ODDM Waveform
Orthogonal Delay-Doppler Division Multiplexing (ODDM)
A novel delay-Doppler domain multi-carrier (DDMC) waveform
based on the newly discovered delay-Doppler domain/plane orthogonal pulse (DDOP)
News:
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- 2025/4/22:
We've moved to a new site: https://oddm.io. This site is no longer updated and is keep online for archival purposes only. - 2025/2/3: An ODDM talk will be delivered in the IEICE Mobile Communication Workshop.
- 2025/1/6: A talk on DD waveform design will be delivered in the IEICE RCS January Conference.
- 2024/7/4: A talk on ODDM modulation will be delivered in the IEEE ICCC 2024.
- 2023/8/03: A preprint "Multi-Carrier Modulation: An Evolution from Time-Frequency Domain to Delay-Doppler Domain" is available at arXiv.
- 2023/7/20: The ICC'22 and GLOBECOM'22 presentation slides and videos are posted. Find them below.
- 2023/1/18: IEEE ComSoC SPCC TC Webinar (2022/12/13) : talk_slides (2.9MB)
- 2025/4/22:
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Publications:
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- H. Lin, J. Yuan, W. Yu, J. Wu, and L. Hanzo, “Multi-Carrier Modulation: An Evolution from Time-Frequency Domain to Delay-Doppler Domain,” 2023, arXiv:2308.01802.
- H. Lin and J. Yuan, “Orthogonal Delay-Doppler Division Multiplexing Modulation,” IEEE Trans. Wireless Commun., vol. 21, no. 12, pp. 11024-11037, Dec. 2022.
- H. Lin and J. Yuan, “On Delay-Doppler Plane Orthogonal Pulse,” IEEE GLOBECOM 2022. gc22_slides (1.5MB) gc22_video
- C. Shen, J. Yuan, and H. Lin, “Error Performance of Rectangular Pulse-shaped OTFS with Practical Receivers,” IEEE Wireless Commun. Lett., vol. 11, no. 12, pp. 2690-2694, Dec. 2022.
- H. Lin and J. Yuan, “Multicarrier Modulation on Delay-Doppler Plane: Achieving Orthogonality with Fine Resolutions,” IEEE ICC 2022. icc22_slides (1.7MB) icc22_video
Q&A: (Questions or comments are appreciated. Email to hai.lin[at]ieee.org)
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- What is the waveform of ODDM?
- An example of ODDM waveform having M multi-carrier (MC) symbols is shown below, where each MC symbol has N=4 subcarriers and pulse-shaped by the DDOP namely a pulse-train being composed of N sub-pulses. In particular, the sub-pulses are root Nyquist pulses, for example, the root raised cosine (RRC) pulses. As a result, each MC symbol has N sections in time domain, and then M symbols form an ODDM frame in a staggered manner.
- An example of ODDM waveform having M multi-carrier (MC) symbols is shown below, where each MC symbol has N=4 subcarriers and pulse-shaped by the DDOP namely a pulse-train being composed of N sub-pulses. In particular, the sub-pulses are root Nyquist pulses, for example, the root raised cosine (RRC) pulses. As a result, each MC symbol has N sections in time domain, and then M symbols form an ODDM frame in a staggered manner.
- What is the waveform of ODDM?
Demo code: Coming soon. Please check our new site at: https://oddm.io
Being a standard multi-carrier waveform, ODDM can be implemented using the methods described in Section III.D of "Multi-Carrier Modulation: An Evolution from Time-Frequency Domain to Delay-Doppler Domain" by replacing the prototype pulse with the DDOP. Additionally, an approximate implementation method for ODDM is presented in Section VII.C of the same paper and Section III.B of "Orthogonal Delay-Doppler Division Multiplexing Modulation." As explained in Remark 4, ODDM is a type of pulse-shaped OFDM waveform and can be approximately generated as a wideband filtered OFDM.