Otfs Modulation

Theory and Applications
1. Auflage 2024
ISBN: 978-1-119-98418-4
Verlag: Wiley

Buch, Englisch, 448 Seiten, Format (B × H): 180 mm x 258 mm, Gewicht: 1125 g

Grasp the future of wireless communication with this groundbreaking introduction
Research and development are already underway on the sixth generation (6G) of wireless communication technology. The new requirements of 6G that arise from challenging new use cases render physical layer waveforms such as CDMA and OFDM inadequate. The OTFS waveform answers these new requirements, and recent research suggests it will play a decisive role in the future of wireless communication.
OTFS Modulation: Theory and Applications provides the first ever foundational textbook that introduces this growing, state-of-the-art, field of research from first principles. Beginning with a thorough discussion of the fundamental principles of OTFS, both physical and theoretical, it rigorously situates OTFS modulation in a mathematical framework analogous to more familiar waveforms. The result is a groundbreaking contribution to communication theory and a must-have volume for wireless communication researchers.
Readers will find: - An expert author team including the inventor of OTFS modulation
- Detailed discussion of topics including the Zak theory of linear time-varying systems, delay-Doppler communication and radar sensing, machine learning, and many more
- MATLAB™ code for OTFS transceiver implementation

OTFS Modulation: Theory and Applications is ideal for researchers, engineers, graduate and advanced undergraduate students, and standardization professionals working with wireless communication, signal processing, and radar sensing.

Autoren/Hrsg.

Mohammed, Saif Khan

Hadani, Ronny

Chockalingam, Ananthanarayanan

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Drahtlostechnologie
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung

Inhaltsverzeichnis

Preface xv

Acknowledgements xvii

Acronyms xxi

1 Introduction 1

1.1 Cellular Mobile Evolution 2

1.1.1 Moore’s Law Drives Rate Increase 4

1.2 Multipath Fading Channels 5

1.2.1 Frequency Domain Characterization 6

1.2.2 Time Domain Characterization 7

1.2.3 Impact of High Dopplers 9

1.2.4 Delay-Doppler Domain Characterization 12

1.2.4.1 Urban Multi-lane Scenario - An Example 14

1.3 Communication Waveforms for Doubly Selective Channels 14

1.3.1 OTFS – A Modulation Waveform for Doubly Selective Channels 16

1.3.2 OTFS Realization – Two Approaches 16

1.4 Waveforms for Radar Sensing 17

1.4.1 OTFS for Integrated Sensing and Communication 18

1.5 Organization of the Book 19

2 Delay-Doppler Signaling and OTFS Modulation 23

2.1 Delay-Doppler Domain 28

2.2 Time and Frequency Domain Modulation 29

2.2.1 Channel Interaction of a TD Pulse 30

2.2.2 Channel Interaction of a FD Pulse 32

2.3 Delay-Doppler (DD) Domain Modulation 34

2.3.1 Origin of Quasi-periodicity 37

2.4 Channel Interaction of a DD Domain Pulse 39

2.4.1 The Channel Interaction is Predictable 40

2.4.2 The Channel Interaction is Non-fading 43

2.4.3 The Channel Interaction is Non-stationary 43

2.5 Time- and Bandwidth-Limited DD Domain Carrier Waveforms 43

2.5.1 Example in Fig. 2.17 47

2.5.2 Orthogonality of Pulsones 49

2.5.3 Optimality as Time- and Bandwidth-limited Signals 50

2.5.4 TDM as a Limiting Case 50

2.5.5 FDM as a Limiting Case 50

2.5.6 TD Pulsones Encode Wireless Channel Dynamics 50

2.5.7 The Fourier Transform as a Composition 51

2.6 Zak-OTFS Modulation and I/O Relation 51

2.6.1 Generalized Transceiver Signal Processing 52

2.6.2 Zak-OTFS Modulation 54

2.6.3 Zak-OTFS Receiver 56

2.6.4 Zak-OTFS I/O Relation 57

2.7 Predictability of the Zak-OTFS I/O Relation in the Crystalline Regime 58

2.7.1 Non-predictability of the Zak-OTFS I/O Relation in the Non-crystalline Regime 61

2.7.2 Crystalline Decomposition 62

2.7.3 Identification of Linear Time-Varying Channels 63

2.7.4 Error in Prediction of the Zak-OTFS I/O Relation 64

2.8 Matrix-vector Description of the I/O Relation 67

2.8.1 Zak-OTFS 67

2.8.2 Tdm 68

2.8.3 Fdm 69

2.9 Impact of Fading in the Crystalline Regime 70

2.10 Model-free Operation in the Crystalline Regime 73

2.10.1 Model-dependent Operation 73

2.10.2 Model-free Operation 74

2.11 Summary 77

Appendix 2.A Cascade of Two Doubly Spread Channels and Twisted Convolution 78

2.a.1 Properties of Twisted Convolution 81

Appendix 2.B Channel Action on DD Domain Signal 83

Appendix 2.C Zak Transform 84

Appendix 2.D Derivation of (2.30) and (2.31) 85

Appendix 2.E Proof of Non-overlapping Received Impulses in a-response 86

Appendix 2.F Inverse Zak Transforms 87

2.f.1 Inverse Time-Zak Transform 87

2.f.2 Derivation of (2.38) 87

2.f.3 Inverse Frequency-Zak Transform 88

Appendix 2.G Twisted Convolution Preserves Quasi-periodicity 88

Appendix 2.H Derivation of TD Pulsone Expression in (2.41) 89

Appendix 2.I Derivation of FD Pulsone Expression in (2.44) 90

Appendix 2.J TDM I/O Relation 90

2.j.1 Proof of Theorem 2.5 91

Appendix 2.K FDM I/O Relation 92

2.k.1 Proof of Theorem 2.6 93

Appendix 2.L Discrete DD Domain Signals 94

2.l.1 Impulse Signal in Discrete DD Domain 95

Appendix 2.M Derivation of Zak-OTFS Modulator Architecture 96

Appendix 2.N Derivation of Zak-OTFS Receiver 97

Appendix 2.O Proof of Theorem 2.1 99

3 Approximations of OTFS Modulation 101

3.1 Pulsones as a Basis for TD Signals 109

3.2 Generating Pulsones Using the Heisenberg Transform 110

3.3 Generating Time- and Bandwidth-Limited Pulsones 113

3.3.1 Comparing MC Pulsones with Zak Pulsones 117

3.4 Multicarrier OTFS (MC-OTFS) Modulation 118

3.4.1 Two-step MC-OTFS Modulator 119

3.4.2 Zak Transform-Based MC-OTFS Modulator 122

3.5 MC-OTFS Receiver 123

3.5.1 Two-step MC-OTFS Receiver 124

3.5.2 Zak Transform-Based MC-OTFS Receiver 125

3.6 MC-OTFS I/O Relation 126

3.6.1 MC-OTFS I/O for a Two-Step Transceiver 126

3.6.2 MC-OTFS I/O Relation for Zak Transform-Based Transceiver 129

3.7 Comparing MC-OTFS to Zak-OTFS 130

Appendix 3.A Proof of Theorem 3.1 133

Appendix 3.B Proof of Corollary 3.14 134

Appendix 3.C Proof of Theorem 3.2 134

Appendix 3.D SFT and Inverse SFT 135

Appendix 3.E Proof of Theorem 3.3 138

Appendix 3.F Proof of Theorem 3.4 138

Appendix 3.G Proof of Theorem 3.5 139

Appendix 3.H Impact of Windowing on a Periodic DD Domain Impulse 140

Appendix 3.I Proof of Theorem 3.6 141

Appendix 3.J Proof of Theorem 3.7 142

Appendix 3.K Proof of Theorem 3.9 143

Appendix 3.L Proof of Theorem 3.10 144

Appendix 3.M Proof of Theorem 3.11 145

Appendix 3.N Derivation of Bi-orthogonality Condition 145

Appendix 3.O Proof of Corollary 3.5 146

Appendix 3.P Derivation of I/O Relation for the Two-step MC-OTFS Transceiver 146

Appendix 3.Q Proof of Theorem 3.13 146

Appendix 3.R Proof of Corollary 3.6 147

4 Delay-Doppler Diversity in OTFS 149

4.1 Diversity in SISO OTFS 150

4.1.1 System Model 150

4.1.2 Diversity Analysis 154

4.1.3 Full Diversity with Phase Rotation 157

4.2 Diversity in MIMO-OTFS 161

4.2.1 MIMO-OTFS Diversity Analysis 162

4.2.2 MIMO-OTFS with Phase Rotation 163

4.3 Diversity in Space–Time Coded OTFS 165

4.3.1 STC-OTFS Scheme 166

4.3.1.1 Encoding and Decoding 166

4.3.1.2 Diversity Analysis 167

4.3.1.3 Phase Rotation in STC-OTFS 168

4.4 Diversity in OTFS with Antenn

Über Autor(innen)

Saif Khan Mohammed, PhD, is a Professor in the Department of Electrical Engineering at IIT Delhi, India. He worked extensively in industry before transitioning to academia, and his research interests include wireless communication, signal processing, OTFS, and related subjects.
Ronny Hadani, PhD, is an Associate Professor in the Department of Mathematics, University of Texas, Austin, USA. He is the co-founder of Cohere Technologies and co-inventor of Cohere’s OTFS modulation scheme. His research focuses on representation theory, harmonic analysis, and signal processing.
Ananthanarayanan Chockalingam, PhD, is a Professor in the Department of Electrical and Communication Engineering, Indian Institute of Science, Bangalore, India. He has made pioneering contributions in the area of large MIMO systems. He has vast industry experience in wireless communications.