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REVIEW 3 major objections 5 minor 1 cited by

Zak-OTFS based Multiuser Uplink in Doubly-Spread Channels

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

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Pith's one-line read A phase-twisted delay-Doppler pulse gives each Zak-OTFS user its own time-frequency tile, so a four-user uplink can match single-user bit error rates without any guard bands.

desk verdict The TF-shifting DD pulse in Theorem 1 is a genuinely new and useful tool, but the multiuser superposition analysis assumes a common Zak period that the paper itself lets each user choose differently—this gap needs to be fixed before the MUI claims can be trusted. read the letter →

arxiv 2507.15621 v1 pith:3CBDEDGD submitted 2025-07-21 eess.SP cs.ITmath.IT

Imran Ali Khan , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank This is my paper · ORCID
classification eess.SPcs.ITmath.IT
keywords Zak-OTFSmultiuseruplinkdelay-Dopplerdomainpulseshapingtime-frequencyresourceallocationdoubly-spreadchannelsmatchedfilteringorthogonalmultipleaccess
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

The paper tries to establish that the predictable input-output relation of Zak-OTFS can be kept in a multiuser uplink by shaping each user's delay-Doppler transmit pulse with a phase twist that shifts the signal's time-frequency location. If true, users with very different mobility can share spectrum without forcing everyone onto one subcarrier spacing, and without paying for guard bands between adjacent allocations. The key quantitative claim is that the interference-to-useful-signal ratio stays below about -30 dB even at 6 kHz Doppler spread, so at practical signal-to-noise ratios the multiuser interference is buried under noise. The result matters because it removes a standard cost of orthogonal multiple access and keeps each user's channel acquisition predictable through its own pilot.

What carries the argument

The central object is the DD-domain transmit pulse-shaping filter carrying the phase factor $e^{j2\pi(\nu_s\tau - \nu\tau_s)}$, applied through twisted convolution to quasi-periodic Dirac-delta DD pulses that carry information symbols. Twisted convolution is the DD-domain operation that combines a filter with a quasi-periodic DD function while preserving quasi-periodicity, and it is what makes the Zak-transform input-output relation associative and tractable. The receiver uses the matched filter in (37), the conjugate time- and frequency-reversed version of the shifted pulse, and Theorem 2 expresses the effective channel as a sum over paths of two separated integrals, one governing frequency-domain overlap and one governing time-domain overlap. That separation is what turns the no-guard-band claim into a calculable interference ratio.

What would settle it

Simulate two users with identical TF allocations but different delay and Doppler periods, then compare the measured leakage ratio $I_{q,s}/S_{s,s}$ against the paper's formula; if the measured leakage departs from the predicted value once the periods differ, the shared-superposition equation (20) needs a per-user Zak basis. A simpler check is to numerically compute the Zak transform of a sum of two signals with different periods and verify the energy relations used in (42)-(45).

Watch

Extended reading notes

Core claim

The paper's central claim is that a transmit delay-Doppler filter of the form $\tilde{w}_{tx,s}(\tau,\nu) = w_{tx,s}(\tau,\nu)e^{j2\pi(\nu_s\tau - \nu\tau_s)}$ shifts the TF occupancy of a Zak-OTFS signal to approximately $[\tau_s - T_s/2, \tau_s + T_s/2] \times [\nu_s - B_s/2, \nu_s + B_s/2]$, while leaving each user free to choose its own delay and Doppler periods. At the base station, the received superposition is match-filtered separately for each user, and the paper derives the effective continuous DD-domain channel between every transmit-receive pair as a sum over propagation paths of two overlap integrals. For an ideal channel the leakage from user $s$ into user $q$'s matched-filter output is bounded by $O(1/K^3)$ with $K = \min(M_s N_s, M_q N_q)$. In simulations on a vehicular-A doubly-spread channel the leakage ratio stays below about $-30$ dB at 6 kHz Doppler spread, and the bit error rate and channel-estimation NMSE for UT-1 in a four-user uplink coincide with the single-user curves, even without guard resources.

Load-bearing premise

The receiver-side derivation assumes that one Zak transform of the received signal is enough to produce a single DD-domain superposition on which every user's matched filter can act, even though each user is allowed a different delay and Doppler period; the paper never specifies a common period for that single transform.

Editorial extensions

If this is right

  • Users with very different Doppler spreads can be assigned different delay and Doppler periods, so the numerology of one fast-moving user no longer dictates the subcarrier spacing of all users.
  • Because the interference-to-useful-signal ratio is below about -30 dB at 6 kHz Doppler spread, at typical SNRs below 30 dB the BER and channel-estimation NMSE are limited by noise rather than by multiuser interference.
  • Adjacent time-frequency allocations need no guard bands: interference that is localized at TF boundaries spreads almost uniformly across DD carriers, so no single carrier is hit disproportionately hard.
  • The rectangular per-user TF allocations line up with 3GPP-style resource blocks, allowing mixed terrestrial and non-terrestrial users to share one uplink frame.
  • Each user's crystallization condition can be satisfied independently, preserving predictable single-pilot channel acquisition for every user.

Reading between the lines

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

  • A testable extension is to push the frame size down: the paper's $O(1/K^3)$ bound implies that for frames with $M_s N_s$ below about a hundred, leakage rises above the -60 dB ideal-channel level, so the no-guard claim should be rechecked in the short-frame regime.
  • The same phase-twist shaping could be reused in a downlink broadcast or relay setting, where the base station transmits a superposition and each user's own matched filter extracts its stream without joint decoding.
  • Because the residual interference is nearly uniform in the DD domain, per-carrier power allocation or simple interference cancellation at the BS could push the operating point even further below noise-limited performance.
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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 multiuser uplink scheme based on Zak-OTFS, where each user's transmit pulse is shaped in the delay-Doppler (DD) domain by a phase factor exp(j2π(ν_s τ − ν τ_s)) so that its time-frequency (TF) occupancy is shifted to an allocated, non-overlapping TF region. Users are allowed to choose independent DD periods (τ_p,s, ν_p,s) to satisfy the crystallization condition for their own channels. The base station applies a DD-domain matched filter per user, and the paper derives expressions for the effective channel and for interference-to-useful-signal ratios, claims an O(1/K^3) leakage bound, and presents simulations for a four-user vehicular-A uplink showing that the multiuser BER of UT-1 coincides with the single-user BER without guard TF resources. The central claim is thus that single-user performance can be achieved in a multiuser Zak-OTFS uplink with independently chosen numerologies and no TF guards.

Significance. If the claimed result holds, it is a substantial contribution: it would give Zak-OTFS the TF-resource allocation flexibility of OFDMA while preserving the predictable DD I/O relation, and would allow users with different delay/Doppler spreads to choose independent numerologies. The TF-shifting mechanism of Theorem 1 is elegant and the single-user derivation in Appendices D and E is a strength, as are the self-contained proofs of supporting lemmas. The paper also ships a detailed simulation setup (Table I, Table II, pilot/data frame structure) that would allow reproduction. However, the analytical multiuser model in Section II is not valid for the multi-period setting, because a single Zak transform of the received superposition cannot represent users with different periods simultaneously; this undermines the derived MUI measures. The O(1/K^3) leakage bound is heuristic. The numerical results may well be correct, but the theoretical framework as written does not yet support them, so the central claim is not established in the present form.

major comments (3)
  1. [Section II, Eqs. (20)-(24)] The derivation of the DD-domain received signal assumes that a single Zak transform of y(t) yields y_dd(τ,ν) equal to the sum of per-user twisted convolutions, but users are explicitly allowed different periods (Eq. (28), Table I: UT-1/2 have ν_p=15 kHz, UT-3/4 have ν_p=30 kHz). The Zak transform in Eq. (7) is defined for a fixed delay period τ_p, and each x_wtx_dd,s is quasi-periodic with period (τ_p,s, ν_p,s). A sum of functions with different quasi-periodicities is not quasi-periodic with any single period, so Eq. (20) cannot hold as an identity in the multi-period setting. Consequently the matched-filter step (21), the effective channel decomposition (22), and the sampling on the lattice Λ_q in (24) are not well-defined for the actual receiver. The paper must either impose a common commensurate period for all users (which would restrict the independent-choice claim made in Section III) or define per-user Zak transforms y_dd,q = Z_{τ_p,q}(y) and re-derive the effective channel and interference expressions accordingly.
  2. [Section III-C, after Eq. (46)] The O(1/K^3) leakage bound is heuristic. The passage from the support and energy properties of h_eff,q,s to the statement that the DD-domain energy of h~_{q,s}^{k,l} is O(1/K^2) over an area O(1/K) neglects the aliasing arising from the infinite Dirac comb in Eq. (4) and gives no rigorous treatment of overlapping shifted supports; no constants or error terms are provided. This bound is used in the text to assert that the interference-to-useful-signal ratio is at most about 10^-6 for moderate/large frames, so it should either be proved or explicitly identified as an approximation. The numerical claims in Section IV do not rest on this bound, but the presentation should not present a heuristic estimate as a theorem.
  3. [Section IV, Figs. 5-7] The paper does not state whether the leakage ratios plotted in Figs. 5-7 are computed from the analytical expression (46) together with (41), or by direct time-domain projection of the received signal onto each user's matched-filter prototype. If the former, the simulations inherit the period-mismatch problem of Eqs. (20)-(24); if the latter, the simulation methodology should be described explicitly and its consistency with (46) justified. This clarification is necessary to confirm that the reported -30 dB MUI level and the single-user BER curves are not artifacts of the undefined algebraic framework.
minor comments (5)
  1. [Section III-A] The text contains a typo: "pulse shaping fillters" should be "pulse shaping filters".
  2. [Section IV, after Fig. 8] The body text states "ν_max = 815 KHz for all UTs" in two places; the figures and the crystallization-condition calculation in Fig. 12 indicate the intended value is 815 Hz.
  3. [Abstract and Section IV] The phrase "Doppler spread of 6 kHz" is used inconsistently: Eq. (28) and the discussion in Fig. 12 imply the Doppler spread is 2ν_max (so 6 kHz spread corresponds to ν_max = 3 kHz), whereas Fig. 5 shows ratios at ν_max up to 6 kHz. Please define the term "Doppler spread" explicitly and use it consistently.
  4. [Eq. (24)] The summation limits in Eq. (24) are written as M-1 and N-1 without subscripts; they should be M_s-1 and N_s-1 to match the per-user notation.
  5. [Eq. (41)] The double sum in Eq. (41) is missing summation limits; it should be over n,m ∈ Z, and the phase factor should be displayed in a way that makes the quasi-periodicity of the sampled function explicit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TF-shifting pulse and effective-channel results are derived in appendices, and the key performance claims rest on independent simulations rather than fitted inputs.

full rationale

The paper's new contributions are derived self-containedly: Theorem 1 is proven in Appendix D from the time/frequency shift property of the pulse-shaping windows, and Theorem 2 is proven in Appendix E by direct twisted-convolution algebra. The cited background results from the same authors' prior works [12], [15], [20] are either reproduced in Appendices A-C or are independent mathematical lemmas whose assumptions (e.g., the crystallization condition) do not include the multiuser result being claimed. The channel-estimation method is adopted from [15], but it is an existing algorithm that is then benchmarked through NMSE and BER simulations, so it is not a fitted input renamed as a prediction. The central claim of single-user performance in the multiuser uplink is supported by new simulations (Figs. 5-13) and by an analytic O(1/K^3) leakage bound derived from Theorem 2, not by a parameter fitted to the output. The possible issue that users are assigned different DD periods while Eqs. (20)-(24) apply a single Zak transform to the received superposition is a mathematical correctness concern about whether the superposition model is well-defined, not a circularity: it does not reduce the paper's derivations to their own inputs. Overall, no circular step is present.

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

The paper introduces no new physical entities; its contribution is signal processing on known Zak-OTFS carriers. The main axiomatic burdens are the common Zak-period assumption at the BS, the approximate TF localization of the pulse shapes, and the crystallization condition inherited from prior work. The listed free parameters are hand-chosen system or simulation parameters rather than unknowns fitted to data; none of them is fitted to force the BER curves.

free parameters (4)
  • Pilot/data guard sizes (a1=2, a2=1, g1=3, g2=2) = a1=2, a2=1, g1=3, g2=2
    Chosen by hand for the embedded pilot frame in Section III-D and used in all simulations; they affect pilot-to-data interference but are not optimized or derived.
  • RRC roll-off factors beta_tau,q = beta_nu,q = 0.1 = 0.1
    Design choice for all users in Eq. (56); the resulting time/bandwidth expansion (1+beta)T_q, (1+beta)B_q affects adjacent-allocation leakage, but no sensitivity analysis is provided.
  • Pilot-to-data power ratio (PDR) = 0 dB for main results
    Chosen for the primary BER and NMSE plots; Fig. 10 shows that 0 dB is an operating point on a U-shaped curve, not an independently fitted constant.
  • Per-user Doppler periods = 15, 15, 30, 30 kHz (Table I)
    Selected manually to satisfy the crystallization condition for each user's channel simulation; the framework allows arbitrary choices, so these are system design parameters, not data-fitted parameters.
assumptions (4)
  • domain assumption The crystallization condition tau_p,s > tau_max,s and nu_p,s > 2 nu_max,s is sufficient for a predictable, non-fading Zak-OTFS I/O relation.
    Invoked in Section III (Eq. (28)) and relied on for pilot-based channel estimation; taken from the authors' prior works [12], [15].
  • domain assumption The pulse-shaping filters are approximately time- and bandwidth-limited with energy leakage of order O(1/B_s) and O(1/T_s) (Eqs. (29)-(30)).
    Used throughout Section III to bound TF localization and MUI; exact rectangular support in both time and frequency is impossible, so all results are approximate.
  • ad hoc to paper A single Zak-transform period can be used at the BS for all users even though users choose different (tau_p,s, nu_p,s); equivalently, y_dd in Eq. (20) is a well-defined common DD-domain signal.
    Eqs. (20)-(22) and (24) require this common-period assumption; the paper does not state the period choice or show how different user periods are reconciled.
  • domain assumption Each user's channel is a finite sum of P_s resolvable paths with independent Doppler angles, and the Veh-A power-delay profile applies to all users.
    Used in Theorem 2 and in the Monte Carlo simulator; standard for vehicular channel evaluation but limits generalization of the numerical claims.

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Cite this review

Pith. "Pith review of Zak-OTFS based Multiuser Uplink in Doubly-Spread Channels." pith.science (2026). https://pith.science/paper/3CBDEDGD

@misc{pith2026250715621,
  author       = {Pith},
  title        = {Pith review of: Zak-OTFS based Multiuser Uplink in Doubly-Spread Channels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3CBDEDGD}},
  note         = {Machine review of arXiv:2507.15621}
}
read the original abstract

Wireless users with different characteristics will be expected to share spectrum in next generation communication networks. One of the great strengths of wireless networks based on Orthogonal Frequency Division Multiplexing (OFDM) is the ease with which different non-overlapping time-frequency (TF) resources can be allocated to different users by simply shifting each user's signal in time and frequency. However, a significant weaknesses of OFDM is the inflexibility of sub-carrier spacing. Since OFDM does not allow users to have different sub-carrier spacing, a single user subject to inter-carrier interference causes carrier spacing to increase for all users. Zak-OTFS is an alternative delay-Doppler (DD) domain modulation scheme, where, in contrast to OFDM, the Input-Output (I/O) relation is predictable. We match the strength of OFDM by designing a novel DD domain method of shaping the transmitted Zak-OTFS pulse on the uplink that enables flexible non-overlapping TF resource allocation. The base station (BS) receives a superposition of uplink signals and applies individual matched filters to obtain the data specific to individual users. We develop theoretical measures of interference between users, and present numerical simulations for a vehicular channel model representative of next generation propagation environments. We demonstrate single-user performance in a multiuser Zak-OTFS uplink system without needing to provision guard bands between TF resources allocated to different users. These performance results demonstrate that the benefits of a predictable Zak-OTFS waveform can be realized within an architecture for uplink communication.

Figures

Figures reproduced from arXiv: 2507.15621 by the authors.

Figure 1
Figure 1. Transmitter and Receiver processing in Zak-OTFS-based uplink multiuser system [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Non-overlapping TF resource allocation for UTs. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. DD domain processing and corresponding TF allocation : (a) Single UT (b) Multiple UTs [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Embedded pilot and data frame for [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Leakage ratio Iq,s Ss,s (see (46)) vs. νmax when only UT-1 is transmitting wtx,q(τ, ν) = p BqTq rrcβτ,q (Bqτ ) rrcβν,q (Tqν) e j2π(νqτ−ντq) , rrcβ (x) = sin(πx(1 − β)) + 4βx cos(πx(1 + β)) πx (1 − (4βx) 2) , (56) where βτ,q and βν,q are the roll-off factors. Due to tim…
Figure 8
Figure 8. Figure 8: BER vs. SNR for UT-1 for proposed multiuser allocation and single [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: NMSE vs. SNR for UT-1 for proposed multiuser allocation and single [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: BER vs. PDR for UT-1 for proposed multiuser allocation and single [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 12
Figure 12. Figure 12: BER vs. νmax for UT-1 for proposed multiuser allocation and single￾user with embedded pilot-data Zak-OTFS frame. Fixed SNR ρq = 20 dB and PDR = 0 dB for all UTs. LSMR equalization. discrete DD channel filter. Again, the NMSE performance for both single- and multiuser …
Figure 13
Figure 13. Figure 13: NMSE vs. νmax for UT-1 for proposed multiuser allocation and single-user with embedded pilot-data Zak-OTFS frame. Fixed SNR ρq = 20 dB and PDR = 0 dB for all UTs. We demonstrated single-user performance in a multiuser Zak￾OTFS uplink system without needing to provisio…

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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. Multiuser Zak-OTFS on the Uplink with Superimposed Spread-Pilots

    cs.IT 2026-07 conditional novelty 5.5 of 10

    TF-shift multiuser Zak-OTFS with heterogeneous frames and superimposed ZC spread-pilots yields near-single-user IOR estimation and filter-dependent spectral-efficiency gains over embedded pilots.

Reference graph

Works this paper leans on

25 extracted references · 22 canonical work pages · cited by 1 Pith paper

  1. [20]

    Zak-OTFS: Pulse Shaping and the Tradeoff between Time/Bandwidth Expansion and Predictability,

    J. Jayachandran, R. K. Jaiswal, S. K. Mohammed, R. Hadani, A. Chockalingam and R. Calderbank, “Zak-OTFS: Pulse Shaping and the Tradeoff between Time/Bandwidth Expansion and Predictability,” arXiv:2405.02718, May 2024

    arXiv 2024

  2. [24]

    Zak-OTFS Implementation via Time and Frequency Windowing,

    S. Gopalam, I. B. Collings, S. V . Hanly, H. Inaltekin, S. R. B. Pillai and P. Whiting, “Zak-OTFS Implementation via Time and Frequency Windowing,” IEEE Transactions on Communications , vol. 72, no. 7, pp. 3873-3889, July 2024

    work page 2024

  3. [1]

    Framework and Overall Objectives of the Future development of IMT for 2030 and beyond,

    “Framework and Overall Objectives of the Future development of IMT for 2030 and beyond,” ITU-R M.2160-0, Nov. 2023. https://www.itu.int/rec/R-REC-M.2160/en

    work page 2023

  4. [2]

    UA V Communications in Integrated Terrestrial and Non-terrestrial Networks,

    M. Benzaghta, G. Geraci, R. Nikbakht and D. L ´opez-P´erez, “UA V Communications in Integrated Terrestrial and Non-terrestrial Networks,” GLOBECOM 2022 - 2022 IEEE Global Communications Conference, Rio de Janeiro, Brazil, 2022, pp. 3706-3711

    work page 2022

  5. [3]

    Orthogonal time frequency space modula- tion,

    R. Hadani, S. Rakib, M. Tsatsanis, A. Monk, A. J. Goldsmith, A. F. Molisch, and R. Calderbank, “Orthogonal time frequency space modula- tion,” Proc. IEEE WCNC’ 2017 , pp. 1-6, Mar. 2017

    work page 2017

  6. [4]

    Raviteja, K

    P. Raviteja, K. T. Phan and Y . Hong, ”Embedded Pilot-Aided Channel Estimation for OTFS in Delay–Doppler Channels,” IEEE Transactions on Vehicular Technology, vol. 68, no. 5, pp. 4906-4917, May 2019

    work page 2019

  7. [5]

    OTFS-Based Multiple-Access in High Doppler and Delay Spread Wireless Channels,

    V . Khammammetti and S. K. Mohammed, “OTFS-Based Multiple-Access in High Doppler and Delay Spread Wireless Channels,” IEEE Wireless Communications Letters, vol. 8, no. 2, pp. 528-531, April 2019

    work page 2019

  8. [6]

    Spectral Efficiency of OTFS Based Orthogonal Multiple Access With Rectangular Pulses,

    V . Khammammetti and S. K. Mohammed, “Spectral Efficiency of OTFS Based Orthogonal Multiple Access With Rectangular Pulses,” IEEE Transactions on Vehicular Technology, vol. 71, no. 12, pp. 12989-13006, Dec. 2022

    work page 2022

Show all 25 references
  1. [7]

    A new path division multiple access for the massive MIMO-OTFS networks,

    M. Li, S. Zhang, F. Gao, P. Fan, and O. A. Dobre, “A new path division multiple access for the massive MIMO-OTFS networks,” IEEE J. Sel. Areas Commun., vol. 39, no. 4, pp. 903–918, Apr. 2021

    2021

  2. [8]

    SC-FDMA as a Delay-Doppler Domain Modulation Technique,

    A. Farhang and M. Bayat, “SC-FDMA as a Delay-Doppler Domain Modulation Technique,” 2024 IEEE International Conference on Com- munications Workshops (ICC Workshops) , Denver, CO, USA, 2024, pp. 69-74

    2024

  3. [9]

    Angle-Delay- Doppler Domain NOMA over Massive MIMO-OTFS Networks,

    W. Shao, S. Zhang, C. Zhong, X. Lei and P. Fan, “Angle-Delay- Doppler Domain NOMA over Massive MIMO-OTFS Networks,” 2020 IEEE/CIC International Conference on Communications in China (ICCC), Chongqing, China, 2020, pp. 74-79

    2020

  4. [10]

    Performance Analysis of OTFS-based Uplink Massive MIMO with ZF Receivers,

    J. Feng, H. Q. Ngo, M. F. Flanagan and M. Matthaiou, “Performance Analysis of OTFS-based Uplink Massive MIMO with ZF Receivers,” 2021 IEEE International Conference on Communications Workshops (ICC Workshops), Montreal, QC, Canada, 2021, pp. 1-7

    2021

  5. [11]

    Time-Domain to Delay-Doppler Domain Conversion of OTFS Signals in Very High Mobility Scenarios,

    S. K. Mohammed, “Time-Domain to Delay-Doppler Domain Conversion of OTFS Signals in Very High Mobility Scenarios,” IEEE Transactions on Vehicular Technology, vol. 70, no. 6, pp. 6178-6183, June 2021

    2021

  6. [12]

    OTFS Modulation: Theory and Applications,

    S. K. Mohammed, R. Hadani and A. Chockalingam, “OTFS Modulation: Theory and Applications,” IEEE Press and Wiley, Nov. 2024

    2024

  7. [13]

    Derivation of OTFS Modulation From First Prin- ciples,

    S. K. Mohammed, “Derivation of OTFS Modulation From First Prin- ciples,” IEEE Transactions on Vehicular Technology , vol. 70, no. 8, pp. 7619-7636, Aug. 2021

    2021

  8. [14]

    S. K. Mohammed, R. Hadani, A. Chockalingam and R. Calderbank, ”OTFS—A Mathematical Foundation for Communication and Radar Sensing in the Delay-Doppler Domain,” in IEEE BITS the Informa- tion Theory Magazine, vol. 2, no. 2, pp. 36-55, 1 Nov. 2022, doi: 10.1109/MBITS.2022.3216536

    2022

  9. [15]

    S. K. Mohammed, R. Hadani, A. Chockalingam and R. Calderbank, ”OTFS - Predictability in the Delay- Doppler Domain and Its Value to Communication and Radar Sensing,” in IEEE BITS the Information Theory Magazine, doi: 10.1109/MBITS.2023.3319595. 16

  10. [16]

    Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication,

    M. Ubadah, S. K. Mohammed, R. Hadani, S. Kons, A. Chockalingam and R. Calderbank, “Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication,” submitted to IEEE, arXiv:2404.04182v2

    arXiv

  11. [17]

    Zak-OTFS with Interleaved Pilots to Extend the Region of Predictable Operation,

    J. Jayachandran, I. A. Khan, S. K. Mohammed, R. Hadani, A. Chock- alingam and R. Calderbank, “Zak-OTFS with Interleaved Pilots to Extend the Region of Predictable Operation,” IEEE Transactions on Vehicular Technology, Early access, June 2025

    2025

  12. [18]

    Multiple Preamble Detection with ZC Sequences in the Presence of Mobility and Delay Spread,

    S. R. Mattu, I. A. Khan, V . Khammammetti, B. Dabak, S. K. Mo- hammed, K. Narayanan and R. Calderbank, “Multiple Preamble Detection with ZC Sequences in the Presence of Mobility and Delay Spread,” IEEE International Symposium on Information Theory ISIT’2025 , June 2025

    2025

  13. [19]

    Guidelines for evaluation of radio transmission tech- nologies for IMT-2000,

    ITU-R M.1225, “Guidelines for evaluation of radio transmission tech- nologies for IMT-2000,”Int. Telecom. Union Radio communication, 1997

    2000

  14. [21]

    Characterization of Randomly Time-Variant Linear Chan- nels,

    P. A. Bello, “Characterization of Randomly Time-Variant Linear Chan- nels,” IEEE Trans. Comm. Syst. , vol. 11, pp. 360-393, 1963

    1963

  15. [22]

    Haykin, Digital Communication Systems , John Wiley & Sons, 2014

    S. Haykin, Digital Communication Systems , John Wiley & Sons, 2014

    2014

  16. [23]

    Optimal Zak- OTFS Receiver and Its Relation to the Radar Matched Filter,

    S. Gopalam, H. Inaltekin, I. B. Collings and S. V . Hanly, “Optimal Zak- OTFS Receiver and Its Relation to the Radar Matched Filter,” IEEE Open Journal of the Communications Society , vol. 5, pp. 4462-4482, 2024

    2024

  17. [25]

    Low-Complexity Symbol Detection and Interference Cancellation for OTFS System,

    H. Qu, G. Liu, L. Zhang, S. Wen and M. A. Imran, “Low-Complexity Symbol Detection and Interference Cancellation for OTFS System,” IEEE Transactions on Communications , vol. 69, no. 3, pp. 1524-1537, March 2021

    2021

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