay-Doppler superimposed pilots and a Landweber equalizer maintains robust uncoded throughput up to 1000 km/h in simulated fractional delay-Doppler channels.","lead":"The authors design an OFDM receiver for 6G high-mobility links that estimates fractional delays and Doppler shifts from a single delay-Doppler superimposed pilot and handles intercarrier interference with a low-complexity Landweber equalizer. Simulations show near-constant throughput up to 1000 km/h at lower complexity than full MMSE.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"IMFC equalizer's convergence is unverified: Algorithm 2 leaves T undefined and η unspecified, so the central Fig. 9 throughput claim is not reproducible.","rationale":"The reader correctly identified the Landweber hyperparameter omission as the weakest assumption. I considered other potential issues, such as the missing comparison to the closest DD-aided OFDM baseline [11], the approximation in Eq. (39) (F_M^H \\tilde{C}(ν)e_i ≈ f_i), and the lack of confidence intervals. While these are worth noting, none is as directly load-bearing as the IMFC convergence question: the central claim in the abstract and Section V-E is the near-constant throughput of Prop. CE + Prop. IMFC, and that specific result is produced by Algorithm 2. Without T and η, the simulation cannot be reproduced, and the robustness claim cannot be separated from possible hyperparameter tuning. The concern is addressable—the authors could report the values, provide code, or add a convergence analysis—so it does not warrant rejection, but it does justify the CONDITIONAL verdict. The paper's mathematical derivations for the CE algorithm are coherent and follow established OTFS disjoint-estimation techniques, and the Landweber approach is standard; the issue is missing implementation details rather than a fundamental flaw.","tokens_in":16807,"tokens_out":14671,"duration_ms":134982,"concrete_test":"Independently implement Algorithm 2 for the fractional-channel setup of Fig. 9 (v_max=1000 km/h, SNR=15 dB, PDR=30 dB, 4-QAM) and sweep η over {0.1, 0.5, 1.0, 2/||H||²} and T over {5, 20, 100}, measuring effective throughput and the relative residual ||R-H(X^(T))||/||R||. If throughput varies by more than ~5% across the grid or the residual does not decrease monotonically, the missing hyperparameters are load-bearing; if throughput is flat and residual converges, the concern is minor.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central performance claim (near-constant effective throughput up to 1000 km/h, Fig. 9) depends on the IMFC equalizer in Algorithm 2, which implements the Landweber iteration (51). However, the pseudocode never defines T (the loop runs 'for t=1 to T' but T is not an input) and the step-size η is only said to be 'chosen empirically or adapted through a decay model' (Section IV-B). No bound such as 0<η<2/||H||² is given, no default value is stated, and no residual-error certificate is provided. Convergence of Landweber for the ICI channel operator H(·) is not automatic: for a linear operator, convergence to the least-squares solution (50) requires this step-size restriction, and the number of iterations controls both accuracy and the claimed O(T P M N) complexity. If the simulations used a tuned (η,T) that works for the specific channel realizations and SNR, the 'robust across speeds' conclusion may be an artifact of that tuning rather than a property of the algorithm. Because no code, hyperparameters, or confidence intervals are reported, the experimental evidence cannot be independently verified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a receiver architecture for OFDM under high mobility using a single delay-Doppler superimposed pilot. The channel estimation method treats fractional delays/Doppler and non-negligible ICI, using a peak-search initialization followed by separate delay and Doppler correlations and a sequential multipath residual update (Algorithm 1). A Landweber-based iterative equalizer, IMFC, is derived from the adjoint of the ICI-aware channel operator and implemented as path-wise single-tap operations plus DFTs (Algorithm 2). The simulation section compares the proposed schemes against TM- and EP-based baselines and a Perfect-CSI + full-MMSE upper bound; the central numerical claim is that the proposed CE + IMFC achieves effective throughput close to the upper bound and nearly constant over speeds up to 1000 km/h in the fractional channel (Fig. 9), at complexity linear in the number of REs.","tokens_in":17125,"tokens_out":7800,"duration_ms":75035,"significance":"Should the results hold, the contribution is practically useful: it removes the integer-delay/Doppler and ICI-free restrictions of the earlier delay-Doppler SP scheme and offers an equalizer with per-iteration complexity O(PMN), avoiding cubic MMSE. The paper is careful in several respects: the ICI-aware input-output model is explicit, the adjoint Landweber steps match the forward operator, the comparisons include a perfect-CSI upper bound and the relevant TM baseline, and the throughput metric accounts for the pilot overhead of EP. The main reservation is that the central numerical results depend on undisclosed parameters of the Landweber iteration, so the experimental evidence is not yet reproducible. The lack of convergence analysis is the primary barrier to acceptance.","major_comments":[{"comment":"The Landweber equalizer is central to the robustness claim, but as written the iteration is not reproducible. Algorithm 2 does not list T in its Input section even though the loop runs 'for t=1 to T'; the step-size η is described only as 'chosen empirically or adapted through a decay model' (Section IV-B). Convergence of (51) to the least-squares solution (50) requires a step-size restriction such as 0<η<2/||H||², and the residual error after T iterations is not bounded. Since the complexity O(T P M N) and the near-constant throughput in Fig. 9 both depend on T and η, please state the values used in simulation, provide a step-size bound or adaptive schedule, and add a convergence check (e.g., relative residual versus iteration).","section":"Section IV-B / Algorithm 2"},{"comment":"The derivation of the Doppler profile contains a mathematically incorrect simplification: \\tilde C(ν) is diagonal with entries e^{j2π qνT/M}, so \\tilde C(ν)e_{m_p+\\hat l}=e^{jθ}e_{m_p+\\hat l} and F_M^H \\tilde C(ν)e_{m_p+\\hat l}=e^{jθ}f_{m_p+\\hat l}, not f_{m_p+\\hat l} as written. The dropped phase is constant in magnitude and hence does not change the arg-max in (40), so the result can be repaired, but the equality chain should be corrected. Relatedly, u and v in (35)/(38) contain the superimposed-data term Y_data, which is then ignored in the correlation maximizations (37)/(40); the conditions under which this is negligible should be stated and ideally quantified.","section":"Section III-D, Eq. (39)"},{"comment":"The central claim of near-constant throughput across speeds is made from simulation curves without any indication of the number of channel realizations or Monte Carlo runs. Because the Doppler angles are random (θ∼U[0,2π]) and the fluctuations in the plotted curves are small, confidence intervals or error bars are needed to establish that the flatness is not sampling noise. Please report the number of trials and add statistical uncertainty or error bars to at least the key figures.","section":"Section V-E / Fig. 9"},{"comment":"The linear-complexity claim is conditional on T remaining bounded independently of speed and channel condition. If T must grow with the operator norm or condition number to maintain the throughput shown in Fig. 9, then the comparison with full MMSE is incomplete. Please report T (or the stopping rule) for each speed/SNR and state whether T was constant or adapted. If it was adapted, the complexity column in Table II should reflect the average or worst-case T.","section":"Section IV-B / Table II"}],"minor_comments":[{"comment":"Typographical issues: 'can ben noted' in Section IV-B and 'embdedded' in the Fig. 1 caption should be corrected.","section":"Section IV-B / Fig. 1"},{"comment":"The refinement correlations do not specify the search grid for τ and ν. A brief statement of the grid resolution used in simulation would improve reproducibility.","section":"Section III-D, Eqs. (37)/(40)"},{"comment":"No code or data availability statement is provided. Given the number of algorithmic parameters, a public implementation or at least a detailed hyperparameter table is recommended.","section":"General"},{"comment":"The sentence explaining why TM+Single-Tap outperforms TM+Full-MMSE under non-negligible ICI is plausible but would benefit from a reference or a short quantitative explanation, e.g., a discussion of the CE model mismatch.","section":"Section V-D"},{"comment":"The gain estimate in (43) is stated as optimal LS for the pilot-only term. The presence of data interference is not included in the optimization, which is consistent with the broader concern in major comment 2; a brief note acknowledging this simplification would be helpful.","section":"Section III-D, Eq. (43)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the core algorithmic idea is sound, but the missing convergence and hyperparameter details for the Landweber equalizer are the main risk. The issues are addressable in revision: supplying η and T values, a step-size bound or adaptive schedule, and a small Monte Carlo analysis would substantially strengthen the paper. I do not think rejection is warranted, but I cannot accept without those details."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a credible incremental contribution that combines fractional delay-Doppler channel estimation with an ICI-aware Landweber equalizer for OFDM with superimposed pilots. The main claim—near-constant throughput up to 1000 km/h—is plausible but rests on an unreported choice of step size and iteration count in the equalizer, so it isn't fully reproducible as written.\n\nThe genuinely new part is the receiver architecture: prior DD-SP OFDM assumed integer delay/Doppler and no ICI; here they handle both by adapting the disjoint fractional estimation from OTFS to OFDM and adding an iterative matched-filter-and-combine equalizer. The system model and the derivation of Algorithms 1 and 2 check out, and the complexity is linear in the number of resource elements, which is a real advantage over full MMSE. The simulation study is reasonably thorough—multiple modulation orders, SNR, and speeds, with TM, EP, and perfect-CSI baselines—and the figures support the qualitative story.\n\nThe soft spots are all in the equalizer. Algorithm 2 loops 'for t=1 to T' but T is never defined, and η is only described as 'chosen empirically.' For a Landweber iteration, convergence to the LS solution requires a step-size bound (0 < η < 2/||H||²), and the number of iterations controls both accuracy and complexity. If the simulations used a tuned (η,T) that works for these specific channel draws, the 'robust across speeds' conclusion could be an artifact of that tuning. There's no ablation showing sensitivity to these parameters, no residual error curve, and no released code. Also, the comparison misses the closest prior art: DD-aided OFDM (ref [11]) is discussed but not simulated, and there's no ICI-mitigation baseline other than full MMSE. These are addressable, not fatal.\n\nWho should read this: anyone working on high-mobility OFDM or delay-Doppler processing for 6G. It's a useful combination and the write-up is clear. I'd send it to a serious referee, but the review should ask for the missing hyperparameters, a sensitivity analysis, and ideally code or at least a detailed description of how η and T were chosen. If that's not provided, the central claim stays a bit soft.\n\nRecommendation: worth engaging, needs revision before I'd trust the headline number.","headline":"Credible incremental OFDM receiver combining fractional delay-Doppler SP estimation and an iterative ICI-aware equalizer; the headline throughput claim depends on unreported Landweber step-size and iteration count.","tokens_in":17562,"tokens_out":2192,"would_cite":false,"duration_ms":21931,"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":"A single superimposed delay-Doppler pilot, paired with a Landweber-based equalizer, keeps OFDM throughput nearly constant up to 1000 km/h in high-mobility 6G channels.","keywords":["OFDM","delay-Doppler superimposed pilots","fractional delay-Doppler estimation","intercarrier interference","Landweber iteration","low-complexity equalization","high mobility","6G"],"falsifier":"Run the speed-sweep simulation of Figure 9 on the fractional channel with the Landweber step size fixed to a principled value (for instance, the reciprocal of the largest eigenvalue of the channel Gram operator) and with T reported; if the residual ‖E(t)‖ fails to decrease to the least-squares level or the effective throughput at 1000 km/h drops noticeably below the perfect-CSI + full-MMSE curve, the claimed robustness is an artifact of an unspecified tuned step-size and iteration count.","tokens_in":16643,"feed_emoji":"🚄","tokens_out":7158,"duration_ms":67214,"temperature":0.7,"pith_summary":"OFDM's subcarrier orthogonality breaks down when a terminal moves fast, because Doppler shifts smear energy between subcarriers. This work asks whether OFDM can still be made to work in 6G high-mobility links by estimating the channel in the delay-Doppler domain from a single superimposed pilot, rather than abandoning the waveform for a new one. It claims yes: the proposed receiver, using a disjoint fractional delay–Doppler estimator and a Landweber-based equalizer that exploits the channel's path structure, keeps effective throughput nearly flat from 0 up to 1000 km/h and close to the perfect-channel-information bound, while equalization cost is linear in the number of resources instead of cubic. The practical stake is that high-speed rail, vehicle-to-everything and drone links could keep OFDM's mature, low-cost infrastructure.","feed_headline":"One pilot keeps OFDM throughput flat at 1000 km/h","feed_subtitle":"A Landweber-based receiver matches perfect-channel throughput at linear cost, so 6G need not abandon OFDM in high-mobility links.","key_machinery":"The load-bearing structure is the channel operator H(·), which splits each propagation path into a slow time–frequency matrix H_tf (outer product of the delay and Doppler steering vectors) and a fast-time ICI matrix H_ICI. The single delay-Doppler superimposed pilot — a one-hot pilot spread over the whole time–frequency plane by the ISFFT — makes the received delay-Doppler profile a superposition of shifted, spread versions of that pilot; the coarse-to-fine estimator uses the profile's peak for integer delay/Doppler and the profile's shape for the fractional refinements. The same operator structure is what the Landweber iteration exploits: the gradient step H^H(R−H(X̂)) reduces to per-path p","core_discovery":"The central claim is that relaxing the two simplifying assumptions in earlier delay-Doppler superimposed-pilot OFDM work — integer delays/Dopplers and ICI-free reception — produces a receiver that is robust across the full 6G mobility range. The estimator first finds each path's coarse delay and Doppler by peak search in the delay-Doppler domain, then refines the fractional parts by correlating the received delay and Doppler profiles with the pilot's spreading terms, and estimates each path gain by least squares before subtracting the path from the residual. The equalizer solves the least-squares detection problem with a Landweber iteration, factored into single-tap matched-filtering operati","pith_inferences":["If the Landweber convergence assumption is robust to step-size choice, the same path-wise operator decomposition could accelerate other iterative estimators (conjugate gradient, ADMM) for the same ICI channel, potentially improving convergence per iteration.","The estimated delay–Doppler parameters are exactly the ones a radar would extract, so the superimposed pilot may double as a sensing signal in integrated sensing and communication; the near-constant throughput at high speed suggests the pilot retains usable energy for ranging at 1000 km/h.","Because the paper leaves η and T unspecified, a fair comparison would fix them from first principles (e.g., η from the spectral radius of H^H H) and re-run Fig. 9; the near-flat throughput curve may depend on per-scenario tuning.","Multiple superimposed pilots, as the authors note as future work, could trade some PAPR for estimation accuracy and might extend the scheme to multi-antenna systems, but would change the single-pilot peak-search structure that makes CE cheap."],"forward_implications":["OFDM can support 6G high-mobility use cases up to 1000 km/h without switching to OTFS or other new waveforms, preserving existing baseband hardware.","ICI-aware equalization complexity drops from cubic in the number of subcarriers to linear in the number of resource elements, with effective throughput close to that of full MMSE.","Fractional delay and Doppler must be modelled explicitly: the threshold-method baseline, which assumes integer parameters, loses throughput rapidly as speed increases in fractional channels.","A single delay-Doppler pilot achieves full data density (no pilot subcarrier loss), and for pilot-to-data ratios below about 23 dB it also gives lower PAPR than embedded pilots."],"fun_headline_variants":["Single pilot keeps OFDM robust at 1000 km/h","One pilot, 1000 km/h: OFDM without ICI meltdown","Landweber equalizer makes OFDM mobile up to 1000 km/h","Fractional delay-Doppler pilot boosts 6G OFDM at speed","OFDM handles 1000 km/h with one superimposed pilot"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The Landweber iteration is assumed to converge to the least-squares solution within the iteration count used, with a step size the paper never specifies; if that convergence fails, the near-MMSE throughput and the linear-complexity claim both collapse.","fun_headline_variants_meta":{"raw":{"variants":["Single pilot keeps OFDM robust at 1000 km/h","One pilot, 1000 km/h: OFDM without ICI meltdown","Landweber equalizer makes OFDM mobile up to 1000 km/h","Fractional delay-Doppler pilot boosts 6G OFDM at speed","OFDM handles 1000 km/h with one superimposed pilot"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000225,"raw_usage":{"total_tokens":1273,"prompt_tokens":687,"completion_tokens":586,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":431,"completion_tokens_details":{"reasoning_tokens":503}},"tokens_in":431,"tokens_out":586,"duration_ms":5983,"temperature":1.0,"reasoning_tokens":503,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T15:31:56.490355+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the speed-sweep simulation of Figure 9 on the fractional channel with the Landweber step size fixed to a principled value (for instance, the reciprocal of the largest eigenvalue of the channel Gram operator) and with T reported; if the residual ‖E(t)‖ fails to decrease to the least-squares level or the effective throughput at 1000 km/h drops noticeably below the perfect-CSI + full-MMSE curve, the claimed robustness is an artifact of an unspecified tuned step-size and iteration count.","supporting_citations":[],"review_version":1}