Zak-OTFS

From HandWiki

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. https://arxiv.org/pdf/2503.23540. 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". https://the-mobile-network.com/2025/10/cohere-launches-the-pulsone-as-it-banks-on-defence-push-for-otfs-commercialisation/. 
  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. doi:10.1109/MBITS.2022.3216536. ISSN 2692-4110. Bibcode: 2022IBITM...2...36M. https://ieeexplore.ieee.org/document/9932333. 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. doi:10.1109/MBITS.2023.3319595. ISSN 2692-4110. Bibcode: 2023IBITM...3....7M. https://ieeexplore.ieee.org/document/10271295. Retrieved March 13, 2026. 
  6. ↑ 6.0 6.1 6.2 Khan, Imran Ali; Mohammed, Saif Khan; Hadani, Ronny; Chockalingam, Ananthanarayanan; Calderbank, Robert; Monk, Anton; Kons, Shachar; Rakib, Shlomo et al. (May 2025). "Waveform for Next Generation Communication Systems: Comparing Zak-OTFS with OFDM". arXiv preprint arXiv:2505.13966. https://arxiv.org/abs/2505.13966. Retrieved March 13, 2026. 
  7. ↑ "Sparse Delay Doppler Estimation for Zak-OTFS Enabled ISAC System". University of Oulu. May 2025. https://oulurepo.oulu.fi/bitstream/handle/10024/58699/nbnfioulu-202510076219.pdf?sequence=1&isAllowed=y. 
  8. ↑ 8.0 8.1 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. https://arxiv.org/abs/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. https://ieeexplore.ieee.org/document/11151885. 
  10. ↑ Morris, Iain (October 20, 2025). "Intel-backed Cohere launches Pulsone in bid to disrupt 6G". Light Reading. https://www.lightreading.com/6g/intel-backed-cohere-launches-pulsone-in-bid-to-disrupt-6g. 
  11. ↑ Raviteja, P.; Phan, Khoa T.; Hong, Yi; Viterbo, Emanuele (October 2018). "Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation". IEEE Transactions on Wireless Communications 17 (10): 6501–6515. doi:10.1109/TWC.2018.2860011. Bibcode: 2018ITWC...17.6501R. https://ecse.monash.edu/staff/eviterbo/papers/twc18Raviteja.pdf. 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. https://arxiv.org/abs/1802.00929. 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. https://arxiv.org/abs/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. doi:10.1109/LCOMM.2019.2956709. Bibcode: 2020IComL..24..330S. https://ui.adsabs.harvard.edu/abs/2020IComL..24..330S. 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. doi:10.1109/TSP.2019.2919411. https://ieeexplore.ieee.org/document/9275333. 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. doi:10.1109/LWC.2021.3125986. Bibcode: 2022IWCL...11..288T. https://ieeexplore.ieee.org/document/9606681. 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. doi:10.1109/ACCESS.2022.3204999. Bibcode: 2022IEEEA..1096026T. https://ieeexplore.ieee.org/document/9880562. 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. https://ieeexplore.ieee.org/document/10171342. Retrieved March 14, 2026. 



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