Zak-OTFS for Integration of Sensing and Communication (2404.04182v1)
Abstract: The Zak-OTFS input/output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition. The filter taps can simply be read off from the response to a single Zak-OTFS point (impulse) pulsone waveform, and the I/O relation can be reconstructed for a sampled system that operates under finite duration and bandwidth constraints. Predictability opens up the possibility of a model-free mode of operation. The time-domain realization of a Zak-OTFS point pulsone is a pulse train modulated by a tone, hence the name, pulsone. The Peak-to-Average Power Ratio (PAPR) of a pulsone is about $15$ dB, and we describe a general method for constructing a spread pulsone for which the time-domain realization has a PAPR of about 6dB. We construct the spread pulsone by applying a type of discrete spreading filter to a Zak-OTFS point pulsone. The self-ambiguity function of the point pulsone is supported on the period lattice ${\Lambda}{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${\Lambda*}$. We show that if the channel satisfies the crystallization conditions with respect to ${\Lambda*}$ then the effective DD domain filter taps can simply be read off from the cross-ambiguity between the channel response to the spread pulsone and the transmitted spread pulsone. If, in addition, the channel satisfies the crystallization conditions with respect to the period lattice ${\Lambda}{p}$, then in an OTFS frame consisting of a spread pilot pulsone and point data pulsones, after cancelling the received signal corresponding to the spread pulsone, we can recover the channel response to any data pulsone.
- R. V. Nee, and R. Prasad, “OFDM for Wireless Multimedia Communications,” Artech House Inc., 2000.
- T. Wang, J. G. Proakis, E. Masry and J. R. Zeidler, “Performance degradation of OFDM systems due to Doppler spreading,” IEEE Trans. on Wireless Commun., vol. 5, no. 6, June 2006.
- S. K. Mohammed, R. Hadani, A. Chockalingam and R. Calderbank, “OTFS - A mathematical foundation for communication and radar sensing in the delay-Doppler domain,” IEEE BITS the Information Theory Magazine, vol. 2, no. 2, pp. 36–55, 1 Nov. 2022.
- S.K. Mohammed, R. Hadani, A. Chockalingam, “OTFS Modulation: Theory and Applications,” Wiley publications and IEEE press, August 2024.
- Y. Rahmatallah and S. Mohan, “Peak-to-average power ratio reduction in OFDM systems: A survey and taxonomy,” IEEE Commun. Surveys Tuts., vol. 15, no. 4, pp. 1567–1592, 4th Quart., 2013.
- T. Thaj, E. Viterbo and Y. Hong, “General I/O relations and low-complexity universal MRC detection for all OTFS variants,” IEEE Access, vol. 10, pp. 96026-96037, 2022.
- R. Hadani, S. Rakib, M. Tsatsanis, A. Monk, A. J. Goldsmith, A. F. Molisch, and R. Calderbank, “Orthogonal time frequency space modulation,” Proc. IEEE WCNC’2017, pp. 1-6, Mar. 2017.
- R. Hadani and A. Monk, “OTFS: a new generation of modulation addressing the challenges of 5G,” arXiv:1802.02623[cs.IT], Feb. 2018.
- “Best Readings in Orthogonal Time Frequency Space (OTFS) and Delay Doppler Signal Processing,” June 2022. https://www.comsoc.org/publications/best-readings/orthogonal-timefrequency-space-otfs-and-delay-doppler-signal-processing
- G. D. Surabhi, R. M. Augustine, and A. Chockalingam, “Peak-to-average power ratio of OTFS modulation,” IEEE Commun. Lett., vol. 23, no. 6, pp. 999-1002, Jun. 2019.
- P. Wei, Y. Xiao, W. Feng, N. Ge, and M. Xiao, “Charactering the peak-to-average power ratio of OTFS signals: A large system analysis,” IEEE Trans. Wireless Commun., vol. 21, no. 6, pp. 3705-3720, Jun. 2022.
- M. N. Hossain, Y. Sugiura, T. Shimamura, and H.-G. Ryu, “DFT-spread OTFS communication system with the reductions of PAPR and nonlinear degradation,” Wireless Pers. Commun., vol. 115, no. 3, pp. 2211-2228, Aug. 2020.
- S. D. Howard, S. Suvorova and W. Moran, “Waveform libraries for radar tracking applications,” 2004 International Waveform Diversity & Design Conference, Edinburgh, UK, 2004.
- S. K. Mohammed, “Derivation of OTFS Modulation from First Principles,” IEEE Trans. on Vehicular Tech., vol. 70, no. 8, August 2021.
- ITU-R M.1225, “Guidelines for evaluation of radio transmission technologies for IMT-2000,” International Telecommunication Union Radio communication, 1997.
- P. Raviteja, K. T. .Phan, Y. Hong and E. Viterbo, “Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation,” IEEE Trans. on Wireless Comm., vol. 17, no. 10, Oct. 2018.
- L. Gaudio, M. Kobayashi, G. Caire and G. Colavolpe, “On the Effectiveness of OTFS for Joint Radar Parameter Estimation and Communication,” IEEE Trans. on Wireless Comm., vol. 19, no. 9, Sept. 2020.
- P. A. Bello, “Characterization of Randomly Time-Variant Linear Channels,” IEEE Trans. Comm. Syst., vol. 11, pp. 360-393, 1963.