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E-raamat: Orthogonal Time Frequency Space Modulation: OTFS a waveform for 6G

(Aarhus University, Denmark), (Indian Institute of Technology Kharagpur, India)
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Orthogonal Time Frequency Space Modulation: OTFS a waveform for 6GSuurem pilt
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Over the last few decades wireless communications, especially Mobile Communication Technology, has evolved by leaps and bounds. The mobile communication industry has named the different major changes as generations namely 1G, 2G,..5G. We are presently looking at deployment of 5G technologies. The work for 6G has already started. This book is focused on the waveform design of 6G. It presents a discourse on a potential waveform for 6G namely Orthogonal Time Frequency Space (OTFS) modulation. OTFS has a distinct feature when compared to earlier generation waveforms such that information bearing signal is placed in the delay Doppler domain as opposed to the usual placement of such signals in the time-frequency domain. This unique feature of OTFS enables it to overcome several disadvantages of a very popular and highly successful waveform namely Orthogonal Frequency Division Multiplexing (OFDM). OTFS is known to be more resilient to frequency offset and Doppler which is one of the key drawbacks of OFDM. With this feature, OTFS, can support higher mobility as well as higher frequency bands of operation which is also one of the key requirements of the next generation wireless communication technologies. The implementation complexity of OTFS remains comparable to that of OFDM. It is found that OTFS provides significant SNR advantage, higher resilience, lower PAPR, lower out of band signal leakage and higher multi-user spectral efficiency than that of OFDM. This book addresses Fundamental signal model of OTFS. Receiver design for OTFS Channel estimation in OTFS Multiple Access through non-orthogonal multiple access (NOMA-OTFS)

The contents of the books are primarily outcome of the research work done at the G. S. Sanyal School of Telecommunications, Indian Institute of Technology Kharagpur, Kharagpur, India.

Orthogonal Time Frequency Space Modulation : A waveform for 6G is ideal for personnel the wireless communication industry as well as academic staff and master/research students in electrical engineering with a specialization in wireless communications.
Preface xv
Acknowledgements xvii
List of Figures
xix
List of Tables
xxv
1 Introduction
1(8)
1.1 Background
1(1)
1.2 1G-2G
1(1)
1.3 2G-3G
2(1)
1.4 3G-4G
3(1)
1.5 Fifth Generation (5G) Mobile Communication Systems
3(2)
1.6 6G
5(4)
2 A Summary of Waveforms for Wireless Channels
9(80)
2.1 Introduction
9(1)
2.1.1
Chapter Outline
9(1)
2.2 Mathematical Foundation to Time-Frequency Analysis
9(8)
2.2.1 Hilbert Space
9(1)
2.2.2 Norm on Vector Space
10(1)
2.2.3 Linear Operators on Hilbert Space
10(1)
2.2.3.1 Functional in Hibert Space
10(1)
2.2.3.2 Adjoint Operator
11(1)
2.2.4 Orthonormal Basis for Hilbert Space
11(1)
2.2.5 Sequence Space l2(N)
12(1)
2.2.6 Function Spaces
13(1)
2.2.7 Fourier Transform
13(1)
2.2.7.1 Operators on L2(R)
13(1)
2.2.8 Frames in Hilbert Spaces
14(1)
2.2.8.1 Frame Operator
14(1)
2.2.8.2 Reisz Basis
15(1)
2.2.8.3 Tight Frame
15(1)
2.2.8.4 Dual Frame
15(1)
2.2.9 Gabor Transform
16(1)
2.3 Time-Frequency Foundations
17(2)
2.3.1 Time-Frequency Uncertainty Principle
17(1)
2.3.2 Short Time Fourier Transform
17(1)
2.3.2.1 Properties
18(1)
2.3.3 Ambiguity Function
18(1)
2.4 Linear Time Varying Channel
19(5)
2.4.1 Delay-Doppler Spreading Function (l H(τ, ν))
19(1)
2.4.2 Time-Varying Transfer Function (l H (t,f))
20(1)
2.4.3 Time-Varying Impulse Response (h(t, τ))
20(1)
2.4.4 Linear Time Invariant (LTI) Channel
20(1)
2.4.5 Stochastic Description
21(1)
2.4.6 Under-Spread Property of Wireless Channel
22(1)
2.4.7 Physical Discrete Path Model
22(1)
2.4.7.1 Virtual Channel Representation: Sampling in Delay-Doppler Domain
23(1)
2.5 Waveform Design in Gabor Setting
24(6)
2.5.1 Digital Communication in Gabor System
25(2)
2.5.2 Waveform Design of Rectangular Lattice
27(2)
2.5.2.1 Ideal Eigenfunction of Jt?
29(1)
2.5.3 Approximate Eigen Function for LTV Channel
29(1)
2.6 OFDM
30(4)
2.6.1 Channel
32(1)
2.6.2 Receiver
33(1)
2.7 5G Numerology
34(3)
2.7.1 Genesis
35(2)
2.8 Windowed OFDM
37(1)
2.8.1 Transmitter
37(1)
2.8.2 Receiver
38(1)
2.9 Filtered OFDM
38(3)
2.9.1 Transmitter
39(1)
2.9.2 Receiver Processing
40(1)
2.10 Filter Bank Multi-Carrier
41(7)
2.10.1 Cosine Modulated Tone
41(3)
2.10.2 Filter Characteristics
44(1)
2.10.3 Simplified Filter Characteristics
45(1)
2.10.4 MMSE Equalizer for FBMC
46(2)
2.11 Universal Filtered Multi-Carrier
48(5)
2.11.1 Structure of UFMC Transceiver
49(1)
2.11.2 System Model for UFMC
49(3)
2.11.3 Output of the Receiver for the UFMC Transceiver Block Diagram
52(1)
2.12 Generalized Frequency Division Multiplexing (GFDM)
53(20)
2.12.1 Introduction
33(20)
2.12.1.1
Chapter Conents
53(1)
2.12.2 GFDM System in LTI Channel
54(1)
2.12.2.1 Transmitter
54(3)
2.12.2.2 Self-interference in GFDM
57(1)
2.12.2.3 Receiver
57(1)
2.12.2.4 Two Stage Equalizer
58(1)
2.12.2.5 One-Stage Equalizer
59(1)
2.12.3 GFDM in Gabor System
60(1)
2.12.3.1 Discrete Gabor Transform
60(2)
2.12.3.2 Critically Sampled Gabor Transform
62(1)
2.12.4 Bit Error Rate Computation for MMSE Receiver
62(1)
2.12.4.1 MMSE Receiver
62(1)
2.12.4.2 SINR Computation
62(1)
2.12.4.3 Frequency Selective Fading Channel (FSFC)
63(1)
2.12.4.4 Additive White Gaussian Noise Channel (AWGN)
63(2)
2.12.4.5 BER Computation
65(1)
2.12.4.6 FSFC
65(1)
2.12.4.7 AWGN Channel
66(1)
2.12.4.8 Results
66(1)
2.12.5 Performance Comparison
67(5)
2.12.6 Issues with GFDM
72(1)
2.12.6.1 High PAPR
72(1)
2.12.6.2 High Computational Complexity
72(1)
2.13 Precoded GFDM System to Combat Inter Carrier Interference: Performance Analysis
73(14)
2.13.1 Section Contents
74(1)
2.13.2 Precoded GFDM System
75(1)
2.13.2.1 Block IDFT Precoded GFDM
75(1)
2.13.2.2 Joint Processing
75(2)
2.13.2.3 Two-Stage Processing
77(3)
2.13.2.4 DFT Precoded GFDM
80(1)
2.13.2.5 SVD Precoded GFDM
80(1)
2.13.2.6 BER Performance of Precoding Techniques
81(1)
2.13.2.7 Computational Complexity
81(1)
2.13.3 Results
82(1)
2.13.3.1 BER Evaluation of Precoded Techniques
83(2)
2.13.3.2 Complexity Computation
85(1)
2.13.3.3 PAPR of Precoding Techniques
86(1)
2.14
Chapter Summary
87(2)
3 OTFS Signal Model
89(14)
3.1 Introduction
89(1)
3.2 OTFS Signal Generation
90(1)
3.3 RCP-OTFS as Block OFDM with Time Interleaving
91(1)
3.4 Performance in AWGN Channel
92(2)
3.4.1 Receiver for AWGN
92(2)
3.4.2 Ber Performance in AWGN
94(1)
3.5 Performance in Time Varying Wireless Channel
94(8)
3.5.1 The Channel
94(2)
3.5.2 Linear Receivers
96(1)
3.5.2.1 MMSE Equalization
96(1)
3.5.2.2 ZF Receiver for TVMC
97(3)
3.5.2.3 BER Evaluation of ZF and MMSE Receiver
100(2)
3.6
Chapter Summary
102(1)
4 Receivers Structures for OTFS
103(26)
4.1 Belief Propagation Receiver for a Sparse Systems
103(5)
4.1.1 Maximum Apposterior Probability (MAP) Decoding
103(1)
4.1.2 Factor Graph Description
104(1)
4.1.3 Equalization Algorithm
105(1)
4.1.3.1 Initiation
105(1)
4.1.3.2 Check Node Update
106(1)
4.1.3.3 Variable Node Update
107(1)
4.1.3.4 Criteria for Variable Node Decision Update
107(1)
4.1.3.5 Termination
108(1)
4.1.4 Complexity Analysis
108(1)
4.1.5 Results
108(1)
4.2 Low Complexity LMMSE Receiver for OTFS
108(10)
4.2.1 Channel
110(1)
4.2.2 Low Complexity LMMSE Receiver Design for OTFS
110(1)
4.2.2.1 Structure of ψ = [ HH† + σv/σ2dI]
111(1)
4.2.2.2 Low Complexity LU Factorization of ψ
112(1)
4.2.2.3 Computation of d
113(1)
4.2.2.4 LMMSE Receiver for OFDM over TVC
114(2)
4.2.3 Result
116(1)
4.2.3.1 Computational Complexity
116(2)
4.2.3.2 BER Evaluation
118(1)
4.3 Iterative Successive Interference Cancellation Receiver
118(9)
4.3.1 Introduction
118(2)
4.3.2 LDPC Coded LMMSE-SIC Reciever
120(2)
4.3.3 Low Complexity Receiver
122(1)
4.3.3.1 Complexity Computation
122(2)
4.3.4 Performance Presents Cumulative Distribution
124(3)
4.4
Chapter Summary
127(2)
5 Circulant Pulse Shaped OTFS
129(10)
5.1
Chapter Outline
129(1)
5.2 Circular Pulse Shaped OTFS (CPS-OTFS)
129(2)
5.3 Low Complexity Transmitter for CPS-OTFS
131(1)
5.4 Circular Dirichlet Pulse Shaped OTFS (CDPS-OTFS)
132(2)
5.5 Remarks on Receiver Complexity
134(1)
5.5.1 LMMSE Receiver for GFDM and OFDM over TVC
135(1)
5.6 Simulation Results
135(3)
5.7
Chapter Summary
138(1)
6 Channel Estimation in OTFS
139(30)
6.1 Delay Doppler Channel Estimation
139(9)
6.1.1 Pilot Structure
139(1)
6.1.2 Delay-Doppler Channel Estimation
140(1)
6.1.3 Channel Equalization
141(1)
6.1.4 Performance of Channel Estimation
141(1)
6.1.5 VSB OFDM Overview
142(1)
6.1.5.1 Transmitter
143(1)
6.1.5.2 Receiver
144(1)
6.1.6 Pilot Power in OTFS and VSB-OFDM
145(1)
6.1.7 Results
145(3)
6.2 Time Domain Channel and Equalization
148(17)
6.2.1 System Model
148(1)
6.2.1.1 Transmitter
148(3)
6.2.2 Effects of Residual Synchronization Errors
151(1)
6.2.2.1 Integer Delay and Integer Doppler Values
151(1)
6.2.2.2 Integer Delay and Fractional Doppler Values
151(1)
6.2.3 Equivalent Channel Matrix for OTFS Including Synchronization Errors
152(3)
6.2.3.1 OTFS Channel Matrices
155(1)
6.2.4 Estimation of Equivalent Channel Matrix
155(1)
6.2.4.1 Pilot Structure in Delay-Doppler Domain
156(1)
6.2.4.2 Channel Estimation
156(2)
6.2.4.3 Time Domain Interpretation of the Channel Estimation
158(1)
6.2.5 LMMSE Equalization
159(1)
6.2.5.1 Structure of ψa = [ H,H]† + σv/σ2dI]
159(1)
6.2.5.2 Computation of d
160(1)
6.2.5.3 Computation Complexity
160(1)
6.2.6 LDPC Coded LMMSE-SIC Reciever
161(1)
6.2.7 Unified Framework for Orthogonal Multicarrier Systems
161(1)
6.2.8 Results
161(1)
6.2.8.1 Block Error Rate (BLER) Performance
162(3)
6.3 Conclusions
165(4)
6.3.1 Proof of Theorem 1
166(1)
6.3.2 Proof of Theorem 2
167(1)
6.3.3 PROOF: Delay-Doppler Input-Output Relation
167(2)
7 Nonorthogonal Multiple Access with OTFS
169(22)
7.1 OTFS Signal Model
169(1)
7.2 Delay-Doppler Power-Domain NOMA-OTFS
170(4)
7.2.1 De-Do PD-NOMA-OTFS Downlink
170(1)
7.2.1.1 Transmit Signal Model
170(1)
7.2.1.2 Receiver Processing, SINR and SE Analysis
171(2)
7.2.2 De-Do PD-NOMA-OTFS Uplink
173(1)
7.2.2.1 Transmit Signal Model
173(1)
7.2.2.2 Receiver Processing, SINR and SE Analysis
173(1)
7.3 Power Allocation Schemes Among Download NOMA-OTFS Users
174(3)
7.3.1 Fixed Power Allocation (FPA)
174(1)
7.3.2 Fractional Transmit Power Allocation (FTPA)
175(1)
7.3.2.1 Average SNR Based FTPA
175(1)
7.3.2.2 Channel Norm Based FTPA
175(1)
7.3.3 Power Allocation for Weighed Sum Rate Maximization (WSRM)
175(1)
7.3.3.1 Average SNR Based WSRM
175(1)
7.3.3.2 Instantaneous Channel Information Based WSRM
176(1)
7.4 Link Level Performance Analysis of NOMA-OTFS Systems
177(3)
7.4.1 Downlink MMSE SIC Receiver with LDPC Coding
177(1)
7.4.1.1 Processing at First User
178(1)
7.4.1.2 Processing at Second User
178(1)
7.4.2 Uplink MMSE SIC Receiver with LDPC Coding
179(1)
7.5 Simulation Results and Discussion
180(10)
7.5.1 System Level Spectral Efficiency Results
181(1)
7.5.1.1 Comparison between NOMA/OMA-OTFS
181(2)
7.5.1.2 Comparison between OTFS and OFDM Performances
183(2)
7.5.1.3 Comparison of Various NOMA Power Allocation Schemes
185(1)
7.5.1.4 Extracting NOMA Gain in OTFS with User Channel Heterogeneity
185(1)
7.5.2 Link Level Performance of NOMA-OTFS
186(1)
7.5.2.1 Performance of NOMA-OTFS in Downlink
186(3)
7.5.2.2 Performance of NOMA-OTFS in Uplink
189(1)
7.6 Conclusion
190(1)
A OTFS Channel Matrix (Ideal) 191(4)
References 195(12)
Index 207(2)
About the Authors 209
Suvra Sekhar Das (Member, IEEE) received the B.Eng. degree in electronics and communication engineering from the Birla Institute of Technology, Ranchi, India, and the Ph.D. degree from Aalborg University, Aalborg, Denmark. He was the Senior Scientist of the Innovation Laboratory, Tata Consultancy Services. He is currently an Associate Professor with the G. S. Sanyal School of Telecommunications, IIT Kharagpur, Kharagpur, India. His current research interests include design of waveform, radio access technology, and radio access networks for QoS traffic.



CTIF Global Capsule, Department of Business Development and Technology, also Aarhus University, Herning Denmark. Dr. Ramjee Prasad, Fellow IEEE, IET, IETE, and WWRF, is a Professor of Future Technologies for Business Ecosystem Innovation (FT4BI) in the Department of Business Development and Technology, Aarhus University, Herning, Denmark. He has published more than 50 books, 1000 plus journal and conference publications, more than 15 patents, over 140 Ph.D. Graduates and a larger number of Masters (over 250). Several of his students are today worldwide telecommunication leaders themselves.
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