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REVIEW 3 major objections 5 minor 33 references

Time and Frequency Synchronization for Multiuser OTFS in Uplink

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Detecting the first major correlation peak instead of the tallest one makes multiuser OTFS timing estimates two orders of magnitude more accurate, and per-user CFO search gains up to 5 dB in channel estimation.

desk verdict First real open-loop MU-OTFS uplink sync scheme, but the headline threshold gain is load-bearing and not convincingly supported as written. read the letter →

arxiv 2507.17966 v1 pith:XJN6FG7R submitted 2025-07-23 eess.SP

Mohsen Bayat , Sanoopkumar P.S. , Arman Farhang This is my paper
classification eess.SP MSC 94A1294A1393E10
keywords OTFSmultiuseruplinksynchronizationtimingoffsetestimationcarrierfrequencyZadoff-Chusequencecyclic-prefixpilotChebyshevpolynomialbasisexpansionmodelmaximumlikelihood
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

Uplink multiuser OTFS modulation remains practical only if the base station can locate each user's pilot in the delay-Doppler plane and remove each user's carrier-frequency offset before channel estimation. This paper proposes two pilot designs—SU-PCP, which separates users by different Zadoff-Chu sequences, and MU-PCP, which lets all users share one pilot region and separates them with a filter bank—and a correlation-based timing estimator that looks for the first major correlation peak rather than the global maximum. The paper derives a mathematical threshold range for that first peak, reports two orders of magnitude improvement in timing-error mean over maximum-peak detection, and then reduces joint CFO estimation from a multidimensional maximum-likelihood search into Q one-dimensional searches using a Chebyshev-polynomial basis expansion model for the time-varying channel. If the claims hold, synchronization in high-mobility multiuser OTFS needs no closed-loop feedback and recovers up to 5 dB of channel-estimation accuracy relative to estimating CFO as part of the channel.

What carries the argument

The machinery has four parts: the PCP pilot, a Zadoff-Chu sequence whose last $L_p-1$ samples are copied to form a cyclic prefix and give the pilot a periodic structure that survives sliding correlation; the timing metric $p_q[l']$ in (9)/(14); the derived threshold range in (20)-(21) that sits between the partial-alignment minor peak and the first full-alignment major peak; and the CPF-BEM expansion $h^q[\ell,\kappa]=\sum_{\gamma=0}^{\beta-1} B[\kappa',\gamma] c^q_\ell[\gamma]$ used to fold time variation into basis functions so the ML cost separates per user.

What would settle it

Compute the correlation values at the two positions $l'_a$ and $l'_b$ of Eq. (20) under a TDL-C channel with weak first tap and finite data-to-pilot power ratio; if the derived lower bound exceeds the upper bound, the threshold range is empty and the first-major-peak rule cannot be applied. An experiment where a fake data-induced peak above the threshold occurs before $l'_b$ would produce a discrete jump in TO error that falsifies the method's accuracy claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that in an asynchronous uplink multiuser OTFS system over a linear time-varying channel, timing and frequency offsets should be estimated and corrected as separate stages before channel estimation, rather than absorbed into the channel. For timing, the received pilots are located by sliding a per-user cyclic-prefix pilot—built from a Zadoff-Chu sequence—and threshold-selecting the first major peak of the correlation function; the paper derives an interval for this threshold and reports that this first-peak rule lowers mean timing error by two orders of magnitude relative to choosing the maximum correlation peak. For frequency, the paper models the compound CFO-and-channel matrix and applies a Chebyshev-polynomial basis expansion model so that each user's CFO can be found by its own one-dimensional maximum-likelihood search, replacing a joint multidimensional search. The payoff stated by the paper is that separating CFO correction from channel estimation avoids an error floor and improves channel-estimation NMSE by up to 5 dB compared with absorbing CFO into the channel, while the proposed MU-PCP pilot keeps spectral efficiency high by letting all users share one pilot region.

Load-bearing premise

The whole timing-accuracy gain rests on the assumption that the first fully aligned half-sequence correlation peak is reliably taller than every partial-alignment and data-interference peak before it, so one threshold can separate them even in channels where the first tap is not the strongest.

Editorial extensions

If this is right

  • Using the first major peak rather than the maximum peak reduces mean timing error by roughly two orders of magnitude in the simulated EVA channel, and this holds for both SU-PCP and MU-PCP.
  • MU-PCP preserves spectral efficiency as the number of users grows, whereas SU-PCP with full guards degrades; the paper derives conditions on Doppler spread and channel length under which MU-PCP is the more efficient choice.
  • Estimating and compensating CFOs before channel estimation avoids an NMSE error floor and yields gains up to about 5 dB over absorbing CFO into the channel estimate.
  • The multidimensional ML CFO search becomes Q parallel one-dimensional searches, so complexity scales linearly with users instead of jointly.
  • Both proposed TO methods work without closed-loop feedback to the mobile terminals, avoiding outdated TO estimates in the next uplink frame.

Reading between the lines

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

  • A natural extension is to set the threshold per user from its power-delay profile rather than a single global range, since the paper's own TDL-C results show the first-peak margin shrinks when the first channel tap is weak.
  • The same first-major-peak logic could be ported to downlink or sidelink OTFS and to non-orthogonal multiple access, where pilot regions overlap by design; the filter-bank separation in MU-PCP is a template for that.
  • The 5 dB channel-estimation gain argues for a protocol change: reserve a short synchronization preamble before channel estimation even at some spectral cost, instead of always absorbing CFO into the channel.
  • A testable prediction is that the threshold range in (20)-(21) becomes empty as the data-to-pilot power ratio $\sigma_s/\sigma_p$ grows; the estimator should then fail abruptly, not gracefully, unless the PCP power is boosted.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper addresses uplink synchronization for multiuser OTFS (MU-OTFS) in high-mobility scenarios. It derives a compound channel model that incorporates timing offsets (TOs) and carrier frequency offsets (CFOs) in the delay-Doppler domain, and then proposes two TO estimation techniques based on two pilot structures: SU-PCP, which assigns different ZC sequences to users in non-overlapping delay regions, and MU-PCP, which lets all users share a common pilot region and separates users with a bank of bandpass filters. The TO estimators use a correlation-based timing metric and detect the 'first major peak' via a threshold, for which a mathematical threshold range is derived in Section IV-C and Appendix B. After TO correction, a maximum-likelihood CFO estimator is developed using a Chebyshev-polynomial basis expansion model (CPF-BEM), reducing the multiuser CFO search to multiple one-dimensional searches. The paper also analyzes spectral efficiency and computational complexity, and presents simulations claiming a two-orders-of-magnitude TO accuracy improvement over maximum-peak detection and up to 5 dB channel-estimation NMSE gains over absorbing CFO into the channel.

Significance. If the claims hold, the paper makes a substantial contribution to an under-explored problem: open-loop synchronization for MU-OTFS uplink. The compound channel model, the two pilot structures, the filter-bank separation, and the CPF-BEM-based ML CFO estimator are coherent and practically motivated. The paper includes explicit complexity and spectral-efficiency analyses, and the simulation study covers both EVA and TDL-C channels. The central quantitative claim, however, is the two-orders-of-magnitude TO accuracy improvement of first-peak detection over max-peak detection, which rests on the threshold-range derivation. That derivation has a load-bearing gap concerning per-tap peak scaling, and the simulations do not disclose the exact threshold values used. These issues must be addressed before the main claim can be considered supported.

major comments (3)
  1. [Section IV-C and Appendix B, Eqs. (38)-(43)] The threshold range is derived using the factor sum_{ell=0}^{Lch-1} rho_ch[ell] = 1, effectively assuming that all channel taps contribute to the first major peak at l'_b = theta - Lp. However, the first major peak is created by the alignment of the two identical ZC halves for a specific received path; other delays have low ZC cross-correlation. Thus the peak amplitude scales with the power of the tap that creates that alignment, not with the total channel power. Under TDL-C, where the first tap is not the strongest, the intended first major peak can fall below the threshold while a later strong tap produces a peak above it, causing the estimator to lock to the later tap and incur a bias equal to that tap's delay. The derivation should condition on the tap that generates the first major peak, or the threshold range must be shown to hold on a per-tap basis.
  2. [Section VII, Fig. 10] The claimed 'two orders of magnitude' improvement of first-peak detection over maximum-peak detection is not verifiable from the information provided, because the simulation threshold T is not reported. The text states that thresholds are selected 'within the derived range,' but does not specify which values are used for each channel model (EVA, TDL-C), number of users, and SNR. Please provide the exact threshold values used, or a sensitivity plot of the mean TO error versus T, to confirm that the plotted curves correspond to thresholds inside the derived range.
  3. [Section IV-C, Eq. (21) and Fig. 12] The normalized threshold range in (21) is obtained by dividing by the expected full-alignment peak amplitude, (2Lp-1)/M * sigma_p^2. This normalization assumes that the full-alignment peak is the maximum of the timing metric. Under TDL-C, a later, stronger tap can produce a higher peak, so the normalized threshold mapping may no longer hold. In addition, the paper observes in Fig. 12 that increasing M narrows the threshold range, but it does not verify that the range in (20) is nonempty for the simulation parameters used (M=128, Lp=10, 16-QAM, with a finite sigma_s/sigma_p ratio). The authors should demonstrate, for the simulated scenarios, that the derived threshold interval is nonempty and that a single threshold in that interval yields the plotted first-peak performance.
minor comments (5)
  1. [Section IV-B] The phrase 'as shown in Appendix A of the revised manuscript' is a revision artifact and should be changed to refer to Appendix A of the current manuscript.
  2. [Table I and Eqs. (11)-(12)] The notation (.)_M is used in Eqs. (11) and (12) for the modulo-M operation, but the table entries for '( (·) )i' and '(·)i' are ambiguous; please clarify at the point of use that the subscript M denotes modulo M, not multiplication by M.
  3. [Fig. 10] The legend contains duplicate entries (e.g., 'MU-PCP: Q = 4 (TDL-C)' appears more than once); the legend should be cleaned up to avoid confusion.
  4. [Section IV-A, Eq. (12)] The channel mean delay lambda_q_ch is used in Eq. (12) but is not included in the notation table; please add a definition in the table or in the text.
  5. [Section VIII] The phrase 'for the first time in literature' is a strong claim that is not fully supported by the literature review; please soften or qualify it.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the TO threshold range and the CPF-BEM-based ML CFO estimator are derived from the stated system model, and the self-citations are contextual rather than load-bearing.

full rationale

The central derivations are self-contained. The TO timing metric in (14) and the threshold range in (20)-(21) follow from the received-signal model (4)-(7), the PCP/ZC pilot definitions, and the triangle-inequality bounds in Appendix B; the threshold range is not fitted to the simulation curves in Figs. 10-12. The CFO estimator (27)-(31) is a standard ML projection onto the CPF-BEM basis, with the channel coefficients treated as nuisance parameters; the reduction from a multidimensional search to parallel one-dimensional searches is obtained by the filter-bank separation in (13) and the per-user pilot extraction, not by assuming the answer. The paper's self-citations, e.g., [16], [17], and [27], supply pilot structures and single-user synchronization concepts, but the multiuser extension, the mathematical threshold derivation, and the CFO decomposition are developed in this manuscript. No step reduces to an imported uniqueness theorem or to a parameter fitted to the claimed output. The paper even concedes that under TDL-C or severely time-varying channels, fake peaks can appear, which is an honest limitation of the first-major-peak approach rather than a hidden circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims rely on the discrete-time LTV channel model, the CPF-BEM representation, and the peak-structure assumption of the PCP correlation. No new physical entities are introduced; the SU-PCP and MU-PCP are signal structures, not entities. The threshold T is the main hand-chosen operating point, though its range is derived.

free parameters (3)
  • Threshold T = not specified; derived range (21) gives 0.25 to 0.5 asymptotically
    The TO estimator in Algorithm 1 needs a scalar threshold. The paper derives a valid range but does not state the exact value used in the simulations, so reproduction requires a choice. The choice is not fitted to the target error rate, but it is a hand-selected operating point within a broad range.
  • Dominant Doppler spread factor alpha = 0.5
    Used in the MU-PCP user-capacity bound Q <= floor(N/(4*alpha*kappa_max+1)). It is chosen as the value for which 90% of the Doppler power is contained, not fitted to the estimation results.
  • CPF-BEM order beta = 1 to 12, dependent on kappa_max (beta >= ceil(2*kappa_max+1))
    The CFO estimator assumes the LTV channel is represented by beta Chebyshev basis functions. The paper sets beta per user in simulations; this is a model-order parameter, not fitted to the output.
assumptions (4)
  • domain assumption The LTV channel per user is accurately represented by CPF-BEM with beta >= ceil(2*kappa_max+1) basis functions, and the basis order is known at the receiver.
    Invoked in Section V, Eq. (25)-(27), to separate channel time variations from the time-invariant part in ML CFO estimation. BEM modeling error is not characterized.
  • domain assumption The PCP correlation produces a detectable first major peak at l'_b = theta - Lp, with a distinct minor peak at l'_a, and the threshold range (20) separates them under the operating channel.
    Invoked in Section IV-C and Appendix B. The paper's own Fig. 10 shows degraded TO accuracy under TDL-C channels where the first tap is not the strongest, and the text concedes 'several fake peaks' may appear.
  • domain assumption All users are quasi-synchronous in time, with TOs bounded such that Lcp = max_q L_ch^q + theta_max - 1 suffices.
    Invoked in Section II. Standard assumption; load-bearing for pilot-region search and CP removal.
  • domain assumption Distinct-root ZC sequences provide sufficient separability between users' pilots in SU-PCP; residual cross-correlation is treated as negligible.
    Invoked in Section IV-A for correlation-based TO estimation; the paper acknowledges ZC sequences are not completely independent from data symbols.

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Pith. "Pith review of Time and Frequency Synchronization for Multiuser OTFS in Uplink." pith.science (2026). https://pith.science/paper/XJN6FG7R

@misc{pith2026250717966,
  author       = {Pith},
  title        = {Pith review of: Time and Frequency Synchronization for Multiuser OTFS in Uplink},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XJN6FG7R}},
  note         = {Machine review of arXiv:2507.17966}
}
read the original abstract

In this paper, we propose time and frequency synchronization techniques for uplink multiuser OTFS (MU-OTFS) systems in high-mobility scenarios. This work focuses on accurately estimating and correcting timing offsets (TOs) and carrier frequency offsets (CFOs). Specifically, TO estimation is essential for locating users' pilots on the delay-time plane, while CFO estimation enhances channel estimation accuracy. First, we propose a TO estimation technique for an existing multiuser pilot structure in MU-OTFS. We replace the impulse pilot (IMP) in this pilot structure with a more practical pilot with a cyclic prefix (PCP), referred to as single-user-inspired PCP (SU-PCP). This structure employs different Zadoff-Chu (ZC) sequences, which enables pilot separation via correlation at the receiver side. Consequently, we introduce a correlation-based TO estimation technique for uplink MU-OTFS using this pilot structure. Next, a spectrally efficient and practical pilot pattern is proposed, where each user transmits a PCP within a shared pilot region on the delay-Doppler plane, referred to as MU-PCP. At the receiver, the second TO estimation technique utilizes a bank of filters to separate different users' signals and accurately estimate their TOs. Then, we derive a mathematical threshold range to enhance TO estimation accuracy by finding the first major peak in the correlation function rather than relying solely on the highest peak. After locating the received users' pilot signals using one of the proposed TO estimation techniques, our proposed CFO estimation technique reduces the multi-dimensional maximum likelihood (ML) search problem into multiple one-dimensional search problems. In this technique, we apply the Chebyshev polynomials of the first kind basis expansion model (CPF-BEM) to effectively handle the time-variations of the channel in obtaining the CFO estimates for all the users.

Figures

Figures reproduced from arXiv: 2507.17966 by the authors.

Figure 1
Figure 1. In GBBMA, guard bands are inserted in the delay [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Data structure of a user at the MT for uplink transmiss [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. SU-PCP structure for MU-OTFS in the delay-Doppler do [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The proposed synchronization block diagram for SU-P [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 3
Figure 3. Figure 3: As will be discussed shortly, to enable differentiat [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]
Figure 5
Figure 5. Figure 5: Proposed MU-PCP structure for MU-OTFS in the delay-D [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The proposed structure for TO, CFO, and channel estim [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 8
Figure 8. Figure 8: Three major peaks in the pilot region relating to PCP. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: The timing metric calculation in detail for a user aft [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 11
Figure 11. Figure 11: Performance of the proposed TO es￾timation techniques versus normalized maximum Doppler spread at SNR = 20 dB for 16-QAM. 64 128 256 512 M 10-4 10-3 10-2 10-1 100 101 Mean (Sample) Q = 4 Q = 2 Max. Peak First Peak [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 13
Figure 13. Figure 13: MSE performance of the proposed CFO estimation technique versus SNR at κmax ≈ 2.91 for 16-QAM. 0 0.58 1.17 1.75 2.33 2.91 max 10-3 10-2 10-1 MSE SU-PCP: Q = 4 MU-PCP: Q = 4 SU-PCP: Q = 2 MU-PCP: Q = 2 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 16
Figure 16. Figure 16: NMSE performance of the channel esti￾mation technique at κmax ≈ 2.91 and SNR = 20 dB for 16-QAM. 0 4 8 12 16 20 24 28 SNR (dB) 10-4 10-3 10-2 10-1 NMSE Absorbed CFO in Channel Estimation Joint CFO and Channel Estimation: SU-PCP Joint CFO and Channel Estimation: MU-PCP…
Figure 19
Figure 19. Figure 19: Number of allowed users versus (a) channel length for SU-PCP, and (b) normalized Doppler spread for MU-PCP. 2 4 6 8 10 12 Q 20 40 60 80 100 Spectral Efficiency (%) MU-PCP SU-PCP: Partial Guards SU-PCP: Full Guards [PITH_FULL_IMAGE:figures/full_fig_p015_19.png]

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Pith tools

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