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

• Author: Das, Suvra Sekhar.
• Place / Publishing House: Aalborg : : River Publishers,, 2021.; Ã2021.
• Year of Publication: 2021
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (238 pages)

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.