Orthogonal Time Frequency and Space (OTFS)

Orthogonal Time Frequency Space (OTFS) is a 2D modulation technique that transforms the information carried in the Delay-Doppler coordinate system. The information is transformed in the similar time-frequency domain as utilized by the traditional schemes of modulation such as TDMA, CDMA, and OFDM.[1] It is being used in 5G technology and being considered for 6G technology.[2]

Overview

OTFS is a modulation scheme where each transmitted symbol experiences a near-constant channel gain even in channels at high carrier frequencies (mm-wave) or with high Doppler. OTFS essentially performs modulation in the Zak domain (also known as the  delay-Doppler domain).[3] [4]

It effectively transforms the time-varying multipath channel into a 2D channel in the delay-Doppler domain. Using this transformation, along with equalization within this domain, each symbol experiences similar channel gain throughout the transmission.[5]

The modulation begins with first mapping the information symbols x[k,l] in the delay–Doppler domain to symbols X [n, m] for creating the time-domain signal s(t) which is transmitted over a wireless channel. At the receiver end, the time-domain signal r(t) is mapped to the domain of time-frequency using the Wigner transform which is the inverse of Heisenberg transform and then for symbol demodulation uses the delay–Doppler domain.[6]

The technology has been used in 5G networks[7][8] and is being considered for 6G networks.[2]

Channel Equalization and Estimation

Low complexity equalization has been proposed based on Message Passing (MP), Markov Chain Monte Carlo (MCMC), and Linear equalization methods.[5][9][10][11] The diversity of OTFS modulation has been studied in .[12][13] Channel estimation pilots are transmitted in the delay Doppler domain.[14][15] The performance of OTFS modulation in static multi-path channels has also been studied.[16]

Practical Pulse Shaping Waveforms

The performance of OTFS modulation with practical pulse shaping waveforms has been studied and it has been shown that the performance penalty due to loss of bi-orthogonality is small. [17]

Application

OTFS offers several advantages in particular environments where the dispersion is at high frequency. Environments such as these are encountered in mm-wave systems, due to both larger Doppler spreads and higher phase noise.[18] Application of OTFS waveforms for Radio Detection and Ranging (RADAR) have also been proposed recently.[19] [20]

Patents

The idea for OTFS was first patented in 2010 by Ronny Hadani and Shlomo Rakib and transferred to Cohere Technologies Inc in 2011.[21][22]

References
  1. Monk, Anton; Hadani, Ronny; Tsatsanis, Michail; Rakib, Shlomo (2016-08-09). "OTFS - Orthogonal Time Frequency Space". arXiv:1608.02993 [cs.IT].
  2. "The OTFS Interview – Implications of a 6G Candidate Technology". 6G World. 2020-12-09. Retrieved 2020-12-11.
  3. Hadani, R.; Rakib, S.; Tsatsanis, M.; Monk, A.; Goldsmith, A. J.; Molisch, A. F.; Calderbank, R. (March 2017). "Orthogonal Time Frequency Space Modulation". 2017 IEEE Wireless Communications and Networking Conference (WCNC): 1–6. arXiv:1808.00519. doi:10.1109/WCNC.2017.7925924. ISBN 978-1-5090-4183-1. S2CID 11938646.
  4. Mohammed, Saif K. (2020-07-28). "Derivation of OTFS Modulation from First Principles". arXiv:2007.14357 [cs.IT].
  5. Raviteja, P; T Phan, Khoa; Hong, Yi; Viterbo, Emanuele (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. doi:10.1109/TWC.2018.2860011. S2CID 3339332.
  6. Farhang, Arman; RezazadehReyhani, Ahmad; Doyle, Linda E.; Farhang-Boroujeny, Behrouz (June 2018). "Low Complexity Modem Structure for OFDM-Based Orthogonal Time Frequency Space Modulation". IEEE Wireless Communications Letters. 7 (3): 344–347. doi:10.1109/LWC.2017.2776942. hdl:2262/82585. ISSN 2162-2345. S2CID 9744219.
  7. Hadani, Ronny; Monk, Anton (2018-02-07). "OTFS: A New Generation of Modulation Addressing the Challenges of 5G". arXiv:1802.02623 [cs.IT].
  8. "5TONIC SUCCESSFULLY TESTS COHERE TECHNOLOGIES OTFS". Retrieved 2020-12-11.
  9. R Murali, K; Chockalingam, A (2018). "On OTFS Modulation for High-Doppler Fading Channels". Information Theory and Applications Workshop: 1–10. arXiv:1802.00929. doi:10.1109/ITA.2018.8503182. ISBN 978-1-7281-0124-8. S2CID 3631894.
  10. Xu, W; Zou, T; Gao, H; Bie, Z; Feng, Z; Ding, Z (2020-07-28). "Low Complexity Linear Equalization for OTFS Systems with Rectangular Waveforms". arXiv:1911.08133v1 [cs.IT].
  11. D. Surabhi, G; Chockalingam, A (2020). "Low Complexity Linear Equalization for OTFS Modulation". IEEE Communications Letters. 24 (2): 330–334. doi:10.1109/LCOMM.2019.2956709. S2CID 211208172.
  12. Raviteja, P; Hong, Yi; Viterbo, Emanuele; Biglieri, E (2020). "Effective Diversity of OTFS Modulation". IEEE Wireless Communications Letters. 9 (2): 249–253. doi:10.1109/LWC.2019.2951758. hdl:10230/43231. S2CID 209766153.
  13. D. Surabhi, G; M. Augustine, R; Chockalingam, A. (2019). "On the Diversity of Uncoded OTFS Modulation in Doubly-Dispersive Channels". IEEE Transactions on Wireless Communications. 18 (6): 3049–3063. arXiv:1808.07747. doi:10.1109/TWC.2019.2909205. S2CID 90260005.
  14. Raviteja, P; T Phan, Khoa; Hong, Yi; Viterbo, Emanuele (2018). "Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation". IEEE Vehicular Technology Conference (VTC-FALL): 1–5. doi:10.1109/VTCFall.2018.8690836. ISBN 978-1-5386-6358-5. S2CID 116865155.
  15. Shen, W; Dai, L; An, J; Fan, P; Heath, R. W. (2019). "Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive MIMO". IEEE Transactions on Signal Processing. 67 (16): 4204–4217. arXiv:1903.09441. Bibcode:2019ITSP...67.4204S. doi:10.1109/TSP.2019.2919411. S2CID 85459691.
  16. Raviteja, P; Hong, Yi; Viterbo, Emanuele (2019). "OTFS Performance on Static Multipath Channels". IEEE Wireless Communications Letters. 8 (3): 745–748. doi:10.1109/LWC.2018.2890643. S2CID 96446604.
  17. Raviteja, P; Hong, Yi; Viterbo, Emanuele; Biglieri, E (2019). "Practical Pulse-Shaping Waveforms for Reduced Cyclic-Prefix OTFS". IEEE Transactions on Vehicular Technology. 68 (1): 957–961. doi:10.1109/TVT.2018.2878891. S2CID 58673701.
  18. Hadani, R.; Rakib, S.; Molisch, A. F.; Ibars, C.; Monk, A.; Tsatsanis, M.; Delfeld, J.; Goldsmith, A.; Calderbank, R. (June 2017). "Orthogonal Time Frequency Space (OTFS) modulation for millimeter-wave communications systems". 2017 IEEE MTT-S International Microwave Symposium (IMS): 681–683. doi:10.1109/MWSYM.2017.8058662. ISBN 978-1-5090-6360-4. S2CID 24798053.
  19. Raviteja, P; T Phan, Khoa; Hong, Yi; Viterbo, Emanuele (2019). "Orthogonal Time Frequency Space (OTFS) Based RADAR Systems". IEEE Radar Conference (RadarConf): 1–6.
  20. Gaudio, L; Kobayashi, M; Caire, G; Colavolpe, G (2020). "On the Effectiveness of OTFS for Joint RADAR Parameter Estimation and Communication". IEEE Transactions on Wireless Communications. 19 (9): 5951–5965. doi:10.1109/TWC.2020.2998583. S2CID 221590125.
  21. "Google Patents". patents.google.com. Retrieved 2020-12-11.
  22. , "Communications method employing orthonormal time-frequency shifting and spectral shaping", issued 2011-05-26
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