Delay-Doppler Communications Principles and Applications

Description

Orthogonal Frequency Division Multiplexing (OFDM) has been the waveform of choice for most wireless communications systems in the past 25 years. This book addresses the “what comes next?” question by presenting the recently proposed waveform known as Orthogonal Time-Frequency-Space (OTFS), which offers a better alternative for high-mobility environments.The OTFS waveform is based on the idea that the mobile wireless channels can be effectively modelled in the delay-Doppler domain. This domain provides a sparse representation closely resembling the physical geometry of the wireless channel. The key physical parameters such as relative velocity and distance of the reflectors with respect to the receiver can be considered roughly invariant in the duration of a frame up to a few millisecond. List of figures Biography Yi Hong Tharaj Thaj Emanuele Viterbo Contents Preface 1 Introduction 1.1 High-mobility wireless channels 1.2 Waveforms for high-mobility wireless channels 1.3 Bibliographical notes References 2 High-mobility wireless channels 2.1 Input–output model of the wireless channel 2.1.1 Geometric model 2.1.2 Delay-Doppler representation 2.2 Continuous-time baseband channel model 2.3 Discrete-time baseband channel model 2.4 Relation among different channel representations 2.5 Channel models for numerical simulations 2.5.1 Standard wireless mobile multipath propagation scenarios 2.5.2 Synthetic propagation scenario 2.6 Bibliographical notes References 3 OFDM review and its limitations 3.1 Introduction 3.2 OFDM system model 3.2.1 Generalized multicarrier modulation 3.2.2 OFDM transmitter 3.3 OFDM frequency domain input–output relation 3.4 Advantages and disadvantages of OFDM 3.4.1 High PAPR 3.4.2 High OOB 3.4.3 Sensitivity to CFO 3.5 OFDM in high-mobility multipath channels 3.6 Bibliographical notes References 4 Delay-Doppler modulation 4.1 System model 4.1.1 Parameter choice for OTFS systems 4.1.2 OTFS modulation 4.1.3 High-mobility channel distortion 4.1.4 OTFS demodulation 4.2 OTFS input–output relation with ideal waveforms 4.2.1 Time-frequency domain analysis 4.2.2 Delay-Doppler domain analysis 4.3 Matrix formulation for OTFS 4.3.1 OTFS modulation 4.3.2 OTFS modulation via the IDZT 4.3.3 OTFS demodulation 4.3.4 OTFS demodulation via the DZT 4.4 OTFS input–output relations in vectorized form 4.4.1 Time domain input–output relation 4.4.2 Time-frequency input–output relation 4.4.3 Delay-time input–output relation 4.4.4 Delay-Doppler input–output relation 4.5 Variants of OTFS 4.5.1 Reduced ZP OTFS RZP-OTFS: time domain analysis RZP-OTFS: delay-time domain analysis RZP-OTFS: delay-Doppler domain analysis RZP-OTFS: fractional delay and fractional Doppler shifts RZP-OTFS: integer delay and fractional Doppler shifts RZP-OTFS: integer delay and integer Doppler shifts 4.5.2 Reduced CP-OTFS RCP-OTFS: time domain analysis RCP-OTFS: delay-time and delay-Doppler domain analysis 4.5.3 CP-OTFS CP-OTFS: time domain analysis CP-OTFS: delay-time domain analysis CP-OTFS: delay-Doppler domain analysis CP-OTFS: fractional delay and fractional Doppler shifts CP-OTFS: integer delay and fractional Doppler shifts CP-OTFS: integer delay and integer Doppler shifts 4.5.4 ZP-OTFS ZP-OTFS: time domain analysis ZP-OTFS: delay-time and delay-Doppler domain analysis 4.6 Summary of channel representations and input–output relations for OTFS variants 4.6.1 Channel representations for OTFS variants 4.6.2 Delay-Doppler input–output relations for OTFS variants 4.6.3 Comparison of OTFS variants 4.7 Bibliographical notes References 5 Zak transform analysis for delay-Doppler communications 5.1 A brief review of the different Fourier transforms 5.2 The Zak transform 5.2.1 Properties of the Zak transform 5.2.2 The inverse Zak transform 5.3 The delay-Doppler basis functions 5.4 Zak transform in delay-Doppler communications 5.4.1 Single path delay-Doppler channel 5.4.2 Multipath and general delay-Doppler channel 5.4.3 Band- and time-limited delay-Doppler basis functions 5.4.3.1 Bandlimited basis functions 5.4.3.2 Time limited basis functions 5.4.3.3 Band- and time-limited basis functions 5.4.4 Communications using band- and time-limited signals 5.5 The discrete Zak transform 5.5.1 The inverse discrete Zak transform 5.5.2 Properties of the DZT 5.6 DZT in delay-Doppler communications 5.6.1 Receiver sampling 5.6.2 Time-windowing at RX and TX 5.6.3 RCP-OTFS with rectangular Tx and Rx window 5.6.4 RZP-OTFS with rectangular Tx and Rx window 5.7 Bibliographical notes References 6 Detection methods 6.1 Overview of OTFS input–output relation 6.2 Single-tap frequency domain equalizer 6.2.1 Single-tap equalizer for RCP-OTFS 6.2.2 Block-wise single-tap equalizer for CP-OTFS 6.2.3 Complexity 6.3 Linear minimum mean-square error detection 6.3.1 Delay-Doppler domain LMMSE detection 6.3.2 Time domain LMMSE detection 6.3.3 Complexity 6.4 Message passing detection 6.4.1 Message passing detection algorithm 6.4.2 Complexity 6.5 Maximum-ratio combining detection 6.5.1 Delay-Doppler domain MRC detection 6.5.2 Complexity Delay-Doppler implementation complexity Initial step complexity 6.5.3 Reduced complexity delay-time domain implementation 6.5.4 Complexity Delay-time implementation complexity Initial step complexity 6.5.5 Low complexity initial estimate Complexity for initial estimate 6.5.6 MRC detection for other OTFS variants 6.6 Iterative rake turbo decoder 6.7 Illustrative results and discussion 6.8 Bibliographical notes References 7 Channel estimation methods 7.1 Introduction 7.2 Embedded pilot delay-Doppler channel estimation 7.2.1 The integer Doppler case 7.2.2 The fractional Doppler case 7.2.3 Effect of channel estimation on spectral efficiency 7.3 Embedded pilot-aided delay-time domain channel estimation 7.3.1 Pilot placement 7.3.2 Delay-time channel estimation 7.3.3 Channel estimation complexity 7.3.4 Extension to other OTFS variants 7.4 Real-time OTFS software-defined radio implementation 7.4.1 Effect of DC offset on channel estimation 7.4.2 Effect of carrier frequency offset on channel estimation 7.4.3 Experiment setup, results, and discussion 7.5 Bibliographical notes References 8 MIMO and multiuser OTFS 8.1 Introduction 8.2 System model for MIMO-OTFS 8.2.1 Transmitter and receiver 8.2.2 Channel 8.2.3 Input–output relation for MIMO-OTFS 8.2.3.1 Time domain 8.2.3.2 Delay-Doppler domain 8.2.3.3 Delay-time domain 8.3 Detection methods 8.3.1 Linear minimum mean-square error detector 8.3.2 Message passing detector 8.3.3 Maximum-ratio combining detector 8.3.3.1 Delay-Doppler domain MRC detection 8.3.3.2 Reduced complexity delay-time domain implementation 8.3.3.3 MRC detection complexity 8.4 MIMO-OTFS channel estimation 8.5 Multiuser OTFS channel estimation 8.6 Numerical results and discussion 8.7 Bibliographical notes References 9 Conclusions and future directions 9.1 OTFS key advantages 9.2 Pros and cons of OTFS variants 9.3 Other research directions 9.3.1 Channel estimation and PAPR reduction 9.3.2 Channels with fast time-varying delay-Doppler paths 9.3.3 Multiuser communications 9.3.4 Massive MIMO-OTFS 9.3.5 OTFS for RadCom 9.3.6 Orthogonal time sequency multiplexing and precoding design 9.3.7 Machine learning for OTFS References A Notation and acronyms B Some useful matrix properties B.1 The DFT matrix B.2 Permutation matrices B.3 Circulant matrices B.4 Linear and circular convolutions B.5 2D transforms, doubly circulant block matrices, and 2D circular convolution C Some MATLAB® code and examples C.1 Transmitter C.2 Channel C.3 Receiver C.4 Generate G matrix and received signal for OTFS variants