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Saif has been pioneering a new modulation waveform Zak-OTFS for 6G scenarios (high mobility/ubiquitous connectivity, integrated sensing and communication and AI enabled networks)
Saif has been pioneering a new modulation waveform Zak-OTFS for 6G scenarios (high mobility/ubiquitous connectivity, integrated sensing and communication and AI enabled networks)
Zak-OTFS (OTFS 2.0) is different from MC-OTFS (Hadani et. al. 2017 paper in WCNC) and unlike MC-OTFS it provides a stationary input-output (I/O) relation in the delay-Doppler (DD) domain. The MC-OTFS I/O relation is not stationary in the DD domain due to which its reliability and throughput performance is inferior when compared to Zak-OTFS. Due to the stationarity of the Zak-OTFS I/O relation, it is robust to high delay/Doppler spread channels which makes it a natural fit for Leo satellite communication systems which experience high Doppler spread and also for large rural cells which experience high delay spread. Leo satellite communication can provide ubiquitous connectivity anytime and anywhere. Zak-OTFS waveform has the unique ability to predict channels several tens of milliseconds in advance which can be used to realize AI enabled networks. Zak-OTFS is also suited for radar as the delay Doppler shift in the location of a pulse in the DD domain can be used to directly read-off the delay and Doppler shift of the target. Zak-OTFS is therefore unique in the sense that it is good for both communication and radar use cases making it a candidate waveform for Integrated sensing and communication.
Zak-OTFS (OTFS 2.0) is different from MC-OTFS (Hadani et. al. 2017 paper in WCNC) and unlike MC-OTFS it provides a stationary input-output (I/O) relation in the delay-Doppler (DD) domain. The MC-OTFS I/O relation is not stationary in the DD domain due to which its reliability and throughput performance is inferior when compared to Zak-OTFS. Due to the stationarity of the Zak-OTFS I/O relation, it is robust to high delay/Doppler spread channels which makes it a natural fit for Leo satellite communication systems which experience high Doppler spread and also for large rural cells which experience high delay spread. Leo satellite communication can provide ubiquitous connectivity anytime and anywhere. Zak-OTFS waveform has the unique ability to predict channels several tens of milliseconds in advance which can be used to realize AI enabled networks. Zak-OTFS is also suited for radar as the delay Doppler shift in the location of a pulse in the DD domain can be used to directly read-off the delay and Doppler shift of the target. Zak-OTFS is therefore unique in the sense that it is good for both communication and radar use cases making it a candidate waveform for Integrated sensing and communication.
Zak-OTFS is a paradigm shift in the way that communication and radar system are designed. It is based on signal processing in the DD domain which is the right way to process/analyze signals since the I/O relation is stationary in the DD domain.
Zak-OTFS is a paradigm shift in the way that communication and radar system are designed. It is based on signal processing in the DD domain which is the right way to process/analyze signals since the I/O relation is stationary in the DD domain.
A good starting point are the following seminal papers on Zak-OTFS, and also the book titled, "OTFS Modulation: Theory and Applications" (see below)
A good starting point are the following seminal papers on Zak-OTFS, and also the book titled, "OTFS Modulation: Theory and Applications" (see below)
Seminal papers on Zak-OTFS:
Seminal papers on Zak-OTFS:
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 Information Theory Magazine, vol. 2, no. 2, pp. 36-55, 1 Nov. 2022, doi: 10.1109/MBITS.2022.3216536. (Link)
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, vol. 3, no. 2, pp. 7-31, June 2023, doi: 10.1109/MBITS.2023.3319595. (Link)
S. K. Mohammed, "Derivation of OTFS Modulation From First Principles," in IEEE Transactions on Vehicular Technology, vol. 70, no. 8, pp. 7619-7636, Aug. 2021, doi: 10.1109/TVT.2021.3069913.(Link)
M. Ubadah, S. K. Mohammed, R. Hadani, S. Kons, A. Chockalingam and R. Calderbank, ``Zak-OTFS for integration of sensing and communication", arXiv preprint arXiv:2404.04182, 2024 (Link)
J. Jayachandran, I. A. Khan, S. K. Mohammed, R. Hadani, A. Chockalingam, and R. Calderbank. "Zak-OTFS with Interleaved Pilots to Extend the Region of Predictable Operation." arXiv preprint arXiv:2408.09379 (2024) (Link)
S. R. Mattu, I. A. Khan, V. Khammammetti, B. Dabak, S. K. Mohammed, K. Narayanan, and R. Calderbank. "Delay-Doppler Signal Processing with Zadoff-Chu Sequences." arXiv e-prints (2024): arXiv-2412. (Link)
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 preprint arXiv:2405.02718 (2024). (Link)
Talk Slides on Zak-OTFS:
Talk Slides on Zak-OTFS:
``Driving the Next Wave of OTFS Research with OTFS 2.0 Modulation", 16 May 2023, OTFS-SIG online seminar (Slide) (Video)
``Zak-OTFS: The Waveform for NextGen Communication Systems", 13 Feb. 2025, Department of Electrical Engineering, IIT Bombay (Slide) (Video)
`Zak-OTFS: The Waveform for 6G Communication Systems", 25 Oct. 2024, Department of Electrical Engineering, IIT Guwahati (Slide)
``Filter Design in OTFS 2.0 (Zak-OTFS)", 7 Oct. 2024, Tutorial on Zak-OTFS at VTC 2024 conference (Slide)
``OTFS 2.0 for Radar", 7 Oct. 2024, Tutorial on Zak-OTFS at VTC 2024 conference (Slide)
``Zak-OTFS (OTFS 2.0) for Joint Sensing and Communication" (Slide)
``Why OTFS 2.0: How to make Communication and Radar Sensing More Predictable in 6G", 8 Dec. 2023, Tutorial at Globecom 2023 (Slide)
``Zak-OTFS: A New Paradigm for Integrated Communication and Radar Sensing", 23 Feb. 2023, Tutorial at NCC 2023 (Slide)
Book on OTFS:
Zak-OTFS has been explained in Chapter 2 in detail (mathematically rigorous) with proofs of results in the appendices. Several examples and illustrations have been provided. The
Matlab programs for some of the figures in Chapter 2 can be freely downloaded by clicking on the download tab (Matlab Dowload )
In Chapter 8, the practical discrete DD domain implementation of the Zak transform has been described.
In Chapter 10, Zak-OTFS based radar has been introduced.
Chapter 3 provides the detailed mathematical derivation of MC-OTFS and explains why it is inferior to Zak-OTFS.
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