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arxiv: 2512.20332 · v4 · pith:GNCKOCY7new · submitted 2025-12-23 · 💻 cs.IT · eess.SP· math.IT

RIS-Empowered OTFS Modulation With Faster-than-Nyquist Signaling in High-Mobility Wireless Communications

Chaorong Zhang , Benjamin K. Ng , Hui Xu , Chan-Tong Lam , Halim Yanikomeroglu This is my paper

Pith reviewed 2026-05-21 15:46 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords RISOTFSFTN signalinghigh-mobility communicationsdelay-Doppler domainspectral efficiencypassive beamformingframe error rate
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The pith

Integrating reconfigurable intelligent surfaces into OTFS modulation with faster-than-Nyquist signaling improves reliability and spectral efficiency in high-mobility wireless systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a RIS-OTFS-FTN scheme that combines reconfigurable intelligent surfaces, orthogonal time frequency space modulation, and faster-than-Nyquist signaling to handle severe Doppler spread and multi-path delay in high-mobility environments. It first derives a unified input-output model in the delay-Doppler domain that incorporates RIS passive beamforming, the inter-symbol interference from tighter symbol packing, and the underlying channel effects. From this model the authors derive closed-form expressions for frame error rate, spectral efficiency, and peak-to-average power ratio, then introduce a quantized phase selection method to maximize effective channel gain. A sympathetic reader would care because the work points to a concrete way to raise both link reliability and data throughput when conventional modulation schemes degrade under rapid movement and limited spectrum.

Core claim

The authors establish a unified delay-Doppler domain input-output relationship that jointly accounts for RIS passive beamforming, FTN-induced inter-symbol interference, and DD-domain channel characteristics, then use it to obtain analytical performance expressions and a practical quantized RIS phase adjustment strategy; Monte Carlo simulations under the extended vehicular A channel confirm that the resulting RIS-OTFS-FTN scheme yields measurable gains in frame error rate and spectral efficiency compared with baselines.

What carries the argument

The unified DD-domain input-output relationship that jointly accounts for RIS passive beamforming, FTN-induced inter-symbol interference, and DD-domain channel characteristics.

If this is right

  • Analytical expressions for frame error rate become available once the unified DD-domain model is in place.
  • Spectral efficiency rises with the intentional symbol packing of FTN while the RIS compensates for the added interference.
  • A quantized phase selection procedure maximizes the effective channel gain without requiring continuous phase control.
  • Trade-offs appear among spectral efficiency, PAPR, input back-off, and error performance that can be explored through the same model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same modeling approach could be tested in other high-mobility settings such as high-speed rail or low-Earth-orbit satellite links to see whether the gains persist.
  • Because the phase adjustment uses only a finite set of values, the scheme may be implementable on low-cost RIS hardware with limited control resolution.
  • The derived expressions for PAPR and IBO suggest that power-amplifier back-off requirements can be traded directly against the chosen FTN packing factor.

Load-bearing premise

The unified DD-domain input-output relationship accurately captures RIS beamforming, FTN interference, and channel effects without significant unmodeled distortions that would change the derived performance expressions.

What would settle it

If Monte Carlo simulations under the standardized extended vehicular A channel model show no improvement in frame error rate or spectral efficiency when the proposed RIS phase adjustment and FTN packing are added to plain OTFS, the claimed performance gains would not hold.

Figures

Figures reproduced from arXiv: 2512.20332 by Benjamin K. Ng, Chan-Tong Lam, Chaorong Zhang, Halim Yanikomeroglu, Hui Xu.

Figure 1
Figure 1. Figure 1: System model of the RIS-OTFS-FTN schemes. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Signal processing of the RIS-OTFS-FTN scheme. B. Channel Models According to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between RIS-OTFS schemes with and without FTN in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: PAPR (a & b) and CCDF (c & d) of the OTFS-FTN and OTFS schemes with [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: IBO of the RIS-OTFS-FTN and OTFS-FTN schemes with α = 0.8 and 1, M = 32 and N = 32. exists no direct vehicle-user channel, with the RIS positioned equidistantly from both the vehicle and the user [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: BER of the MMSE detector-assisted RIS-OTFS-FTN scheme with various comparing cases: (a) Q = 4 and α = 0.7, 0.8, 0.9; (b) α = 0.8 and Q = 8, 16, 32; (c) α = 0.8, Q = 8, 16, 32 in optimal phase adjustment (Opt.) and the random phase one (Ran.). rise by enhancing the effective channel gain, thereby enabling reduced transmit power while meeting the same quality-of￾service constraints. Therefore, despite the mi… view at source ↗
Figure 8
Figure 8. Figure 8: BER of the RIS-OTFS-FTN scheme with/without RIS, FTN, MP detector, as well different M and N. velocity. For the configuration with M = N = 16 and Q = 16, the system exhibits robust performance up to approximately 1, 700 km/h. This indicates that for standard high-speed vehicular or railway scenarios (< 500 km/h), the proposed scheme operates well within its safety margin with negligible Doppler-induced deg… view at source ↗
Figure 9
Figure 9. Figure 9: Spectral efficiency of the RIS-OTFS-FTN scheme with different cases in (a) α = 1, 0.9, 0.8, 0.7, Q = 30, 20, 10, 0, M = 16, and N = 16; (b) α = 1, 0.9, 0.8, 0.7, Q = 10, M = 8, 16, 32, and N = 8, 16, 32. (b) (a) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: BER of the RIS-OTFS-FTN scheme with imperfect CSI in different δ 2 e2 and varing number of quantized adjusted phases B. Velocity (km/h) 50 80 100 300 500 800 1000 1200 1500 1800 2000 2500 3000 4000 5000 6000 M=N=16, Q=16 M=N=32, Q=16 M=N=32, Q=32 10 -3.0 10 -2.5 10 -2.0 10 -1.5 10 -1.0 10 -0.5 B E R [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Operating limits analysis of the RIS-FTN-OTFS: BER versus User Velocity (km/h) at SNR = 20 dB [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

High-mobility wireless communication systems suffer from severe Doppler spread and multi-path delay, which degrade the reliability and spectral efficiency of conventional modulation schemes. Orthogonal time frequency space (OTFS) modulation offers strong robustness in such environments by representing symbols in the delay-Doppler (DD) domain, while faster-than-Nyquist (FTN) signaling can further enhance spectral efficiency through intentional symbol packing. Meanwhile, reconfigurable intelligent surfaces (RIS) provide a promising means to improve link quality via passive beamforming. Motivated by these advantages, we propose a novel RIS-empowered OTFS modulation with FTN signaling (RIS-OTFS-FTN) scheme. First, we establish a unified DD-domain input-output relationship that jointly accounts for RIS passive beamforming, FTN-induced inter-symbol interference, and DD-domain channel characteristics. Based on this model, we provide comprehensive analytical performance for the frame error rate, spectral efficiency, and peak-to-average power ratio (PAPR), etc. Furthermore, a practical RIS phase adjustment strategy with quantized phase selection is designed to maximize the effective channel gain. Extensive Monte Carlo simulations under a standardized extended vehicular A (EVA) channel model validate the theoretical results and provide key insights into the trade-offs among spectral efficiency, PAPR, input back-off (IBO), and error performance, with some interesting insights.The proposed RIS-OTFS-FTN scheme demonstrates notable performance gains in both reliability and spectral efficiency, offering a viable solution for future high-mobility and spectrum-constrained wireless systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a RIS-empowered OTFS modulation scheme with faster-than-Nyquist (FTN) signaling for high-mobility wireless communications. It derives a unified delay-Doppler (DD) domain input-output relationship that incorporates RIS passive beamforming, FTN-induced inter-symbol interference, and DD-domain channel effects. Closed-form analytical expressions are provided for frame error rate (FER), spectral efficiency (SE), and peak-to-average power ratio (PAPR). A quantized RIS phase selection strategy is designed to maximize effective channel gain. Monte Carlo simulations under the standardized extended vehicular A (EVA) channel model are used to validate the analysis and illustrate trade-offs among SE, PAPR, input back-off, and error performance.

Significance. If the unified DD-domain model is free of unexamined linearizations or truncations in the cross-terms, the work would usefully combine three established techniques (OTFS Doppler resilience, FTN spectral-efficiency gain, and RIS passive beamforming) and supply both analytical performance metrics and practical design guidelines for spectrum-constrained high-mobility links. The explicit treatment of PAPR/IBO trade-offs and the quantized phase strategy add engineering relevance.

major comments (2)
  1. [§III-B, Eq. (8)–(11)] §III-B, Eq. (8)–(11): the unified DD-domain input-output relation is presented as jointly embedding the RIS phase matrix, the non-orthogonal FTN pulse-shaping matrix, and the time-varying EVA Doppler shifts. It is not shown whether higher-order Doppler–FTN coupling terms are retained exactly or linearized/truncated; any such approximation would directly affect the accuracy of the subsequent closed-form FER and SE expressions in §IV.
  2. [§IV-A, Eq. (15)] §IV-A, Eq. (15): the frame-error-rate expression is derived from the effective channel gain after RIS phase selection. If the phase-selection procedure (described as “quantized phase selection”) is performed after observing the instantaneous channel rather than being a fixed, non-adaptive rule, the reported FER curves become optimistic relative to a practical implementation that must choose phases without future channel knowledge.
minor comments (2)
  1. Notation for the FTN acceleration factor α and the RIS phase quantization levels is introduced without a consolidated table; a single reference table would improve readability.
  2. Figure 4 (PAPR vs. IBO) uses the same legend style as Figure 3; distinguishing line styles or markers would reduce visual ambiguity when printed in black-and-white.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, providing clarifications on the model derivation and performance analysis. Revisions have been made to improve clarity and add relevant discussion where appropriate.

read point-by-point responses

  1. Referee: [§III-B, Eq. (8)–(11)] §III-B, Eq. (8)–(11): the unified DD-domain input-output relation is presented as jointly embedding the RIS phase matrix, the non-orthogonal FTN pulse-shaping matrix, and the time-varying EVA Doppler shifts. It is not shown whether higher-order Doppler–FTN coupling terms are retained exactly or linearized/truncated; any such approximation would directly affect the accuracy of the subsequent closed-form FER and SE expressions in §IV.

    Authors: The unified DD-domain input-output relation in Section III-B is obtained by direct discretization of the time-domain received signal expression that incorporates the RIS phase matrix, the FTN pulse-shaping matrix, and the time-varying channel matrix. All cross terms arising from Doppler shifts interacting with the non-orthogonal FTN pulses are retained exactly in the resulting effective channel matrix; no linearization or truncation is performed. This exact formulation underpins the closed-form FER and SE expressions in Section IV. We have added an explicit remark in the revised Section III-B confirming that Eqs. (8)–(11) contain no approximations. revision: yes

  2. Referee: [§IV-A, Eq. (15)] §IV-A, Eq. (15): the frame-error-rate expression is derived from the effective channel gain after RIS phase selection. If the phase-selection procedure (described as “quantized phase selection”) is performed after observing the instantaneous channel rather than being a fixed, non-adaptive rule, the reported FER curves become optimistic relative to a practical implementation that must choose phases without future channel knowledge.

    Authors: The quantized phase selection is performed adaptively using instantaneous channel state information to maximize the effective gain, consistent with standard RIS beamforming assumptions. The FER expression in Eq. (15) is therefore derived under perfect instantaneous CSI. We acknowledge that this yields an optimistic bound relative to scenarios with CSI delay or estimation error. In the revised manuscript we have added a new discussion subsection and corresponding EVA-channel simulations that quantify the performance loss under delayed CSI, thereby clarifying the gap between the analytical curves and practical non-causal implementations. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained with independent modeling and simulation validation

full rationale

The paper establishes a new unified DD-domain input-output relationship jointly incorporating RIS passive beamforming, FTN-induced ISI, and DD-domain channel effects under the EVA model. From this model it derives closed-form expressions for frame error rate, spectral efficiency, and PAPR, then proposes a quantized phase selection strategy. These steps are followed by Monte Carlo simulations that validate the analytics. No quoted equations or self-citations reduce any load-bearing claim to a fitted parameter, prior ansatz, or self-referential definition; the central results rest on the newly stated model plus external channel statistics rather than circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The scheme rests on standard wireless channel assumptions and RIS capabilities; no explicit free parameters or invented entities are named in the abstract, but the unified model implicitly assumes accurate joint representation of beamforming, ISI, and DD effects.

axioms (2)
  • domain assumption The delay-Doppler domain accurately captures high-mobility channel effects including Doppler spread and multi-path delay
    Invoked when establishing the unified input-output relationship
  • domain assumption RIS passive beamforming can be jointly modeled with FTN-induced ISI in the DD domain
    Central to the proposed unified model

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Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

  1. [1]

    Q. Deng, Y . Ge, and Z. Ding, ”A unifying view of OTFS and its many variants,”IEEE Commun. Surveys Tuts., vol. 27, no. 6, pp. 3561–3586, Dec. 2025

    work page 2025

  2. [2]

    Fractional delay and Doppler estimation for OTFS systems with Doppler squint effect,

    M. Zhanget al., “Fractional delay and Doppler estimation for OTFS systems with Doppler squint effect,” inProc. IEEE Wireless Commun. Netw. Conf. (WCNC), Milan, Italy, 2025, pp. 1–6

    work page 2025

  3. [3]

    A survey on orthogonal time frequency space modulation,

    M. Aldababsa,et al., “A survey on orthogonal time frequency space modulation,”IEEE Open J. Commun. Soc., vol. 5, pp. 4483–4518, 2024

    work page 2024

  4. [4]

    OTFS vs. OFDM in the pres- ence of sparsity: A fair comparison,

    L. Gaudio, G. Colavolpe, and G. Caire, “OTFS vs. OFDM in the pres- ence of sparsity: A fair comparison,”IEEE Trans. Wireless Commun., vol. 21, no. 6, pp. 4410–4423, Jun. 2022

    work page 2022

  5. [5]

    Z. Zhou, L. Liu, J. Xu, and R. Calderbank, ”Learning to equalize OTFS,” IEEE Trans. Wireless Commun., vol. 21, no. 9, pp. 7723–7736, Sep. 2022

    work page 2022

  6. [6]

    Orthogonal time frequency space modulation,

    R. Hadaniet al., “Orthogonal time frequency space modulation,” in Proc. IEEE Wireless Commun. Netw. Conf. (WCNC), San Francisco, CA, USA, 2017, pp. 1–6

    work page 2017

  7. [7]

    New delay Doppler communication paradigm in 6G era: A survey of orthogonal time frequency space (OTFS),

    W. Yuanet al., “New delay Doppler communication paradigm in 6G era: A survey of orthogonal time frequency space (OTFS),”China Commun., vol. 20, no. 6, pp. 1–25, Jun. 2023

    work page 2023

  8. [8]

    Active terminal identification, channel estimation, and signal detection for grant-free NOMA-OTFS in LEO satellite Internet-of-Things,

    X. Zhouet al., “Active terminal identification, channel estimation, and signal detection for grant-free NOMA-OTFS in LEO satellite Internet-of-Things,”IEEE Trans. Wireless Commun., vol. 22, no. 4, pp. 2847–2866, Apr. 2023

    work page 2023

  9. [9]

    Faster-than-Nyquist signaling for MIMO communications,

    Z. Zhang, M. Yuksel, and H. Yanikomeroglu, “Faster-than-Nyquist signaling for MIMO communications,”IEEE Trans. Wireless Commun., vol. 22, no. 4, pp. 2379–2392, Apr. 2023

    work page 2023

  10. [10]

    Exploiting faster-than-Nyquist signaling,

    A. D. Liveris and C. N. Georghiades, “Exploiting faster-than-Nyquist signaling,”IEEE Trans. Commun., vol. 51, no. 9, pp. 1502–1511, Sep. 2003

    work page 2003

  11. [11]

    FTN-assisted SWIPT-NOMA design for IoT wireless networks: A paradigm in wireless efficiency and energy utilization,

    H. Xu, C. Zhang, Q. Wu, B. K. Ng, C.-T. Lam, and H. Yanikomeroglu, “FTN-assisted SWIPT-NOMA design for IoT wireless networks: A paradigm in wireless efficiency and energy utilization,”IEEE Sensors J., vol. 25, no. 4, pp. 7431–7444, Feb. 2025

    work page 2025

  12. [12]

    Low-complexity detection for faster-than-Nyquist sig- naling based on probabilistic data association,

    M. Kulhandjian, E. Bedeer, H. Kulhandjian, C. D’Amours, and H. Yanikomeroglu, “Low-complexity detection for faster-than-Nyquist sig- naling based on probabilistic data association,”IEEE Commun. Lett., vol. 24, no. 4, pp. 762–766, Apr. 2020

    work page 2020

  13. [13]

    Bacchielli, L

    T. Bacchielli, L. Pucci, E. Paolini, and A. Giorgetti, ”A low-complexity detector for OTFS-based sensing,”IEEE Trans. Wireless Commun., vol. 24, no. 6, pp. 5227–5240, Jun. 2025

    work page 2025

  14. [14]

    Zhang, M

    Z. Zhang, M. Yuksel, G. M. Guvensen, and H. Yanikomeroglu, ”Ca- pacity and IAPR analysis for MIMO faster-than-Nyquist signaling with high acceleration rate,”IEEE Trans. Wireless Commun., vol. 25, pp. 1451–1466, 2026

    work page 2026

  15. [15]

    FTN-based non- orthogonal signal detection technique with machine learning in quasi- static multipath channel,

    M.-S. Baek, E.-S. Jung, Y . S. Park, and Y .-T. Lee, “FTN-based non- orthogonal signal detection technique with machine learning in quasi- static multipath channel,”IEEE Trans. Broadcast., vol. 70, no. 1, pp. 78–86, Mar. 2024

    work page 2024

  16. [16]

    Yang,et al., ”Frequency diverse array-enabled RIS-aided integrated sensing and communication,”IEEE Trans

    H. Yang,et al., ”Frequency diverse array-enabled RIS-aided integrated sensing and communication,”IEEE Trans. Wireless Commun., vol. 24, no. 9, pp. 7546–7562, Sep. 2025

    work page 2025

  17. [17]

    Pan et al., ”An overview of signal processing techniques for RIS/IRS- aided wireless systems,”IEEE J

    C. Pan et al., ”An overview of signal processing techniques for RIS/IRS- aided wireless systems,”IEEE J. Sel. Topics Signal Process., vol. 16, no. 5, pp. 883-917, Aug. 2022

    work page 2022

  18. [18]

    Wang, C.-T

    K. Wang, C.-T. Lam, B. K. Ng, and Y . Liu, ”On the impact of phase errors in phase-dependent amplitudes of near-field RISs,”IEEE Trans. Veh. Technol., Dec., 2025, early access

    work page 2025

  19. [19]

    RIS-assisted differential transmitted spatial modulation design,

    C. Zhang, Y . Liu, B. K. Ng, and C.-T. Lam, “RIS-assisted differential transmitted spatial modulation design,”Signal Process., vol. 230, p. 109767, 2025

    work page 2025

  20. [20]

    How phase errors influence phase-dependent amplitudes in near-field RISs?,

    K. Wang, R. Chen, C.-T. Lam, B. K. Ng, and C. Zhang, “How phase errors influence phase-dependent amplitudes in near-field RISs?,” in Proc. IEEE V eh. Technol. Conf. (VTC2024-Fall), Washington, DC, USA, 2024, pp. 1–6

    work page 2024

  21. [21]

    RIS-aided OTFS modulation in high-Doppler channels,

    G. Harshavardhan, V . S. Bhat, and A. Chockalingam, “RIS-aided OTFS modulation in high-Doppler channels,” inProc. IEEE 33rd Annu. Int. Symp. Pers. Indoor Mobile Radio Commun. (PIMRC), Kyoto, Japan, 2022, pp. 409–415

    work page 2022

  22. [22]

    IRS-assisted OTFS system: Design and analysis,

    A. Thomas, K. Deka, S. Sharma, and N. Rajamohan, “IRS-assisted OTFS system: Design and analysis,”IEEE Trans. V eh. Technol., vol. 72, no. 3, pp. 3345–3358, Mar. 2023

    work page 2023

  23. [23]

    Reconfigurable- intelligent-surface-aided OTFS: Transmission scheme and channel es- timation,

    Z. Li, W. Yuan, B. Li, J. Wu, C. You, and F. Meng, “Reconfigurable- intelligent-surface-aided OTFS: Transmission scheme and channel es- timation,”IEEE Internet Things J., vol. 10, no. 22, pp. 19518–19532, Nov. 2023

    work page 2023

  24. [24]

    IRS-assisted high mobility communications using OTFS modulation,

    A. S. Bora, K. T. Phan, and Y . Hong, “IRS-assisted high mobility communications using OTFS modulation,”IEEE Wireless Commun. Lett., vol. 12, no. 2, pp. 376–380, Feb. 2023

    work page 2023

  25. [25]

    OTFS-aided RIS-assisted SAGIN systems outperform their OFDM counterparts in doubly selective high-Doppler scenarios,

    C. Xuet al., “OTFS-aided RIS-assisted SAGIN systems outperform their OFDM counterparts in doubly selective high-Doppler scenarios,”IEEE Internet Things J., vol. 10, no. 1, pp. 682–703, Jan. 2023

    work page 2023

  26. [26]

    RIS-aided OTFS with index modu- lation,

    V . S. Bhat and A. Chockalingam, “RIS-aided OTFS with index modu- lation,” inProc. IEEE Wireless Commun. Netw. Conf. (WCNC), Dubai, United Arab Emirates, 2024, pp. 1–6

    work page 2024

  27. [27]

    Precoded faster-than- Nyquist signaling for OTFS,

    Z. Hong, S. Sugiura, C. Xu, and L. Hanzo, “Precoded faster-than- Nyquist signaling for OTFS,”IEEE Wireless Commun. Lett., vol. 14, no. 1, pp. 173–177, Jan. 2025

    work page 2025

  28. [28]

    M. Tong, X. Huang, J. Andrew Zhang, and L. Hanzo, ”Adaptive FTN signaling over rapidly-fading channels,”IEEE Trans. Commun., vol. 73, no. 9, pp. 7166–7178, Sep. 2025

    work page 2025

  29. [29]

    X. Wang, S. Gong, W. Shen, C. Xing, and J. A. Zhang, ”Multi-carrier faster-than-Nyquist signaling for OTFS systems,”IEEE Trans. Veh. Technol., vol. 74, no. 12, pp. 19339–19354, Dec. 2025

    work page 2025

  30. [30]

    Adaptive damping log-domain message-passing algorithm for FTN-OTFS in V2X communications,

    H. Xu, C. Zhang, Q. Wu, B. K. Ng, and C.-T. Lam, “Adaptive damping log-domain message-passing algorithm for FTN-OTFS in V2X communications,”Sensors, vol. 25, no. 12, p. 3692, Jun. 2025

    work page 2025

  31. [31]

    Hong and S

    Z. Hong and S. Sugiura, ”Reduced-complexity MIMO faster-than- Nyquist signaling transceiver for OTFS modulation,”IEEE Open J. Commun. Soc., vol. 6, pp. 6126–6141, 2025

    work page 2025

  32. [32]

    Low complexity iterative rake decision feedback equalizer for zero-padded OTFS systems,

    T. Thaj and E. Viterbo, “Low complexity iterative rake decision feedback equalizer for zero-padded OTFS systems,”IEEE Trans. V eh. Technol., vol. 69, no. 12, pp. 15606–15622, Dec. 2020

    work page 2020

  33. [33]

    M. K. Simon and M.-S. Alouini,Digital Communication over Fading Channels, 2nd ed. Wiley, 2005

    work page 2005

  34. [34]

    J. G. Proakis and M. Salehi,Digital Communications, 5th ed. McGraw- Hill, 2008

    work page 2008

  35. [35]

    Peak-to-average power ratio of OTFS modulation,

    G. D. Surabhi, R. M. Augustine, and A. Chockalingam, “Peak-to-average power ratio of OTFS modulation,”IEEE Commun. Lett., vol. 23, no. 6, pp. 999–1002, Jun. 2019

    work page 2019

  36. [36]

    Evolved Universal Terrestrial Radio Access (E- UTRA); User Equipment (UE) radio transmission and reception,

    3GPP TS 36.101, “Evolved Universal Terrestrial Radio Access (E- UTRA); User Equipment (UE) radio transmission and reception,”3GPP, 2023

    work page 2023