Orthogonal Frequency Division Multiplexing (OFDM) has been the waveform of choice for most wireless communications systems in the past 25 years. This book addresses the “what comes next? question by presenting the recently proposed waveform known as Orthogonal Time-Frequency-Space (OTFS), which offers a better alternative for high-mobility environments.
The OTFS waveform is based on the idea that the mobile wireless channels can be effectively modelled in the delay-Doppler domain. This domain provides a sparse representation closely resembling the physical geometry of the wireless channel. The key physical parameters such as relative velocity and distance of the reflectors with respect to the receiver can be considered roughly invariant in the duration of a frame up to a few milliseconds. This enables the information symbols encoded in the delay-Doppler domain to experience a flat fading channel even when they are affected by multiple Doppler shifts present in high-mobility environments.
Delay-Doppler Communications: Principles and Applications covers the fundamental concepts and the underlying principles of delay-Doppler communications. Readers familiar with OFDM will be able to quickly understand the key differences in delay-Doppler domain waveforms that can overcome some of the challenges of high-mobility communications. For the broader readership with a basic knowledge of wireless communications principles, the book provides sufficient background to be self-contained. The book provides a general overview of future research directions and discusses a range of applications of delay-Doppler domain signal processing.
With this book, the reader will be able to:
1. Chapter 1 Introduction - p. 1 2. Chapter 2 High-mobility wireless channels - p. 13 3. Chapter 3 OFDM review and its limitations - p. 29 4. Chapter 4 Delay-Doppler modulation - p. 47 5. 4.1: System model - p. 49 6. 4.2: OTFS input–output relation with ideal waveforms - p. 54 7. 4.3: Matrix formulation for OTFS - p. 57 8. 4.4: OTFS input–output relations in vectorized form - p. 61 9. 4.5: Variants of OTFS - p. 70 10. 4.6: Summary of channel representations and input–output relations for OTFS variants - p. 85 11. 4.7: Bibliographical notes - p. 89 12. Chapter 5 Zak transform analysis for delay-Doppler communications - p. 93 13. 5.1: A brief review of the different Fourier transforms - p. 94 14. 5.2: The Zak transform - p. 96 15. 5.3: The delay-Doppler basis functions - p. 100 16. 5.4: Zak transform in delay-Doppler communications - p. 102 17. 5.5: The discrete Zak transform - p. 112 18. 5.6: DZT in delay-Doppler communications - p. 114 19. 5.7: Bibliographical notes - p. 121 20. Chapter 6 Detection methods - p. 123 21. Chapter 7 Channel estimation methods - p. 153 22. Chapter 8 MIMO and multiuser OTFS - p. 177 23. Chapter 9 Conclusions and future directions - p. 201 24. Appendix A Notation and acronyms - p. 215 25. Appendix B Some useful matrix properties - p. 219 26. Appendix C Some MATLAB® code and examples - p. 223 27. Index - p. 233
Orthogonal Frequency Division Multiplexing (OFDM) has been the waveform of choice for most wireless communications systems in the past 25 years. This book addresses the “what comes next? question by presenting the recently proposed waveform known as Orthogonal Time-Frequency-Space (OTFS), which offers a better alternative for high-mobility environments.
The OTFS waveform is based on the idea that the mobile wireless channels can be effectively modelled in the delay-Doppler domain. This domain provides a sparse representation closely resembling the physical geometry of the wireless channel. The key physical parameters such as relative velocity and distance of the reflectors with respect to the receiver can be considered roughly invariant in the duration of a frame up to a few milliseconds. This enables the information symbols encoded in the delay-Doppler domain to experience a flat fading channel even when they are affected by multiple Doppler shifts present in high-mobility environments.
Delay-Doppler Communications: Principles and Applications covers the fundamental concepts and the underlying principles of delay-Doppler communications. Readers familiar with OFDM will be able to quickly understand the key differences in delay-Doppler domain waveforms that can overcome some of the challenges of high-mobility communications. For the broader readership with a basic knowledge of wireless communications principles, the book provides sufficient background to be self-contained. The book provides a general overview of future research directions and discusses a range of applications of delay-Doppler domain signal processing.
With this book, the reader will be able to:
1. Chapter 1 Introduction - p. 1 2. Chapter 2 High-mobility wireless channels - p. 13 3. Chapter 3 OFDM review and its limitations - p. 29 4. Chapter 4 Delay-Doppler modulation - p. 47 5. 4.1: System model - p. 49 6. 4.2: OTFS input–output relation with ideal waveforms - p. 54 7. 4.3: Matrix formulation for OTFS - p. 57 8. 4.4: OTFS input–output relations in vectorized form - p. 61 9. 4.5: Variants of OTFS - p. 70 10. 4.6: Summary of channel representations and input–output relations for OTFS variants - p. 85 11. 4.7: Bibliographical notes - p. 89 12. Chapter 5 Zak transform analysis for delay-Doppler communications - p. 93 13. 5.1: A brief review of the different Fourier transforms - p. 94 14. 5.2: The Zak transform - p. 96 15. 5.3: The delay-Doppler basis functions - p. 100 16. 5.4: Zak transform in delay-Doppler communications - p. 102 17. 5.5: The discrete Zak transform - p. 112 18. 5.6: DZT in delay-Doppler communications - p. 114 19. 5.7: Bibliographical notes - p. 121 20. Chapter 6 Detection methods - p. 123 21. Chapter 7 Channel estimation methods - p. 153 22. Chapter 8 MIMO and multiuser OTFS - p. 177 23. Chapter 9 Conclusions and future directions - p. 201 24. Appendix A Notation and acronyms - p. 215 25. Appendix B Some useful matrix properties - p. 219 26. Appendix C Some MATLAB® code and examples - p. 223 27. Index - p. 233
