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019 $a1290414003$a1290430955$a1290447948$a1290482486$a1290485470
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020 $a9781003339021$q(electronic bk.)
020 $a1003339026$q(electronic bk.)
020 $a9781000797015$q(electronic bk. ;$qEPUB)
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024 7 $a10.1201/9781003339021$2doi
035 $a(OCoLC)1290376117$z(OCoLC)1290414003$z(OCoLC)1290430955$z(OCoLC)1290447948$z(OCoLC)1290482486$z(OCoLC)1290485470
037 $a9661096$bIEEE
037 $a9781003339021$bTaylor & Francis
050 4 $aTK5103.2$b.D37 2021
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072 7 $aTEC$x061000$2bisacsh
072 7 $aTJKW$2bicssc
082 04 $a621.384$223
049 $aZCUA
100 1 $aDas, Suvra Sekhar,$eauthor.
245 10 $aOTFS :$borthogonal time frequency space modulation : a waveform for 6G /$cSuvra Sekhar Das, Ramjee Prasad.
264 1 $aAlsbjergvej, Gistrup, Denmark :$bRiver Publishers,$c[2021]
264 4 $c©2021
300 $a1 online resource
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aRiver Publishers Series in Communications
520 $aOver 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.
505 0 $6880-01$aFront Cover -- OTFS: Orthogonal Time Frequency Space Modulation -- Contents -- Preface -- Acknowledgements -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Background -- 1.2 1G -- 2G -- 1.3 2G -- 3G -- 1.4 3G -- 4G -- 1.5 Fifth Generation (5G) Mobile Communication Systems -- 1.6 6G -- 2 A Summary of Waveforms for Wireless Channels -- 2.1 Introduction -- 2.1.1 Chapter Outline -- 2.2 Mathematical Foundation to Time-Frequency Analysis -- 2.2.1 Hilbert Space -- 2.2.2 Norm on Vector Space -- 2.2.3 Linear Operators on Hilbert Space -- 2.2.3.1 Functional in Hibert Space
505 8 $a2.2.3.2 Adjoint Operator -- 2.2.4 Orthonormal Basis for Hilbert Space -- 2.2.5 Sequence Space l2(N) -- 2.2.6 Function Spaces -- 2.2.7 Fourier Transform -- 2.2.7.1 Operators on L2(R) -- 2.2.8 Frames in Hilbert Spaces -- 2.2.8.1 Frame Operator -- 2.2.8.2 Reisz Basis -- 2.2.8.3 Tight Frame -- 2.2.8.4 Dual Frame -- 2.2.9 Gabor Transform -- 2.3 Time-Frequency Foundations -- 2.3.1 Time-Frequency Uncertainty Principle -- 2.3.2 Short Time Fourier Transform -- 2.3.2.1 Properties -- 2.3.3 Ambiguity Function -- 2.4 Linear Time Varying Channel -- 2.4.1 Delay-Doppler Spreading Function (SH(,))
505 8 $a2.4.2 Time-Varying Transfer Function (LH(t, f)) -- 2.4.3 Time-Varying Impulse Response (h(t,)) -- 2.4.4 Linear Time Invariant (LTI) Channel -- 2.4.5 Stochastic Description -- 2.4.6 Under-Spread Property of Wireless Channel -- 2.4.7 Physical Discrete Path Model -- 2.4.7.1 Virtual Channel Representation: Sampling in Delay-Doppler Domain -- 2.5 Waveform Design in Gabor Setting -- 2.5.1 Digital Communication in Gabor System -- 2.5.2 Waveform Design of Rectangular Lattice -- 2.5.2.1 Ideal Eigenfunction of H -- 2.5.3 Approximate Eigen Function for LTV Channel -- 2.6 OFDM -- 2.6.1 Channel
505 8 $a2.6.2 Receiver -- 2.7 5G Numerology -- 2.7.1 Genesis -- 2.8 Windowed OFDM -- 2.8.1 Transmitter -- 2.8.2 Receiver -- 2.9 Filtered OFDM -- 2.9.1 Transmitter -- 2.9.2 Receiver Processing -- 2.10 Filter Bank Multi-Carrier -- 2.10.1 Cosine Modulated Tone -- 2.10.2 Filter Characteristics -- 2.10.3 Simplified Filter Characteristics -- 2.10.4 MMSE Equalizer for FBMC -- 2.11 Universal Filtered Multi-Carrier -- 2.11.1 Structure of UFMC Transceiver -- 2.11.2 System Model for UFMC -- 2.11.3 Output of the Receiver for the UFMC Transceiver Block Diagram
505 8 $a2.12 Generalized Frequency Division Multiplexing (GFDM) -- 2.12.1 Introduction -- 2.12.1.1 Chapter Conents -- 2.12.2 GFDM System in LTI Channel -- 2.12.2.1 Transmitter -- 2.12.2.2 Self-interference in GFDM -- 2.12.2.3 Receiver -- 2.12.2.4 Two Stage Equalizer -- 2.12.2.5 One-Stage Equalizer -- 2.12.3 GFDM in Gabor System -- 2.12.3.1 Discrete Gabor Transform -- 2.12.3.2 Critically Sampled Gabor Transform -- 2.12.4 Bit Error Rate Computation for MMSE Receiver -- 2.12.4.1 MMSE Receiver -- 2.12.4.2 SINR Computation -- 2.12.4.3 Frequency Selective Fading Channel (FSFC)
545 0 $aSuvra Sekhar Das, Ramjee Prasad
650 0 $aWireless communication systems.
650 0 $aModulation (Electronics)
650 6 $aTransmission sans fil.
650 6 $aModulation (Électronique)
650 7 $aModulation (Electronics)$2fast$0(OCoLC)fst01024511
650 7 $aWireless communication systems.$2fast$0(OCoLC)fst01176209
650 7 $aSCIENCE$xEnergy.$2bisacsh
700 1 $aPrasad, Ramjee,$eauthor.
776 08 $iPrint version:$z8770226563$z9788770226561$w(OCoLC)1267584486
830 0 $aRiver Publishers series in communications.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio16870853$zTaylor & Francis eBooks
880 0 $6505-01/(S$aPreface xv Acknowledgements xvii List of Figures xix List of Tables xxv 1 Introduction 1 1.1 Background 1 1.2 1G- 2G 1 1.3 2G- 3Ge 2 1.4 3G- 4G 3 1.5 Fifth Generation (5G) Mobile Communication Systems 3 1.6 6G 5 2 A Summary of Waveforms for Wireless Channels 9 2.1 Introduction 9 2.1.1 Chapter Outline 9 2.2 Mathematical Foundation to Time-Frequency Analysis 9 2.2.1 Hilbert Space 9 2.2.2 Norm on Vector Space 10 2.2.3 Linear Operators on Hilbert Space 10 2.2.3.1 Functional in Hibert Space 10 2.2.3.2 Adjoint Operator 11 2.2.4 Orthonormal Basis for Hilbert Space 11 2.2.5 Sequence Space l2(N) 12 2.2.6 Function Spaces 13 2.2.7 Fourier Transform 13 2.2.7.1 Operators on L2(R) 13 2.2.8 Frames in Hilbert Spaces 14 2.2.8.1 Frame Operator 14 2.2.8.2 Reisz Basis 15 2.2.8.3 Tight Frame 15 2.2.8.4 Dual Frame 15 2.2.9 Gabor Transform 16 2.3 Time-Frequency Foundations 17 2.3.1 Time-Frequency Uncertainty Principle 17 2.3.2 Short Time Fourier Transform 17 2.3.2.1 Properties 18 2.3.3 Ambiguity Function 18 2.4 Linear Time Varying Channel 19 2.4.1 Delay-Doppler Spreading Function (SH (τ, ν)) 19 2.4.2 Time-Varying Transfer Function (LH (t, f)) 20 2.4.3 Time-Varying Impulse Response (h(t, τ)) 20 2.4.4 Linear Time Invariant (LTI) Channel 20 2.4.5 Stochastic Description 21 2.4.6 Under-Spread Property of Wireless Channel 22 2.4.7 Physical Discrete Path Model 22 2.4.7.1 Virtual Channel Representation: Sampling in Delay-Doppler Domain 23 2.5 Waveform Design in Gabor Setting 24 2.5.1 Digital Communication in Gabor System 25 2.5.2 Waveform Design of Rectangular Lattice 27 2.5.2.1 Ideal Eigenfunction of H 29 2.5.3 Approximate Eigen Function for LTV Channel 29 2.6 OFDM 30 2.6.1 Channel 32 2.6.2 Receiver 33 2.7 5G Numerology 34 2.7.1 Genesis 35 2.8 Windowed OFDM 37 2.8.1 Transmitter 37 2.8.2 Receiver 38 2.9 Filtered OFDM 38 2.9.1 Transmitter 39 2.9.2 Receiver Processing 40 2.10 Filter Bank Multi-Carrier 41 2.10.1 Cosine Modulated Tone 41 2.10.2 Filter Characteristics 44 2.10.3 Simplified Filter Characteristics 45 2.10.4 MMSE Equalizer for FBMC 46 2.11 Universal Filtered Multi-Carrier 48 2.11.1 Structure of UFMC Transceiver 49 2.11.2 System Model for UFMC 49 2.11.3 Output of the Receiver for the UFMC Transceiver Block Diagram 52 2.12 Generalized Frequency Division Multiplexing (GFDM) 53 2.12.1 Introduction 53 2.12.1.1 Chapter Conents 53 2.12.2 GFDM System in LTI Channel 54 2.12.2.1 Transmitter 54 2.12.2.2 Self-interference in GFDM 57 2.12.2.3 Receiver 57 2.12.2.4 Two Stage Equalizer 58 2.12.2.5 One-Stage Equalizer 59 2.12.3 GFDM in Gabor System 60 2.12.3.1 Discrete Gabor Transform 60 2.12.3.2 Critically Sampled Gabor Transform 62 2.12.4 Bit Error Rate Computation for MMSE Receiver 62 2.12.4.1 MMSE Receiver 62 2.12.4.2 SINR Computation 62 2.12.4.3 Frequency Selective Fading Channel (FSFC) 63 2.12.4.4 Additive White Gaussian Noise Channel (AWGN) 63 2.12.4.5 BER Computation 65 2.12.4.6 FSFC 65 2.12.4.7 AWGN Channel 66 2.12.4.8 Results 66 2.12.5 Performance Comparison 67 2.12.6 Issues with GFDM 72 2.12.6.1 High PAPR 72 2.12.6.2 High Computational Complexity 72 2.13 Precoded GFDM System to Combat Inter Carrier Interference: Performance Analysis 73 2.13.1 Section Contents 74 2.13.2 Precoded GFDM System 75 2.13.2.1 Block IDFT Precoded GFDM 75 2.13.2.2 Joint Processing 75 2.13.2.3 Two-Stage Processing 77 2.13.2.4 DFT Precoded GFDM 80 2.13.2.5 SVD Precoded GFDM 80 2.13.2.6 BER Performance of Precoding Techniques 81 2.13.2.7 Computational Complexity 81 2.13.3 Results 82 2.13.3.1 BER Evaluation of Precoded Techniques 83 2.13.3.2 Complexity Computation 85 2.13.3.3 PAPR of Precoding Techniques 86 2.14 Chapter Summary 87 3 OTFS Signal Model 89 3.1 Introduction 89 3.2 OTFS Signal Generation 90 3.3 RCP-OTFS as Block OFDM with Time Interleaving 91 3.4 Performance in AWGN Channel 92 3.4.1 Receiver for AWGN 92 3.4.2 Ber Performance in AWGN 94 3.5 Performance in Time Varying Wireless Channel 94 3.5.1 The Channel 94 3.5.2 Linear Receivers 96 3.5.2.1 MMSE Equalization 96 3.5.2.2 ZF Receiver for TVMC 97 3.5.2.3 BER Evaluation of ZF and MMSE Receiver 100 3.6 Chapter Summary 102 4 Receivers Structures for OTFS 103 4.1 Belief Propagation Receiver for a Sparse Systems 103 4.1.1 Maximum Apposterior Probability (MAP) Decoding 103 4.1.2 Factor Graph Description 104 4.1.3 Equalization Algorithm 105 4.1.3.1 Initiation 105 4.1.3.2 Check Node Update 106 4.1.3.3 Variable Node Update 107 4.1.3.4 Criteria for Variable Node Decision Update 107 4.1.3.5 Termination 108 4.1.4 Complexity Analysis 108 4.1.5 Results 108 4.2 Low Complexity LMMSE Receiver for OTFS 108 4.2.1 Channel 110 4.2.2 Low Complexity LMMSE Receiver Design for OTFS 110 4.2.2.1 Structure of Ψ = [HH† + σ2νσ2dI] 111 4.2.2.2 Low Complexity LU Factorization of Ψ 112 4.2.2.3 Computation of ˆd. 113 4.2.2.4 LMMSE Receiver for OFDM over TVC 114 4.2.3 Result 116 4.2.3.1 Computational Complexity 116 4.2.3.2 BER Evaluation 118 4.3 Iterative Successive Interference Cancellation Receiver 118 4.3.1 Introduction 118 4.3.2 LDPC Coded LMMSE-SIC Reciever 120 4.3.3 Low Complexity Receiver 122 4.3.3.1 Complexity Computation 122 4.3.4 Performance Presents Cumulative Distribution 124 4.4 Chapter Summary 127 5 Circulant Pulse Shaped OTFS 129 5.1 Chapter Outline 129 5.2 Circular Pulse Shaped OTFS (CPS-OTFS) 129 5.3 Low Complexity Transmitter for CPS-OTFS 131 5.4 Circular Dirichlet Pulse Shaped OTFS (CDPS-OTFS) 132 5.5 Remarks on Receiver Complexity 134 5.5.1 LMMSE Receiver for GFDM and OFDM over TVC 135 5.6 Simulation Results 135 5.7 Chapter Summary 138 6 Channel Estimation in OTFS 139 6.1 Delay Doppler Channel Estimation 139 6.1.1 Pilot Structure 139 6.1.2 Delay-Doppler Channel Estimation 140 6.1.3 Channel Equalization 141 6.1.4 Performance of Channel Estimation 141 6.1.5 VSB OFDM Overview 142 6.1.5.1 Transmitter 143 6.1.5.2 Receiver 144 6.1.6 Pilot Power in OTFS and VSB-OFDM 145 6.1.7 Results 145 6.2 Time Domain Channel and Equalization 148 6.2.1 System Model 148 6.2.1.1 Transmitter 148 6.2.2 Effects of Residual Synchronization Errors 151 6.2.2.1 Integer Delay and Integer Doppler Values 151 6.2.2.2 Integer Delay and Fractional Doppler Values 151 6.2.3 Equivalent Channel Matrix for OTFS Including Synchronization Errors 152 6.2.3.1 OTFS Channel Matrices 155 6.2.4 Estimation of Equivalent Channel Matrix 155 6.2.4.1 Pilot Structure in Delay-Doppler Domain 156 6.2.4.2 Channel Estimation 156 6.2.4.3 Time Domain Interpretation of the Channel Estimation 158 6.2.5 LMMSE Equalization 159 6.2.5.1 Structure of Ψq = [˜Hq ˜H†q + σ2νσ2dI] 159 6.2.5.2 Computation of ˆd 160 6.2.5.3 Computation Complexity 160 6.2.6 LDPC Coded LMMSE-SIC Reciever 161 6.2.7 Unified Framework for Orthogonal Multicarrier Systems 161 6.2.8 Results 161 6.2.8.1 Block Error Rate (BLER) Performance 162 6.3 Conclusions 165 6.3.1 Proof of Theorem 1 166 6.3.2 Proof of Theorem 2 167 6.3.3 PROOF: Delay-Doppler Input-Output Relation 167 7 Nonorthogonal Multiple Access with OTFS 169 7.1 OTFS Signal Model 169 7.2 Delay-Doppler Power-Domain NOMA-OTFS 170 7.2.1 De-Do PD-NOMA-OTFS Downlink 170 7.2.1.1 Transmit Signal Model 170 7.2.1.2 Receiver Processing, SINR and SE Analysis 171 7.2.2 De-Do PD-NOMA-OTFS Uplink 173 7.2.2.1 Transmit Signal Model 173 7.2.2.2 Receiver Processing, SINR and SE Analysis 173 7.3 Power Allocation Schemes Among Download NOMA-OTFS Users 174 7.3.1 Fixed Power Allocation (FPA) 174 7.3.2 Fractional Transmit Power Allocation (FTPA) 175 7.3.2.1 Average SNR Based FTPA 175 7.3.2.2 Channel Norm Based FTPA 175 7.3.3 Power Allocation for Weighed Sum Rate Maximization (WSRM) 175 7.3.3.1 Average SNR Based WSRM 175 7.3.3.2 Instantaneous Channel Information Based WSRM 176 7.4 Link Level Performance Analysis of NOMA-OTFS Systems 177 7.4.1 Downlink MMSE SIC Receiver with LDPC Coding 177 7.4.1.1 Processing at First User 178 7.4.1.2 Processing at Second User 178 7.4.2 Uplink MMSE SIC Receiver with LDPC Coding 179 7.5 Simulation Results and Discussion 180 7.5.1 System Level Spectral Efficiency Results 181 7.5.1.1 Comparison between NOMA/OMA-OTFS 181 7.5.1.2 Comparison between OTFS and OFDM Performances 183 7.5.1.3 Comparison of Various NOMA Power Allocation Schemes 185 7.5.1.4 Extracting NOMA Gain in OTFS with User Channel Heterogeneity 185 7.5.2 Link Level Performance of NOMA-OTFS 186 7.5.2.1 Performance of NOMA-OTFS in Downlink 186 7.5.2.2 Performance of NOMA-OTFS in Uplink 189 7.6 Conclusion 190 A OTFS Channel Matrix (Ideal) 191 References 195 Index 207 About the Authors 209.
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