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REVIEW 3 major objections 5 minor 1 cited by

Zak-OTFS Based Coded Random Access for Uplink mMTC

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

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Pith's one-line read Zak-OTFS keeps the channel nearly constant across a frame, making collision-cancelling random access work under high mobility.

desk verdict A promising DD-domain CRA scheme whose central claim is undercut by an unfair full-frame baseline; the core idea deserves review but needs the missing OFDM-with-SIC comparison. read the letter →

arxiv 2507.22013 v1 pith:PODCHS36 submitted 2025-07-29 eess.SP

Alessandro Mirri , Venkatesh Khammammetti , Beyza Dabak , Enrico Paolini , Krishna Narayanan , Robert Calderbank This is my paper · ORCID
classification eess.SP
keywords CodedRandomAccessDelay-DopplerCommunicationInternetofThingsSuccessiveInterferenceCancellationZak-OTFSMassiveMachine-TypeCommunicationsDoublySelectiveChannelsPacketLossRate
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

SIC-based coded random access only works if a base station can predict each user's channel in every slot where its packet repeats, because decoded packets must be subtracted from colliding slots. Under high mobility, OFDM's channel changes too fast between slots for that prediction to hold, so collided packets are lost. This paper argues that moving the same protocol to the delay-Doppler domain with Zak-OTFS modulation makes the effective channel nearly invariant across the whole frame, so a channel estimate from one slot stays valid everywhere. The paper demonstrates with Veh-A simulations that this Zak-OTFS scheme keeps packet loss low for far more active users than the OFDM baseline, pointing to a PHY-layer fix for grant-free access in vehicular and industrial mMTC.

What carries the argument

The load-bearing object is the Zak-OTFS delay-Doppler frame, a p by q grid of slots in which each slot is a pilot tile plus a data tile in the delay-Doppler domain. The crystalline condition (channel delay spread less than the delay period and Doppler spread less than the Doppler period) makes the sampled effective channel $h_{\text{eff}}[k,l]$ nearly identical for every slot; this near-invariance is what lets the receiver estimate the channel from a singleton slot's point pilot and reuse it for MMSE equalization and for SIC across all of that user's replicas. The receiver extracts the channel estimate with a cross-ambiguity operation on the pilot tile, and the quasi-periodic structure of the DD signal makes the input-output relation predictable enough for this reuse to work.

What would settle it

Rerun the Fig. 7 frame-level simulation with the same Veh-A channel but remove the base station's knowledge of the users' repetition patterns, forcing it to discover which slots each user occupies from the received signal. If the Zak-OTFS packet-loss curve at $K_a = 60$ rises above $10^{-3}$ or falls to the OFDM no-SIC level, the claim that Zak-OTFS enables reliable grant-free CRA would be refuted. A second check is to push the Doppler period below $2\nu_{\max}$, violating the crystalline condition, and observe whether the Zak-OTFS advantage collapses.

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Extended reading notes

Core claim

The central claim is that switching the physical layer from OFDM to Zak-OTFS changes SIC-based CRA from a protocol that degrades sharply under Doppler spread into one that stays reliable. In Zak-OTFS, a single pilot per slot is enough to estimate the user's effective channel, and that estimate stays valid across all slots because the delay-Doppler response is quasi-static when the channel's delay spread is below the delay period and its Doppler spread is below the Doppler period. Once a user is decoded in a singleton slot, its contribution can be reconstructed and subtracted from every other slot where its replicas collide, so SIC proceeds as if the channel were fixed. Frame-level Monte Carlo simulations with 128 slots, three replicas per user, and a 25 dB SNR show Zak-OTFS with Gaussian pulse shaping keeping packet loss below $10^{-3}$ up to roughly 60 active users, while the OFDM baseline, whose SIC is ineffective at this mobility, saturates at a much smaller user count.

Load-bearing premise

The base station must already know the repetition pattern, meaning the set of slots each user picked, because decoding starts by recognizing singleton slots from that knowledge; the paper states that automatic preamble detection is left to future work.

Editorial extensions

If this is right

  • With the larger slot configuration, the Zak-OTFS scheme with Gaussian pulse shaping keeps packet loss below $10^{-3}$ for up to about 60 active users per 128-slot frame at 25 dB SNR, while the OFDM baseline without working SIC saturates at much lower user counts.
  • In the two-user SIC experiment, OFDM's ability to cancel a collided user degrades as the temporal distance $\delta$ between the decoded slot and the canceled slot grows, whereas Zak-OTFS shows only a small degradation for collided users.
  • Because the channel estimate from one slot is reusable across all slots, the Zak-OTFS receiver needs only a single pilot per slot, while OFDM needs pilots interleaved across subcarriers and MMSE interpolation to predict channels across time.
  • The performance advantage of Zak-OTFS persists when the Doppler period is reduced to 5 kHz, a regime where OFDM suffers severe inter-carrier interference and a packet-loss floor between $10^{-1}$ and $10^{-2}$.

Reading between the lines

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

  • If automatic preamble detection is added, the same near-invariant-channel argument could be carried over to other grant-free schemes such as coded compressed sensing, which the paper lists as future work.
  • The Gaussian-versus-sinc comparison suggests a receiver-complexity trade-off: Gaussian shaping buys lower packet loss at higher equalization cost, so a practical system might adapt the filter to the operating SNR.
  • The paper's frame-level results are all at 25 dB SNR over one Veh-A profile; testing at lower SNR or with Doppler spreads closer to the crystalline bound would show how quickly the advantage erodes.
  • Combining Zak-OTFS CRA with massive MIMO spatial separation, which the paper defers to future work, could extend the user count well beyond the reported $K_a \approx 60$.
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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 proposes a grant-free coded random access (CRA) scheme for uplink massive machine-type communications based on Zak-OTFS modulation in the delay-Doppler domain. Each active user transmits replicas of a packet in randomly selected OTFS slots, and the receiver identifies singleton slots, decodes packets, and performs successive interference cancellation across replica slots. The central claim is that Zak-OTFS keeps the effective channel nearly invariant across the frame, which makes channel estimates reusable for SIC under high mobility, whereas OFDM-based CRA suffers from unreliable inter-slot channel prediction. The paper presents single-user PLR-vs-SNR results for two slot sizes and two pulse-shaping filters, two-user SIC experiments with varying temporal distance between slots, and a full-frame PLR-vs-number-of-active-users comparison under the ITU Veh-A channel. The main reported conclusion is that Zak-OTFS-based CRA achieves a substantially lower packet loss rate than OFDM-based CRA, particularly at high user densities and high mobility.

Significance. If the headline frame-level gain is confirmed, the paper would be a useful demonstration that the physical-layer waveform choice materially affects the viability of SIC in coded random access, and that delay-Doppler-domain modulation can extend CRA from idealized flat-fading or AWGN models to doubly selective channels. The paper has clear strengths: the system model and protocol are described in detail; the comparison controls total energy and time-bandwidth product; the evaluation uses a standardized Veh-A channel; and both Gaussian and sinc pulse shaping are considered, with an honest discussion of their trade-offs. The central hypothesis is falsifiable and the main result is a clean scalability curve. However, the paper ships no code or data, and the full-frame comparison is not a CRA-to-CRA comparison because the OFDM baseline is evaluated without SIC. The known-preambles assumption at the receiver is also a significant scope limitation for a scheme described as grant-free.

major comments (3)
  1. [Section IV-C3, Fig. 7] The headline frame-level comparison is not a CRA-to-CRA comparison: the OFDM curve in Fig. 7 is explicitly computed with SIC disabled ('OFDM - r = 3, No SIC'). The paper justifies this by stating that SIC is ineffective in the high-mobility regime, citing the two-user experiments of Section IV-C2. However, the two-user experiments cover only delta = 1 and delta = 2, lack error bars, and do not quantify how residual SIC errors accumulate under full user density or after multiple successive cancellations. The central contribution of the paper is precisely that Zak-OTFS enables SIC while OFDM does not; this is not directly established by comparing an SIC-enabled Zak-OTFS scheme against a DSA-only OFDM baseline. Please add a full-frame OFDM CRA curve with SIC enabled under the same protocol, channel, SNR, and number of replicas, with confidence intervals. If OFDM-SIC collapses to the no-SIC curve, that should be demonstrated rather than assumed; if it does not collapse, the stated comparison should be revised accordingly.
  2. [Section III-C and Section V] The decoding procedure starts from the assumption that the BS knows the repetition pattern (or preambles) of all active users; this knowledge is what allows the BS to identify singleton slots and trigger SIC. In a grant-free mMTC setting, preamble or pattern discovery is part of the random-access problem, and the paper explicitly defers this to future work (Section V). This is a load-bearing system-side oracle: without it, the proposed decoding procedure cannot start. Please either add a preamble-detection mechanism, even a simplified one, or explicitly recast the contribution as a PHY-layer enabler that assumes an upper-MAC oracle, and discuss how unknown or imperfect preamble knowledge would affect the reported PLR. As written, the abstract and introduction overstate the grant-free nature of the scheme.
  3. [Section IV-C2, Figs. 5 and 6] The two-user evidence for OFDM SIC failure is incomplete in a way that matters for the frame-level claim. In the small-slot configuration only delta = 1 and delta = 2 are tested, and no confidence intervals are given. In the large-slot configuration the text reports that SIC is 'effectively disabling' OFDM, but the figure legend and caption do not clearly identify the OFDM collided-user curve, and no quantitative residual-SIC metric is provided. As a result, the reader cannot assess how prediction error grows with delta or how it translates into frame-level PLR under many active users and multiple cancellations. Please strengthen this evidence or explicitly de-emphasize it when making the frame-level comparison.
minor comments (5)
  1. [Section IV-C2] The sentence 'The PLR for the collided user in this setup corresponds to the solid curves in Fig. 4' is confusing; please clarify which curves in Fig. 6 are collided-user curves and which are uncollided-user curves.
  2. [Figs. 3-7] The figures do not report the number of Monte Carlo trials or confidence intervals. Please add this information, at least for the frame-level results in Fig. 7 where the scalability claim is the main conclusion.
  3. [Figs. 4 and 6] The legends are incomplete relative to the captions: Fig. 4 mentions dashed curves for nu_p = 5 kHz but the legend does not clearly list a dashed OFDM curve, and Fig. 6's legend lacks an explicit 'OFDM collided' entry despite the caption describing collided-user PLR for both schemes.
  4. [Section III-D] The statement that the CP-OFDM system is configured with 'N = p * q * N_OFDM time indices per frame' appears inconsistent with matching the Zak-OTFS frame duration T = tau_p * N; please check whether the time-bandwidth product is actually matched or whether the total number of time indices should be q * N_OFDM.
  5. [General] No code or data are provided. A reproducibility statement or data-availability note would be helpful, especially because the paper relies entirely on Monte Carlo simulations.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the PLR gains come from independent Monte Carlo simulation, and the Zak-OTFS predictability premise is a prior mathematical property, not a fit or a definitional restatement.

full rationale

The central PLR comparison in Fig. 7 is produced by simulating the full transmitter/receiver chain defined in Sections III and IV; no parameter is fitted to the reported curves, and the Zak-OTFS advantage is not a renamed input. The load-bearing premise that Zak-OTFS makes the DD channel approximately invariant across a frame is taken from prior Zak-OTFS theory ([16], [24], [30]), some co-authored by R. Calderbank, but that theory is parameter-free and rests on stated crystalline conditions (delay spread below the delay period, Doppler spread below the Doppler period), with this paper's own Fig. 4 independently showing the expected stability. This is therefore a real external result rather than an unverified self-citation chain. The known-preambles assumption of Section III-C is a strong but acknowledged side condition (Section V), and the missing OFDM-with-SIC frame-level curve in Fig. 7 is a baseline-fairness concern, not a demonstration that the Zak-OTFS result is equivalent to its input by construction. Accordingly, no circular step can be quoted and reduced from the paper's own equations.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper contains no fitted constants in the parameter-estimation sense; its claims are driven by hand-set simulation parameters and by prior Zak-OTFS predictability results. The strongest auxiliary input is the known-preambles assumption, which is not solved here.

free parameters (3)
  • Doppler period νp = 30 kHz, with one scenario at 5 kHz
    Hand-chosen system parameter; sets τp=1/νp and must satisfy the crystalline condition. Results depend on it, especially the OFDM comparison.
  • Number of replicas r = 3
    Set to a standard CRA value; larger r improves diversity and SIC opportunities.
  • Frame-level SNR = 25 dB
    Operating point used for the main scalability result in Fig. 7.
assumptions (5)
  • domain assumption Under the crystalline condition, the Zak-OTFS effective channel is near-invariant across the frame, so a channel estimate from one slot can be reused for SIC in all other slots.
    Invoked in Sections III-C and IV-C; sourced from references [16,24,35], not re-derived.
  • ad hoc to paper The BS knows the repetition pattern or preambles of all active users.
    Assumed in Section III-C; enables singleton slot identification and SIC. Preamble detection is deferred to future work in Section V.
  • domain assumption All active users are frame-synchronized.
    Assumed at the start of Section III-C; no synchronization acquisition is modeled.
  • domain assumption The Veh-A six-path channel with normalized powers and i.i.d. Doppler angles is representative of high-mobility mMTC.
    Section IV-B; all performance conclusions depend on this standardized model.
  • standard math Standard signal processing identities for Zak-OTFS, twisted convolution, MMSE, and cross-ambiguity are correct.
    Used throughout Sections II and III; accepted background, not proven in this paper.

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Cite this review

Pith. "Pith review of Zak-OTFS Based Coded Random Access for Uplink mMTC." pith.science (2026). https://pith.science/paper/PODCHS36

@misc{pith2026250722013,
  author       = {Pith},
  title        = {Pith review of: Zak-OTFS Based Coded Random Access for Uplink mMTC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PODCHS36}},
  note         = {Machine review of arXiv:2507.22013}
}
read the original abstract

This paper proposes a grant-free coded random access (CRA) scheme for uplink massive machine-type communications (mMTC), based on Zak-orthogonal time frequency space (Zak-OTFS) modulation in the delay-Doppler domain. The scheme is tailored for doubly selective wireless channels, where conventional orthogonal frequency-division multiplexing (OFDM)-based CRA suffers from unreliable inter-slot channel prediction due to time-frequency variability. By exploiting the predictable nature of Zak-OTFS, the proposed approach enables accurate channel estimation across slots, facilitating reliable successive interference cancellation across user packet replicas. A fair comparison with an OFDM-based CRA baseline shows that the proposed scheme achieves significantly lower packet loss rates under high mobility and user density. Extensive simulations over the standardized Veh-A channel confirm the robustness and scalability of Zak-OTFS-based CRA, supporting its applicability to future mMTC deployments.

Figures

Figures reproduced from arXiv: 2507.22013 by the authors.

Figure 1
Figure 1. Comparison between (a) conventional coded random access in the time-frequency domain and (b) proposed Zak-OTFS-based coded random access in the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Structure of a single slot in the coded random access scheme, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. PLR versus SNR for a single-user, interference-free scenario with slot [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: PLR versus SNR for a simplified two-user scenario with [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 3
Figure 3. Figure 3: In the OFDM-based case, we introduce the variable [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 6
Figure 6. Figure 6: PLR versus SNR for a two-user scenario with slot configuration [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: PLR versus number of active users per frame, [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Approximate Message Passing for Multi-Preamble Detection in OTFS Random Access

    eess.SP 2025-09 conditional novelty 5.0 of 10

    A complex-domain AMP algorithm with a denoiser combining elementwise and group sparsity is proposed for OTFS preamble detection, achieving simulated gains over existing methods.

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Pith tools

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