Orthogonal Time Frequency Space Explained

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 was first used for fixed wireless, and is now a contending waveform for 6G technology due to its robustness in high-speed vehicular scenarios.[2]

__TOC__

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. This OTFS signal is well localized in both time and frequency domain. The transmitted signal is in the delay-doppler domain. OTFS waveform remains invariant under the operation of the time and frequency domains. When we transmit an OTFS waveform in the delay-doppler domain, we use the Zak transform. This OTFS will satisfy Heisenberg Uncertainty principle (signal is localized in delay-doppler representation). [3] [4] [5]

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. [6]

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.[7]

The technology is being considered for 6G networks.

In terms of transmission, the transmit signals of OTFS in either discrete time sequence or continuous time waveform are the same as that of single antenna vector OFDM (VOFDM) systems (Proceedings of ICC 2000, New Orleans, and IEEE Trans. on Communications, Aug. 2001), no matter a channel is stationary or not.

Channel Equalization and Estimation

Low complexity equalization has been proposed based on Message Passing (MP), Markov Chain Monte Carlo (MCMC), and Linear equalization methods.[8] [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] Iterative Rake decision feedback equalization achieves equivalent performance to message passing with a much lower complexity that is independent of the modulation size.[16] [17] [18] [19] The performance of OTFS modulation in static multi-path channels has also been studied.[20]

Practical Pulse Shaping Waveforms

It is impossible to transmit an ideal pulse shape due to the time-frequency uncertainty principle.[21] This motivated some works for practical pulse shaped OTFS systems.[22] [23]

Pulsone

A pulsone (stands for pulse + tone) is the time realization of a quasi-periodic pulse in delay-Doppler and it serves as the carrier waveform of the OTFS modulation format. Of particular interest are pulsones in the crystalline regime (when the periods are greater than the spread of the channel). In this regime, the pulsone remains invariant under the operations of time delay and Doppler shift which results with non-fading and predictable channel interaction, rendering pulsones ideal for mobility and machine learning applications.[24] [25]

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.[26] Application of OTFS waveforms for Radio Detection and Ranging (RADAR) have also been proposed recently.[27] [28]

High mobility scenarios, such as fast-moving vehicles or dynamic wireless networks, introduce severe channel impairments due to rapid time-varying fading, Doppler shift, and time dispersion. OFDM, with its fixed orthogonal subcarriers, struggles to cope with severe channel variations. As a result, the performance of OFDM degrades significantly, leading to reduced data rates and increased error rates.[29] [30]

OTFS addresses  the challenges posed by high mobility scenarios by employing time and frequency transformations. OTFS converts the time-varying fading channel into a quasi-static channel, eliminating the need for Doppler compensation. This transformation turns the time-varying channel into stable  flat fading, improving signal reception and reducing packet loss significantly.[31] [32]

OTFS achieves better spectral efficiency due to its ability to mitigate inter-symbol interference (ISI) and inter-carrier interference (ICI), which are common in OFDM systems under high mobility.[33] [34]

OTFS also demonstrates improved energy efficiency compared to OFDM in high mobility scenarios. The reduced packet loss and improved spectral efficiency in OTFS lead to fewer retransmissions, resulting in lower power consumption and increased battery life in mobile devices.[35] [36]

Patents

The idea for OTFS was first patented in 2010 by Ronny Hadani and Shlomo Rakib and transferred to Cohere Technologies Inc in 2011.[37] In December 2022, during the inaugural 6G Evolution Summit event opening keynote, Fierce Wireless moderator referred to Hadani as “The Father of OTFS.”[38]

References

https://amsayeed.files.wordpress.com/2021/09/otfs_vs_stf_gcom21_final.pdf A. Sayeed, How is Time Frequency Space Modulation Related to Short Time Fourier Signaling?, IEEE Globecom 2021, Dec. 7-11, 2021, Madrid. arXiv:2109.06047.

https://amsayeed.files.wordpress.com/2021/09/otfs_vs_stf_gcom21_final.pdf K. Liu, T. Kadous, and A. Sayeed, Orthogonal Time-Frequency Signaling Over Doubly Dispersive Channels, IEEE Transactions on Information Theory, pp. 2583-2603, Nov. 2004.

Notes and References

  1. Monk. Anton. Hadani. Ronny. Tsatsanis. Michail. Rakib. Shlomo. 2016-08-09. OTFS - Orthogonal Time Frequency Space. cs.IT. 1608.02993.
  2. Web site: 2020-12-09. The OTFS Interview – Implications of a 6G Candidate Technology. 2020-12-11. 6G World. en-US.
  3. Book: Hadani. R.. Rakib. S.. Tsatsanis. M.. Monk. A.. Goldsmith. A. J.. Molisch. A. F.. Calderbank. R.. 2017 IEEE Wireless Communications and Networking Conference (WCNC) . Orthogonal Time Frequency Space Modulation . March 2017. 1–6. 10.1109/WCNC.2017.7925924. 1808.00519. 978-1-5090-4183-1. 11938646.
  4. Mohammed. Saif K.. Derivation of OTFS Modulation from First Principles. IEEE Transactions on Vehicular Technology. 2021. 70. 8. 7619–7636. 10.1109/TVT.2021.3069913. 2007.14357. 220831518.
  5. Book: Hong. Yi. Thaj. Tharaj. Viterbo. Emanuele. Delay-Doppler Communications: Principles and Applications. Academic Press, Elsevier. February 2022. 9780323859660.
  6. Raviteja. P. T Phan. Khoa. Hong. Yi. Viterbo. Emanuele. Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation. IEEE Transactions on Wireless Communications. 2018. 17. 10. 6501–6515. 10.1109/TWC.2018.2860011. 1802.05242. 3339332.
  7. 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. 10.1109/LWC.2017.2776942. 2262/82585. 9744219. 2162-2345. free.
  8. Book: R Murali. K. Chockalingam. A. 2018. 2018 Information Theory and Applications Workshop (ITA). On OTFS Modulation for High-Doppler Fading Channels. 2018. 1–10. 10.1109/ITA.2018.8503182. 1802.00929. 978-1-7281-0124-8. 3631894.
  9. 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. cs.IT. 1911.08133v1.
  10. D. Surabhi. G. Chockalingam. A. Low Complexity Linear Equalization for OTFS Modulation. IEEE Communications Letters. 2020. 24. 2. 330–334. 10.1109/LCOMM.2019.2956709. 211208172.
  11. Tiwari. Shashank. Das. Suvra Sekhar. Rangamgari. Vivek. December 2019. Low complexity LMMSE Receiver for OTFS. IEEE Communications Letters. 23. 12. 2205–2209. 10.1109/LCOMM.2019.2945564. 1089-7798. 1910.01350. 203641881.
  12. Raviteja. P. Hong. Yi. Viterbo. Emanuele. Biglieri. E. Effective Diversity of OTFS Modulation. IEEE Wireless Communications Letters. 2020. 9. 2. 249–253. 10.1109/LWC.2019.2951758. 10230/43231. 209766153. free.
  13. D. Surabhi. G. M. Augustine. R. Chockalingam. A.. On the Diversity of Uncoded OTFS Modulation in Doubly-Dispersive Channels. IEEE Transactions on Wireless Communications. 2019. 18. 6. 3049–3063. 10.1109/TWC.2019.2909205. 1808.07747. 90260005.
  14. Book: Raviteja. P. T Phan. Khoa. Hong. Yi. Viterbo. Emanuele. 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall). Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation. 2018. 1–5. 10.1109/VTCFall.2018.8690836. 978-1-5386-6358-5. 116865155.
  15. Shen. W. Dai. L. An. J. Fan. P. Heath. R. W.. Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive MIMO. IEEE Transactions on Signal Processing. 2019. 67. 16. 4204–4217. 10.1109/TSP.2019.2919411. 1903.09441. 2019ITSP...67.4204S. 85459691.
  16. Thaj. Tharaj . Viterbo. Emanuele. Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS Systems. IEEE Transactions on Vehicular Technology. 2020. 69. 12. 15606-15622. 10.1109/TVT.2020.3044276. 2005.02192.
  17. Thaj. Tharaj . Viterbo. Emanuele. Low-Complexity Linear Diversity-Combining Detector for MIMO-OTFS. IEEE Wireless Communications Letters. 2022. 11. 2. 288-292. 10.1109/LWC.2021.3125986. 2201.11317.
  18. Thaj. Tharaj . Viterbo. Emanuele. Hong. Yi. General I/O Relations and Low-Complexity Universal MRC Detection for All OTFS Variants. IEEE Access. 2022. 2. 96026-96037. 10.1109/ACCESS.2022.3204999. free.
  19. Priya. Preety. Viterbo. Emanuele. Hong. Yi. Low Complexity MRC Detection for OTFS Receiver with Oversampling. IEEE Transactions on Wireless Communications. 2023. 10.1109/TWC.2023.3289610.
  20. Raviteja. P. Hong. Yi. Viterbo. Emanuele. OTFS Performance on Static Multipath Channels. IEEE Wireless Communications Letters. 2019. 8. 3. 745–748. 10.1109/LWC.2018.2890643. 96446604.
  21. Kozek. W.. Molisch. A.F.. 1998. Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels. IEEE Journal on Selected Areas in Communications. 16. 8. 1579–1589. 10.1109/49.730463. 0733-8716.
  22. Raviteja. P.. Hong. Yi. Viterbo. Emanuele. Biglieri. Ezio. January 2019. Practical Pulse-Shaping Waveforms for Reduced-Cyclic-Prefix OTFS. IEEE Transactions on Vehicular Technology. 68. 1. 957–961. 10.1109/tvt.2018.2878891. 58673701. 0018-9545.
  23. Tiwari. S.. Das. S.S.. February 2020. Circularly pulse‐shaped orthogonal time frequency space modulation. Electronics Letters. 56. 3. 157–160. 10.1049/el.2019.2503. 1350-911X. 1910.10457. 2020ElL....56..157T. 204837937.
  24. Calderbank . Robert . October 2022 . Learning in the Delay-Doppler Domain . Duke.edu.
  25. Web site: Air Force Center of Excellence . 2022-10-15 . Duke Rhodes iiD . en-US.
  26. Book: Hadani. R.. Rakib. S.. Molisch. A. F.. Ibars. C.. Monk. A.. Tsatsanis. M.. Delfeld. J.. Goldsmith. A.. Calderbank. R.. 2017 IEEE MTT-S International Microwave Symposium (IMS) . Orthogonal Time Frequency Space (OTFS) modulation for millimeter-wave communications systems . 24798053. June 2017. 681–683. 10.1109/MWSYM.2017.8058662. 978-1-5090-6360-4.
  27. Raviteja. P. T Phan. Khoa. Hong. Yi. Viterbo. Emanuele. Orthogonal Time Frequency Space (OTFS) Based RADAR Systems. IEEE Radar Conference . 2019. 1–6.
  28. Gaudio. L. Kobayashi. M. Caire. G. Giuseppe Caire. Colavolpe. G. On the Effectiveness of OTFS for Joint RADAR Parameter Estimation and Communication. IEEE Transactions on Wireless Communications. 2020. 19. 9. 5951–5965. 10.1109/TWC.2020.2998583. 221590125.
  29. Lidström . T. . Svensson . T. . Sternad . M. . May 2005 . Impact of velocity-dependent Doppler spread on OFDM-systems . IEEE Transactions on Communications . 53 . 5 . 861–870.
  30. Jaaidi . I. . Anpalagan . A. . Twan . R. S. L. . September 2014 . Effect of Doppler shift on the performance of OFDM system . 2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication . 604–609.
  31. Younis . A. . Zayed . A. . Juntti . M. . March 2017 . Orthogonal time frequency space modulation for high mobility wireless communications . 2017 IEEE Wireless Communications and Networking Conference Workshops (WCNCW) . 1–6.
  32. Valenzuela . R. . Galvan Tejada . G. D. . July 2017 . Orthogonal time frequency space modulation: A nonlinear modulation scheme using pseudounitary space-time modulation . IEEE Transactions on Communications . 65 . 7 . 3077–3087.
  33. Younis . A. . Eldar . Y. . Hadani . R. . Eldar . H. . January 2017 . Orthogonal time frequency space modulation for dispersive channels . IEEE Transactions on Information Theory . 63 . 1 . 212–234.
  34. Ribeiro . N. M. . Dinis . R. . Silva . J.C. . February 2019 . Orthogonal time-frequency space for MIMO systems with high mobility . IEEE Transactions on Communications . 67 . 2 . 1536–1545.
  35. Sun . C. . Jiang . H. . Zhang . L. . February 2020 . Energy efficient resource allocation for OTFS-based massive IoT systems . IEEE Internet of Things Journal . 7 . 2 . 475–485.
  36. T. Datta, S. Mandal, A. A. Datta . December 2019 . Energy efficiency and fairness enhancement using cyclic convolutional codes in OTFS . 2019 3rd International Conference on Microwave and Photonics (ICMAP) . 1–4.
  37. Communications method employing orthonormal time-frequency shifting and spectral shaping. 2011-05-26. US. 8547988. Hadani. Ronny. Rakib. Selim Shlomo.
  38. Web site: 2022-12-12 . 6G Evolution Summit Keynote . 2023-02-10 . onlinexperiences.com.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Orthogonal Time Frequency Space".

Except where otherwise indicated, Everything.Explained.Today is © Copyright 2009-2024, A B Cryer, All Rights Reserved. Cookie policy.