Zak-OTFS

Zak-OTFS is the primary implementation of OTFS, a 2D modulation technique that transforms the information carried in the Delay-Doppler coordinate system. Zak-OTFS is designed to integrate with the 3GPP stack so that scheduling and resource element allocation is unchanged.[1]

It is optimized for wireless communication environments applicable to 6G use cases, such as FR3, NTN and ISAC.[2][3] Zak-OTFS is supports different channel conditions in real time.[4][5]

Capabilities

Capacity Performance in Doubly Spread Channels

The transmit signals of Zak-OTFS are similar to OFDM systems, but OFDM operates in the time-frequency domain where high Doppler shifts and delay spreads cause inter-carrier interference (ICI) and inter-symbol interference (ISI), while Zak-OTFS operates in the delay-Doppler domain where the channel appears quasi-static even under high mobility.[6] Also, Zak-OTFS can achieve full diversity in time selective and frequency selective fading channels.[6]

Integrated Sensing and Communications (ISAC)

Zak-OTFS has natural applications in radar and sensing due to its delay-Doppler domain representation. The delay-Doppler grid directly corresponds to the range and velocity information of radar targets, making Zak-OTFS suited for integrated sensing and communications (ISAC) systems.[7] The self-ambiguity function of the Zak-OTFS waveform in the delay-Doppler domain is a lattice, which allows it to identify the range and velocity of multiple targets without dividing the available time-bandwidth region.[8]

In addition to direct extraction of range and velocity from the delay-Doppler grid, Zak-OTFS also demonstrates the ability to simultaneously communicate and sense using the same waveform, perform in high-mobility scenarios,[9] and efficiently separate multiple targets in delay-Doppler space.[8]

Research has demonstrated OTFS-based ISAC systems for automotive radar, aviation surveillance, and maritime monitoring applications.[6]

Non-Terrestrial Networks

Through its fundamental delay-Doppler domain operation, Zak-OTFS is able to process signals from multiple satellites at different delay-Doppler coordinates, achieve full-frequency reuse through delay-Doppler domain separation, and reduce GNSS-based pre-compensation.

Channel Equalization and Estimation

Zak-OTFS processing techniques have culminated in the creation of a Neural Receiver by Virginia Tech that is part of a development environment created by Cohere Technologies, Duke University, and Virginia Tech.[10]

Prior to the creation of the Neural Receiver, low complexity equalization had been proposed based on Message Passing (MP), Markov Chain Monte Carlo (MCMC), and Linear equalization methods.[11][12][13][14]Iterative Rake decision feedback equalization achieved equivalent performance to message passing with a lower complexity that was independent of the modulation size.[15][16][17][18]

References

  1. ^ Doran, K.; Holdsworth, S.; Simpkin, R. (March 2025). "Zak-OTFS for Mutually Unbiased Sensing and Communication". eess.SP. Retrieved March 13, 2026.
  2. ^ Next-generation waveform design: Experimental ZAK-OTFS evaluation across FR1, FR2, and FR3 for mobility and doppler robustness (Thesis). Rutgers University - School of Graduate Studies. 2026.
  3. ^ Dyer, Keith (2025-10-20). "Cohere launches the Pulsone as it banks on defence push for OTFS commercialisation". The Mobile Network. Retrieved 2026-03-13.
  4. ^ Mohammed, Saif Khan; Hadani, Ronny; Chockalingam, Ananthanarayanan; Calderbank, Robert (November 2022). "OTFS—A Mathematical Foundation for Communication and Radar Sensing in the Delay-Doppler Domain". IEEE BITS the Information Theory Magazine. 2 (2): 36–55. arXiv:2302.08696. Bibcode:2022IBITM...2...36M. doi:10.1109/MBITS.2022.3216536. ISSN 2692-4110. Retrieved March 13, 2026.
  5. ^ Mohammed, Saif Khan; Hadani, Ronny; Chockalingam, Ananthanarayanan; Calderbank, Robert (June 2023). "OTFS—Predictability in the Delay-Doppler Domain and Its Value to Communication and Radar Sensing". IEEE BITS the Information Theory Magazine. 3 (2): 7–31. arXiv:2302.08705. Bibcode:2023IBITM...3....7M. doi:10.1109/MBITS.2023.3319595. ISSN 2692-4110. Retrieved March 13, 2026.
  6. ^ a b c Khan, Imran Ali; Mohammed, Saif Khan; Hadani, Ronny; Chockalingam, Ananthanarayanan; Calderbank, Robert; Monk, Anton; Kons, Shachar; Rakib, Shlomo; Hebron, Yoav (May 2025). "Waveform for Next Generation Communication Systems: Comparing Zak-OTFS with OFDM". arXiv preprint arXiv:2505.13966. Retrieved March 13, 2026.
  7. ^ "Sparse Delay Doppler Estimation for Zak-OTFS Enabled ISAC System" (PDF). University of Oulu. May 2025. Retrieved March 13, 2026.
  8. ^ a b Nisar, Danish; Mohammed, Saif Khan; Hadani, Ronny; Chockalingam, Ananthanarayanan; Calderbank, Robert (March 2025). "Zak-OTFS for Identification of Linear Time-Varying Systems". arXiv preprint arXiv:2503.18900. Retrieved March 13, 2026.
  9. ^ "Pulse Shaping in High Mobility Zak-OTFS Radar Sensing". 2025 32nd International Conference on Systems, Signals and Image Processing (IWSSIP): 1–5. 2025-06-02. doi:10.1109/IWSSIP66997.2025.11151885.
  10. ^ Morris, Iain (October 20, 2025). "Intel-backed Cohere launches Pulsone in bid to disrupt 6G". Light Reading. Retrieved March 13, 2026.
  11. ^ Raviteja, P.; Phan, Khoa T.; Hong, Yi; Viterbo, Emanuele (October 2018). "Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation" (PDF). IEEE Transactions on Wireless Communications. 17 (10): 6501–6515. arXiv:1802.05242. Bibcode:2018ITWC...17.6501R. doi:10.1109/TWC.2018.2860011. S2CID 3339332. Retrieved March 13, 2026.
  12. ^ Murali, R.; Chockalingam, A. (February 2018). "On OTFS Modulation for High-Doppler Fading Channels". 2018 Information Theory and Applications Workshop (ITA): 1–10. doi:10.1109/ITA.2018.8503182. ISBN 978-1-7281-0124-8. S2CID 3631894. Retrieved March 14, 2026.
  13. ^ Xu, Wenjun; Zou, Tingting; Gao, Hui; Bie, Zhisong; Feng, Zhiyong; Ding, Zhiguo (July 2020). "Low-Complexity Linear Equalization for OTFS Systems with Rectangular Waveforms". arXiv preprint arXiv:1911.08133. Retrieved March 14, 2026.
  14. ^ Surabhi, G. D.; Chockalingam, A. (February 2020). "Low Complexity Linear Equalization for OTFS Modulation". IEEE Communications Letters. 24 (2): 330–334. Bibcode:2020IComL..24..330S. doi:10.1109/LCOMM.2019.2956709. S2CID 211208172. Retrieved March 14, 2026.
  15. ^ Thaj, Tharaj; Viterbo, Emanuele (December 2020). "Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS Systems". IEEE Transactions on Vehicular Technology. 69 (12): 15606–15622. arXiv:1903.09441. doi:10.1109/TSP.2019.2919411. S2CID 85459691. Retrieved March 14, 2026.
  16. ^ Thaj, Tharaj; Viterbo, Emanuele (February 2022). "Low-Complexity Linear Diversity-Combining Detector for MIMO-OTFS". IEEE Wireless Communications Letters. 11 (2): 288–292. arXiv:2201.11317. Bibcode:2022IWCL...11..288T. doi:10.1109/LWC.2021.3125986. Retrieved March 14, 2026.
  17. ^ Thaj, Tharaj; Viterbo, Emanuele; Hong, Yi (September 2022). "General I/O Relations and Low-Complexity Universal MRC Detection for All OTFS Variants". IEEE Access. 10: 96026–96037. Bibcode:2022IEEEA..1096026T. doi:10.1109/ACCESS.2022.3204999. Retrieved March 14, 2026.
  18. ^ Priya, Preety; Viterbo, Emanuele; Hong, Yi (February 2024). "Low Complexity MRC Detection for OTFS Receiver with Oversampling". IEEE Transactions on Wireless Communications. 23 (2): 1459–1473. doi:10.1109/TWC.2023.3289610. Retrieved March 14, 2026.
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