Orthogonal Time Frequency Space Modulation : : OTFS a Waveform For 6G.

Orthogonal Time Frequency Space Modulation : : OTFS a Waveform For 6G.

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Bibliographic Details
:
Das, Suvra Sekhar.
Place / Publishing House:Aalborg : : River Publishers,, 2021.
Ã2021.
Year of Publication:2021
Edition:1st ed.
Language:English
Online Access:
Physical Description:1 online resource (238 pages)
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Table of Contents:
  • Front 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
  • 2.2.3.2 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(,))
  • 2.4.2 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
  • 2.6.2 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
  • 2.12 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)
  • 2.12.4.4 Additive White Gaussian Noise Channel (AWGN)
  • 2.12.4.5 BER Computation
  • 2.12.4.6 FSFC
  • 2.12.4.7 AWGN Channel
  • 2.12.4.8 Results
  • 2.12.5 Performance Comparison
  • 2.12.6 Issues with GFDM
  • 2.12.6.1 High PAPR
  • 2.12.6.2 High Computational Complexity
  • 2.13 Precoded GFDM System to Combat Inter Carrier Interference: Performance Analysis
  • 2.13.1 Section Contents
  • 2.13.2 Precoded GFDM System
  • 2.13.2.1 Block IDFT Precoded GFDM
  • 2.13.2.2 Joint Processing
  • 2.13.2.3 Two-Stage Processing
  • 2.13.2.4 DFT Precoded GFDM
  • 2.13.2.5 SVD Precoded GFDM
  • 2.13.2.6 BER Performance of Precoding Techniques
  • 2.13.2.7 Computational Complexity
  • 2.13.3 Results
  • 2.13.3.1 BER Evaluation of Precoded Techniques
  • 2.13.3.2 Complexity Computation
  • 2.13.3.3 PAPR of Precoding Techniques
  • 2.14 Chapter Summary
  • 3 OTFS Signal Model
  • 3.1 Introduction.
  • 3.2 OTFS Signal Generation
  • 3.3 RCP-OTFS as Block OFDM with Time Interleaving
  • 3.4 Performance in AWGN Channel
  • 3.4.1 Receiver for AWGN
  • 3.4.2 Ber Performance in AWGN
  • 3.5 Performance in Time Varying Wireless Channel
  • 3.5.1 The Channel
  • 3.5.2 Linear Receivers
  • 3.5.2.1 MMSE Equalization
  • 3.5.2.2 ZF Receiver for TVMC
  • 3.5.2.3 BER Evaluation of ZF and MMSE Receiver
  • 3.6 Chapter Summary
  • 4 Receivers Structures for OTFS
  • 4.1 Belief Propagation Receiver for a Sparse Systems
  • 4.1.1 Maximum Apposterior Probability (MAP) Decoding
  • 4.1.2 Factor Graph Description
  • 4.1.3 Equalization Algorithm
  • 4.1.3.1 Initiation
  • 4.1.3.2 Check Node Update
  • 4.1.3.3 Variable Node Update
  • 4.1.3.4 Criteria for Variable Node Decision Update
  • 4.1.3.5 Termination
  • 4.1.4 Complexity Analysis
  • 4.1.5 Results
  • 4.2 Low Complexity LMMSE Receiver for OTFS
  • 4.2.1 Channel
  • 4.2.2 Low Complexity LMMSE Receiver Design for OTFS
  • 4.2.2.1 Structure of =[HH+2d2I]
  • 4.2.2.2 Low Complexity LU Factorization of
  • 4.2.2.3 Computation of
  • 4.2.2.4 LMMSE Receiver for OFDM over TVC
  • 4.2.3 Result
  • 4.2.3.1 Computational Complexity
  • 4.2.3.2 BER Evaluation
  • 4.3 Iterative Successive Interference Cancellation Receiver
  • 4.3.1 Introduction
  • 4.3.2 LDPC Coded LMMSE-SIC Reciever
  • 4.3.3 Low Complexity Receiver
  • 4.3.3.1 Complexity Computation
  • 4.3.4 Performance Presents Cumulative Distribution
  • 4.4 Chapter Summary
  • 5 Circulant Pulse Shaped OTFS
  • 5.1 Chapter Outline
  • 5.2 Circular Pulse Shaped OTFS (CPS-OTFS)
  • 5.3 Low Complexity Transmitter for CPS-OTFS
  • 5.4 Circular Dirichlet Pulse Shaped OTFS (CDPS-OTFS)
  • 5.5 Remarks on Receiver Complexity
  • 5.5.1 LMMSE Receiver for GFDM and OFDM over TVC
  • 5.6 Simulation Results
  • 5.7 Chapter Summary
  • 6 Channel Estimation in OTFS
  • 6.1 Delay Doppler Channel Estimation
  • 6.1.1 Pilot Structure.
  • 6.1.2 Delay-Doppler Channel Estimation
  • 6.1.3 Channel Equalization
  • 6.1.4 Performance of Channel Estimation
  • 6.1.5 VSB OFDM Overview
  • 6.1.5.1 Transmitter
  • 6.1.5.2 Receiver
  • 6.1.6 Pilot Power in OTFS and VSB-OFDM
  • 6.1.7 Results
  • 6.2 Time Domain Channel and Equalization
  • 6.2.1 System Model
  • 6.2.1.1 Transmitter
  • 6.2.2 Effects of Residual Synchronization Errors
  • 6.2.2.1 Integer Delay and Integer Doppler Values
  • 6.2.2.2 Integer Delay and Fractional Doppler Values
  • 6.2.3 Equivalent Channel Matrix for OTFS Including Synchronization Errors
  • 6.2.3.1 OTFS Channel Matrices
  • 6.2.4 Estimation of Equivalent Channel Matrix
  • 6.2.4.1 Pilot Structure in Delay-Doppler Domain
  • 6.2.4.2 Channel Estimation
  • 6.2.4.3 Time Domain Interpretation of the Channel Estimation
  • 6.2.5 LMMSE Equalization
  • 6.2.5.1 Structure of q =[qq+2d2I]
  • 6.2.5.2 Computation of
  • 6.2.5.3 Computation Complexity
  • 6.2.6 LDPC Coded LMMSE-SIC Reciever
  • 6.2.7 Unified Framework for Orthogonal Multicarrier Systems
  • 6.2.8 Results
  • 6.2.8.1 Block Error Rate (BLER) Performance
  • 6.3 Conclusions
  • 6.3.1 Proof of Theorem 1
  • 6.3.2 Proof of Theorem 2
  • 6.3.3 PROOF: Delay-Doppler Input-Output Relation
  • 7 Nonorthogonal Multiple Access with OTFS
  • 7.1 OTFS Signal Model
  • 7.2 Delay-Doppler Power-Domain NOMA-OTFS
  • 7.2.1 De-Do PD-NOMA-OTFS Downlink
  • 7.2.1.1 Transmit Signal Model
  • 7.2.1.2 Receiver Processing, SINR and SE Analysis
  • 7.2.2 De-Do PD-NOMA-OTFS Uplink
  • 7.2.2.1 Transmit Signal Model
  • 7.2.2.2 Receiver Processing, SINR and SE Analysis
  • 7.3 Power Allocation Schemes Among Download NOMA-OTFS Users
  • 7.3.1 Fixed Power Allocation (FPA)
  • 7.3.2 Fractional Transmit Power Allocation (FTPA)
  • 7.3.2.1 Average SNR Based FTPA
  • 7.3.2.2 Channel Norm Based FTPA
  • 7.3.3 Power Allocation for Weighed Sum Rate Maximization (WSRM).
  • 7.3.3.1 Average SNR Based WSRM
  • 7.3.3.2 Instantaneous Channel Information Based WSRM
  • 7.4 Link Level Performance Analysis of NOMA-OTFS Systems
  • 7.4.1 Downlink MMSE SIC Receiver with LDPC Coding
  • 7.4.1.1 Processing at First User
  • 7.4.1.2 Processing at Second User
  • 7.4.2 Uplink MMSE SIC Receiver with LDPC Coding
  • 7.5 Simulation Results and Discussion
  • 7.5.1 System Level Spectral Efficiency Results
  • 7.5.1.1 Comparison between NOMA/OMA-OTFS
  • 7.5.1.2 Comparison between OTFS and OFDM Performances
  • 7.5.1.3 Comparison of Various NOMA Power Allocation Schemes
  • 7.5.1.4 Extracting NOMA Gain in OTFS with User Channel Heterogeneity
  • 7.5.2 Link Level Performance of NOMA-OTFS
  • 7.5.2.1 Performance of NOMA-OTFS in Downlink
  • 7.5.2.2 Performance of NOMA-OTFS in Uplink
  • 7.6 Conclusion
  • A OTFS Channel Matrix (Ideal)
  • References
  • Index
  • About the Authors
  • Back Cover.

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