References & Further Reading

References

  1. P. A. Bello, Characterization of Randomly Time-Variant Linear Channels, 1963

    The foundational paper introducing the four system functions of time-varying channels. Required reading for anyone working in fading or OTFS — the entire DD-domain vocabulary originates here.

  2. R. Hadani, S. Rakib, M. Tsatsanis, A. Monk, A. J. Goldsmith, A. F. Molisch, R. Calderbank, Orthogonal Time Frequency Space Modulation, 2017

    The paper that introduced OTFS as a waveform. Concise and readable — skip to Section III for the core modulation construction.

  3. P. Raviteja, K. T. Phan, Y. Hong, E. Viterbo, Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation, 2018

    The most-cited OTFS detection paper. Establishes the discrete DD input-output relation used throughout the literature (Eq. 14 in particular).

  4. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 5th ed., 2007

    Chapter 14 provides the standard textbook treatment of WSSUS fading, Bello's system functions, and scattering function fundamentals.

  5. D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005

    Chapter 2 gives a concise derivation of coherence time and coherence bandwidth from the Jakes spectrum; Chapter 3 extends to capacity under fading.

  6. W. Yuan, R. Schober, G. Caire, Orthogonal Time Frequency Space (OTFS) Modulation — Part III: ISAC and Potential Applications, 2024

    The third of a three-part tutorial on OTFS. Part III focuses on ISAC — why the DD-plane ambiguity function makes OTFS a natural joint sensing and communication waveform.

  7. G. Matz and F. Hlawatsch, Time-Frequency Characterization of Nonstationary Random Processes, CRC Press, 2003

    An advanced treatment of non-stationary processes and their representations; Chapter 9 extends Bello's framework beyond WSSUS to general non-stationary channels.

  8. Z. Wei, W. Yuan, S. Li, J. Yuan, G. Bharatula, R. Hadani, L. Hanzo, Orthogonal Time-Frequency Space Modulation: A Promising Next-Generation Waveform, 2020

    Readable survey of OTFS, with physical intuition for the DD domain. A good first reference for a new reader.

  9. A. Monk, R. Hadani, S. Rakib, M. Tsatsanis, OTFS — Orthogonal Time Frequency Space: A Novel Modulation Meeting 5G High Mobility and Massive MIMO Challenges, 2016. [Link]

    An early (pre-WCNC) technical report from Cohere Technologies framing OTFS in the 5G context. Informal but offers insight into the design philosophy.

  10. 3GPP, 3GPP TS 38.104: NR; Base Station (BS) radio transmission and reception, 2024

    Specifies the mobility and numerology constraints for 5G NR base stations. Referenced here for the concrete mobility requirements of 3GPP.

  11. Cohere Technologies, OTFS Modulation for Next-Generation Cellular Networks, 2019. [Link]

    Industry white paper with performance benchmarks of OTFS vs OFDM under mobility. Useful for calibration of expected system gains.

  12. G. Durisi, G. Liva, T. Koch, Toward Massive, Ultrareliable, and Low-Latency Wireless Communication with Short Packets, 2016

    Establishes the finite-blocklength framework relevant to analyzing OTFS under short frame durations. Useful context for later chapters.

Further Reading

For readers who want to go deeper into specific topics introduced in this chapter.

  • Historical context of time-varying channel characterization

    Bello, 'Characterization of Randomly Time-Variant Linear Channels' (1963); Kennedy, *Fading Dispersive Communication Channels* (1969)

    Kennedy's monograph extends Bello's formalism to cover detection-theoretic questions; it remains the most thorough treatment of the mathematical structure of doubly selective channels.

  • Scattering function estimation from measurements

    COST 2100 Channel Model Final Report (2012); 3GPP TR 38.901 (2023)

    Empirical path counts, delay spreads, and Doppler spectra for realistic deployment scenarios. Essential for realistic OTFS simulation parameters.

  • Doppler radar and ambiguity functions

    Skolnik, *Introduction to Radar Systems* (3rd ed., 2001), Ch. 3; Levanon, *Radar Signals* (2004), Ch. 3

    The DD-plane viewpoint of OTFS is essentially identical to that of pulse-Doppler radar. Levanon in particular develops the ambiguity function that will reappear in Chapter 11.

  • Mathematical underpinnings — the Heisenberg–Weyl group

    Folland, *Harmonic Analysis in Phase Space* (1989), Ch. 1–2

    The spreading function is a coefficient of the channel as an element of the Heisenberg–Weyl group algebra. Folland's treatment is the standard reference for this structure.

  • OTFS vs OFDM quantitative comparison

    Raviteja, Phan, Hong, Viterbo (2018); Anwar et al., 'Performance Analysis of OTFS-Based Random Access' (2021)

    For those who want to see the numerical tradeoffs between OTFS and OFDM before reading our derivation in Chapter 9.

ExercisesCh 2 →