OTFS Modulation E-Book

Saif Khan Mohammed

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 764

Veröffentlichungsjahr: 2024

Beschreibung

Grasp the future of wireless communication with this groundbreaking introduction

Research and development are already underway on the sixth generation (6G) of wireless communication technology. The new requirements of 6G that arise from challenging new use cases render physical layer waveforms such as CDMA and OFDM inadequate. The OTFS waveform answers these new requirements, and recent research suggests it will play a decisive role in the future of wireless communication.

OTFS Modulation – Theory and Applications provides the first ever foundational textbook that introduces this growing, state-of-the-art, field of research from first principles. Beginning with a thorough discussion of the fundamental principles of OTFS, both physical and theoretical, it rigorously situates OTFS modulation in a mathematical framework analogous to more familiar waveforms. The result is a groundbreaking contribution to communication theory and a must-have volume for wireless communication researchers.

OTFS Modulation – Theory and Applications readers will also find:

• An expert author team including the inventor of OTFS modulation
• Detailed discussion of topics including the Zak theory of linear time-varying systems, delay-Doppler communication and radar sensing, machine learning, and many more
• Matlab code for OTFS transceiver implementation.

OTFS Modulation – Theory and Applications is ideal for researchers, engineers, graduate and advanced undergraduate students, and standardization professionals working with wireless communication, signal processing, and radar sensing.

Leseprobe

IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardSarah Spurgeon, Editor-in-Chief

Moeness Amin

Jón Atli Benediktsson

Adam Drobot

James Duncan

Ekram Hossain

Brian Johnson

Hai Li

James Lyke

Joydeep Mitra

Desineni Subbaram Naidu

Tony Q. S. Quek

Behzad Razavi

Thomas Robertazzi

Diomidis Spinellis

OTFS Modulation

Theory and Applications

Saif Khan Mohammed

Indian Institute of Technology

New Delhi, India

Ronny Hadani

University of Texas

Austin, USA

Ananthanarayanan Chockalingam

Indian Institute of Science

Bangalore, India

Copyright © 2024 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Names: Mohammed, Saif Khan, author. | Hadani, Ronny, author. |  Chockalingam, Ananthanarayanan, author.

Title: OTFS modulation : theory and applications / Saif Khan Mohammed,  Ronny Hadani, Ananthanarayanan Chockalingam.

Description: Hoboken, New Jersey : Wiley, [2024] | Includes bibliographical  references and index.

Identifiers: LCCN 2024023399 (print) | LCCN 2024023400 (ebook) | ISBN  9781119984184 (hardback) | ISBN 9781119984207 (adobe pdf) | ISBN  9781119984214 (epub)

Subjects: LCSH: Modulation (Electronics) | Wireless communication systems.

Classification: LCC TK5102.5 .M635 2024 (print) | LCC TK5102.5 (ebook) |  DDC 621.3815/36–dc23/eng/20240801

LC record available at https://lccn.loc.gov/2024023399

LC ebook record available at https://lccn.loc.gov/2024023400

Cover Design: WileyCover Images: Courtesy of Shailesh Rao M.

To my parents, my wife, and my daughter

– Saif Khan Mohammed

In memory of Noga Porat

– Ronny Hadani

In memory of my elder brother S. A. Anbumani

– Ananthanarayanan Chockalingam

Preface

This book is about a new waveform and its associated promising modulation format called orthogonal time frequency and space (OTFS for short) suited for next-generation wireless communication systems such as 6G. Historically, physical layer waveform has been a key differentiator between different generations of wireless systems. Specifically, 2G/3G systems are based on code division multiple access (CDMA), and 4G/5G systems are based on orthogonal frequency division multiplexing (OFDM). Both CDMA and OFDM waveforms enjoy certain beneficial attributes that have resulted in enhanced quality of communications. The increased relevance and use of mobile internet demand a more capable mobile communication infrastructure compared to what is currently deployed. Specifically, the rate, reliability, robustness, and spectral/energy efficiency requirements are envisioned to be an order of magnitude higher in 6G compared to those in 5G. In addition to that, 6G brings in several interesting new use cases that challenge the boundaries of conventional systems. One such use case is high-mobility communication. A fundamental challenge in this context is the rapidly time-varying nature of the underlying channel due to the increased Doppler shifts at high user speeds and high carrier frequencies, rendering waveforms such as OFDM inadequate. Another such use case is intelligent transportation systems where radar sensing capability has become an additional new requirement, which is not adequately accounted for by contemporary waveforms.

The OTFS waveform and its associated modulation format were invented by Ronny Hadani, an applied mathematician (also an author of this book), and were first reported in the literature in 2017. This invention has created wide interest and stimulated a growing body of research in the past few years, mainly due to the demonstrated superior performance of OTFS compared to existing waveforms, particularly under challenging channel conditions involving high Doppler and delay spreads.

Two key aspects of the OTFS communication paradigm are responsible for its superior performance. They are (i) channel representation in the delay-Doppler domain and (ii) signaling of information in the delay-Doppler domain. Both these aspects stand in sharp contrast with the conventional multicarrier communication paradigm where both channel representation and information signaling are carried out in the time-frequency domain. In this regard, OTFS constitutes a fundamental paradigm shift in communication theory, moving it away from traditional time-frequency (TF) signal processing to delay-Doppler (DD) signal processing.

Depending on how the delay-Doppler multiplexed information symbols are converted to time domain for transmission, OTFS research from 2017 until now has evolved in two phases. In the early version of OTFS introduced in 2017, this conversion was done in two steps, namely, DD domain-to-TF domain conversion followed by TF domain-to-time domain conversion. This approach was motivated by compatibility with existing multicarrier modulation in 4G/5G. The first five years of OTFS research since 2017 has adopted this two-step conversion approach. During this period, our independent research following this approach has resulted in some of the early contributions to OTFS. In the last one year, a more fundamental and promising approach to direct conversion from DD domain to time domain using a Zak theoretic framework has emerged out of our research collaboration, setting a new direction for OTFS research. Two key aspects are central to the Zak approach to OTFS. First, it provides a formal mathematical framework using Zak theory for describing OTFS and studying its fundamental properties, in a manner analogous to how Fourier theory constitutes an appropriate mathematical framework for describing and understanding OFDM. Second, the Zak-based OTFS waveform is more robust to a larger range of delay and Doppler spreads of the channel. This is because the relation between channel input and output in Zak-based OTFS is localized, non-fading, and predictable, even in the presence of significant delay and Doppler spreads, and as a consequence, the channel can be efficiently acquired and equalized.

The academic research on OTFS is growing, and so is the interest from the industry and the community at large, clearly marking the need for a good textbook on OTFS that lays the theory of OTFS ground up and discusses the systems, signal processing, algorithmic, and application aspects. So, when IEEE Press-Wiley evinced interest in a book on new modulation waveforms, we took it as an opportunity to write this book on OTFS. In writing this book, our aim has been to introduce OTFS modulation to the readers in a fundamental, structured, and accessible way emphasizing its key strengths and highlighting its potential for becoming a widely adopted waveform in a variety of use cases and applications. A broader goal is to introduce the delay-Doppler signal processing framework and hint toward its wider applicability in the context of communication theory, radar theory, and signal processing. In this effort, we have been guided by our past research in OTFS, our recent research collaboration on Zak-based OTFS, and our interactions with students, researchers, industry engineers, and the community at large during classroom lectures, tutorial talks, and presentations and discussions in various forums.

The book covers various aspects of OTFS including a thorough discussion of its physical foundation and theoretical underpinnings as well as aspects of system design and algorithms. In this context, the book includes a comprehensive description of the underlying mathematical theory while emphasizing its structural connections to conventional modulation formats and drawing parallels between the Fourier theory of linear time-invariant systems and the more general Zak theory of linear time-varying systems. We hope the book will benefit practicing engineers, researchers, academics, and graduate/senior undergraduate students interested in emerging wireless communication systems and advanced physical layer waveforms/techniques. We also hope the book will be of interest to radar signal processing engineers, as the OTFS waveform and its underlying theory are very well suited for radar applications. People involved in standardization of wireless systems will also find this book useful in their quest to know new waveforms suitable for future wireless systems and standards.

September 2024   

Saif Khan Mohammed

New Delhi

Ronny Hadani

Austin

Ananthanarayanan Chockalingam

Bangalore

Acknowledgements

This book is the outcome of our individual and collaborative research on OTFS. It would not have been possible without the active collaboration, support, help, and encouragement we received from many. Our students and research collaborators from both academia and industry were pivotal for sustaining our research interest on OTFS. Our sincere thanks to all of them.Our deep appreciation and special thanks are due to Prof. Robert Calderbank, Duke University, USA, for his inspiring research collaboration on Zak-OTFS that led to the two seminal papers on Zak-OTFS published in IEEE BITS the Information Theory Magazine.We had the opportunity to deliver talks and tutorials on OTFS on several occasions in various forums that served as ideal platforms for interaction with the research community. These interactions have contributed to our deeper understanding and appreciation of OTFS. We thank the hosts and organizers of these events.

We thank Wiley and IEEE for accepting our proposal to write this book. It was a pleasure to work with the Wiley team throughout this book writing project. We thank Michelle Dunckley, Vishal Paduchuru, Elisha Benjamin, and Kavipriya Ramachandran for their help and guidance at various stages of the project that helped us to keep the project on track. Our special thanks are due to Mustaq Ahamed Noorullah and Sundaramoorthy Balasubramani for patiently working with us in the copy editing and proof reading stages of the production process.We appreciate their meticulous efforts.

A brief note on the cover design of the book is due here.We express our sincere thanks to Dr. Shailesh Rao M. for his help in getting the photograph of the crystalline rock formation in St. Mary’s island, Udupi, Karnataka state, India, used in the cover design. A noticeable structural similarity between the crystalline rocks in the island and the 3D-rendering of the received delay-Doppler power profile in Zak-OTFS in the crystalline regime (see Fig. 2.37) has been an inspiration for us to use the crystalline rock image in the cover design. Of course, the waveform (the pulsone) responsible for the delay-Doppler crystallization phenomenon has also found its place along with the Arabian sea waves in the cover design.

– Saif Khan Mohammed, Ronny Hadani, and Ananthanarayanan Chockalingam

I thank my students for being a part of my research on OTFS and also for constantly pushing me to write a book on OTFS – Venkatesh Khammammetti, Imran Ali Khan, Muhammad Ubadah, Rahul Kumar Jaiswal, Danish Nisar, Jinu Jayachandran, Alok Kumar Sinha, Saurabh Prakash, and Brijesh Chander Pandey. I would like to thank Prof. Emanuele Viterbo and Prof. Yi Hong at Monash University, Australia, for collaborating in the area of multiuser OTFS precoding and synchronization.

I would like to thank my PhD supervisor Prof. A. Chockalingam, IISc, Bangalore (coauthor of this book), for bringing out the best inme in terms of research and fromwhom I have inherited the art of perseverance in research. It is Prof. Chockalingam who introduced me to OTFS in 2017.

This book could not have been a reality without the support from Prof. Kishan and Pramila Gupta, Chair Professor position at IIT Delhi. I would specially thank Dr. Surendra Prasad, Honorary Professor, IIT Delhi, for being a mentor and a source of inspiration at the Department of Electrical Engineering, IIT Delhi. I would also like to thank Dr. M. Balakrishnan, Honorary Professor, IIT Delhi, who was my BTech project supervisor when I was an undergraduate student at IIT Delhi and under whom I learnt the basics of digital hardware and microprocessor design. I thankDr. M. Balakrishnan for introducing me to the world of scientific research and innovation, which is why I chose to be an academic.

I cannot forget to thank my parents for their constant and unconditional support and encouragement and without whom I would not be what I am,my wife and daughter for sacrificing family time so that I could devote more time to book writing and research. I specially thank my wife Shaba for being an unconditional source of support for the last 20 years and also for encouraging me to pursue a career in academics, a decision which I will always be happy about. I also thankmy parents in-law who have always helped me whenever I needed them.

Lastly, I thank Almighty God for enlightening me and my coauthors, which has enabled us to write this book.

– Saif Khan Mohammed

My OTFS journey began when I first met Shlomo Rakib in 2008 during one of my lectures on the canonical basis of eigen vectors of the finite Fourier transform (FFT). We immediately resonated on the personal level, however, only by the end of 2009, we started to work on a project together. The early discussions were conducted on Skype, after working hours, before miraculously converging to an intuitive idea of a communication method based on delay-Doppler shifts. From that point on, over a period of three years, we established the basic principles of OTFS, built a radio implementation, demonstrated its superior performance to a third party and built a company around it called Cohere Technologies. Shlomo has always been a source of knowledge and inspiration for me, and I am grateful for having the opportunity of learning and working side by side with him until today.

I would like to acknowledge the imminent contribution of Clayton Ambrose and Norm Rayes during these early years of development. Clayton, single handedly put together a comprehensive demonstration platform that provided deep insights about the interaction between the OTFS waveform and the wireless channel – confirming our theoretical hypothesis. Jointly with Clayton we performed extensive over-the-air testing under various mobility conditions both indoor and outdoor, at times employing unorthodox methods like driving a car with one hand and holding an antenna with another or holding a transmitter in front of a rotating fan. Norm joined our small team shortly after Clayton and put together the first OTFS radio and conducted a successful over-the-air demonstration to Sprint (telecom company) in their Kansas campus. This facilitated the first substantial Venture capital investment in Cohere. Norm always impressed me as a “renaissance man” – an orchestra of hardware and software engineers distilled in one man!

Although OTFS basic transceiver was in place as early as 2013, it took another several years to reveal its underlying mathematical structure. During this second period of development, I had the pleasure of working closely, as part of a due diligence process, with John Campbell from Telstra and Giovanni Vannucci from Bell labs. Their insights helped tremendously in explaining the value of OTFS and clarifying its conceptual structure.

Another important stimulator was Cohere’s attempt to promote orthogonal time frequency space (OTFS) into the emerging 3GPP 5G standard. Since orthogonal frequency division multiplexing (OFDM) was the waveform of choice at that time, our focus revolved around a multi-carrier variant of the waveform, referred to in this book as MC-OTFS. I would like to thank Anton Monk, the director of the Cohere standards team and my coauthor of the OTFS white paper, who led the audacious effort of promoting OTFS into 3GPP. Anton put together a team of experts and established strategic relations with telecom partners and carriers. The standards team wrote multiple high-quality technical contributions to 3GPP which laid the basis for all future developments. I would like to acknowledge the contribution of Shachar Kons, Yoav Hevron, Michael Tsatsanis, Anthony Ekpenyong, Cristian Ibars, and Paul Harris. Their deep knowledge of theory and vast practical experience combined with a healthy dose of skepticism helped mature OTFS into a complete architecture with comprehensive performance evaluation.

The cherry on top was our conference paper that was published in 2017 and constituted the first peer reviewed publication that exposed OTFS to the academic community. I would like to thank Prof. Andrea Goldsmith, who served as chair of Cohere Technical Advisory Board (TAB), Prof. AndreasMolisch and Prof. Robert Calderbank, both members of Cohere TAB, for putting the time and effort in organizing the writing of this pioneering paper.

In my mind, there were always two parallel derivations of OTFS. One was using the Zak transform giving rise to what we refer to in this book as Zak-OTFS and the other was using the symplectic finite Fourier transform (SFFT), giving rise to MC-OTFS. Until around 2017, I believed that the two derivations are mathematically equivalent and it is a matter of convenience which one to use. However, as often happens in mathematics, beliefs are proved to be false. Eventually, I came to realize that the two derivations are not equivalent and, moreover, got convinced that the Zak-theoretic derivation is the “correct” one while the SFFT derivation is merely an approximation. This realization marks the third period of OTFS development. Most of my work in Cohere on this topic at an early stage was conducted in close collaboration with my former PhD student Jim Delfeld who had numerous key insights and helped develop comprehensive simulations. A later stage collaboration which continues until today is conducted with Shachar Kons who made fundamental contributions to the development and implementation of a complete transceiver structure.

In parallel to the research activity, there was a continuous effort by Cohere to develop a viable product based on OTFS technology. This parallel path turns out to reinforce the research, revealing gaps and inspiring new ideas and directions. The process of building a product is complicated and demanding. It requires collaboration between professionals from multiple disciplines, such as system engineers, communication engineers, hardware and software engineers, testing and quality assurance, and of course programmanagement.

I would like to thank Mike Grimwood and Yoav Hevron for leading system engineering, Naveen Rawat for leading software engineering, Norm Reyes for leading hardware engineering, Venu Gopal Reddy Vennapusa for leading the testing and quality assurance, and Ashish Yadav for taking care of program management. I would also like to conveymy sincere admiration to Ray Dolan, Cohere CEO, for carrying the heavy responsibility of navigating our precious “OTFS cargo” through, in times, challenging commercial circumstances, allowing it to mature into what we know it today. Another important component is the support of operators. I would like to thank Telstra for their continued support to Cohere on numerous fronts including validation trials, standardization efforts, over-the-air testing, and giving us access to people, bandwidth, and facilities. At the same note, I would also like to thank Steven Bye from Sprint, Andrew Ip from Cablevision, Peter Ledl from Deutsche Telekom, and Santiago Tenorio and Francisco Martin Pignatelli from Vodafone for facilitating validation testing. Our work at Cohere would not be possible without continuous financial backing. I would like to extend my gratitude to Chris Schaepe from light speed, Ron Bernal from NEA, Mark Sherman from Telstra Ventures, David Dibble from Cablevision, Sachin Katti from VMware, Caroline Chen from Intel, the venture arm of Koch industries and Bell Canada.

Finally, I would like to thankmy wifeNoga Porat who supportedmeover themany years of intense work and emotional struggle, associated with navigating a start-up company through the challenging telecom industry. Turns out, the OTFSmeme eventually percolated into our personal lives – we decided to call our son Gal which means wave in Hebrew.

– Ronny Hadani

I got to know about OTFS when it was first presented in a session on Modulation in IEEE Wireless Communications and Networking Conference (IEEE WCNC’2017) held in San Francisco in March 2017. Incidentally, I, along with my coauthors Swaroop Jacob and Dr. Lakshmi Narasimhan Theagarajan (now a faculty at IIT Madras), had a paper on Space-Time Index Modulation in the same session. Lakshmi Narasimhan presented our paper in the session. The OTFS paper was presented by Dr. AntonMonk, one of the authors of the OTFS paper (also my research collaborator during my post-doc days at UCSD with Prof. Larry Milstein). On his return fromthe conference, Lakshmi Narasimhan told me that the OTFS paper created big excitement in the session. We felt that the paper talked about something new and interesting. Our journey on OTFS research started from there and I am thankful to many in this exciting journey. I thank all my students who have participated in this journey and have contributed immensely to the advancement of OTFS research. These students had to work with very limited literature on OTFS in the early days, yet they made a big difference through their dedicated efforts and talent. My big thanks are due to my students K. R. Murali, Rosemary Augustine, G. D. Surabhi, Rasheed O. K., Vighnesh Bhat S., Jickson K. F., Ashwitha Naikoti, Sujata Sinha, Sandesh Rao Mattu, Vineetha Yogesh, Fathima Jesbin, Sai Pradeep Muppaneni, Gandhodi Harshavardhan, Anagha V., Jaswanth Bodempudi, Nabarun Roy, Arpan Das, Abhishek Bairwa, Naveed Bin Nazir, and all other students and colleagues for their interest in OTFS and contributions to OTFS research. I have taught parts from early drafts of this book on Zak-OTFS in my graduate level course and I thank the students for attending the course and offering valuable feedback. I gratefully acknowledge the support of the J. C. Bose Fellowship, Department of Science and Technology, Government of India, and the Intel India Faculty Excellence Program. As we conclude writing this book, I am reminded of the immense understanding and support I received from my family all along, and I express my special and sincere thanks to my family.

– Ananthanarayanan Chockalingam

Acronyms

1G

first generation

2D

two-dimensional

2G

second generation

3G

third generation

3GPP

third generation partnership project

4G

fourth generation

5G

fifth generation

5G NR

5G new radio

6G

sixth generation

ACF

auto-correlation function

AI

artificial intelligence

AJ

anti-jamming

AWGN

additive white Gaussian noise

BCE

binary cross entropy

BER

bit error rate

BPCM

basic circulant permutation matrix

BPSK

binary phase shift keying

BS

base station

CCDF

complementary cumulative distribution function

CDMA

code division multiple access

CFO

carrier frequency offset

CLT

central limit theorem

CMOS

complementary metal-oxide semiconductor

CNN

convolutional neural network

CP

cyclic prefix

CP-OFDM

cyclic prefix OFDM

CPSC

cyclic prefix single carrier

CSI

channel state information

CW

continuous wave

DD

delay-Doppler

DDRE

delay-Doppler resource element

DFRC

dual-function radar communication

DFT

discrete Fourier transform

DL

downlink/deep learning

DNN

deep neural network

DZT

discrete Zak transform

EDGE

enhanced data rates for GSM evolution

ELBO

evidence lower bound

EM

expectation maximization

ETU

extended typical urban

FCNN

fully connected neural network

FD

frequency domain

FDM

frequency domain modulation

FDMA

frequency division multiple access

FFT

fast Fourier transform

FLOPS

floating-point operations per second

FMCW

frequency modulated continuous wave

GB

guard band

Gbps

gigabits per second

GFDM

generalized frequency division multiplexing

GHz

gigahertz

GMSK

Gaussian minimum shift keying

GPRS

generalized packet radio service

GPS

global positioning system

GRU

gated recursive unit

HSDPA

high-speed downlink packet access

HSPA

high-speed packet access

I/O

input–output

IAPR

instantaneous-to-average power ratio

ICI

inter-carrier interference

IDD

interleaved delay-Doppler

IDFT

inverse discrete Fourier transform

IF

intermediate frequency

IFFT

inverse fast Fourier transform

IoT

Internet of things

IQ

in-phase quadrature-phase

IQI

IQ imbalance

IS-95

Interim standard-95

ISAC

integrated sensing and communication

ISFFT

inverse symplectic finite Fourier transform

ISFT

inverse symplectic Fourier transform

ISI

inter-symbol interference

ITF

interleaved time-frequency

IZT

inverse Zak transform

kbps

kilobits per second

kHz

kilohertz

LDPC

low density parity check

LHS

left-hand side

LMMSE

linear minimum mean square error

LOS

line-of-sight

LPI

low probability of intercept

LSTM

long short-term memory

LTE

long-term evolution

LTI

linear time-invariant

LTV

linear time-varying

MA

multiple access

MAI

multiple access interference

MAP

maximum a posteriori

Mbps

megabits per second

MC

multicarrier

MCMC

Markov chain Monte Carlo

MHz

megahertz

MIMO

multiple-input multiple-output

ML

maximum-likelihood/machine learning

MLSE

maximum-likelihood sequence estimation

MMSE

minimum mean square error

mmWave

millimeter wave

MP

message passing

MRC

maximal ratio combining

MRT

maximal ratio transmission

MSE

mean square error

MUI

multiuser interference

NLOS

non-line-of-sight

NMSE

normalized mean square error

NOMA

non-orthogonal multiple access

ODC

orthogonal downlink communication

OFDM

orthogonal frequency division multiplexing

OFDMA

orthogonal frequency division multiple access

OMA

orthogonal multiple access

OMP

orthogonal matching pursuit

OOB

out-of-band

OTFS

orthogonal time frequency space

PA

power amplifier

PAPR

peak-to-average power ratio

PDMA

path division multiple access

PDP

power-delay profile

PEP

pairwise error probability

PIC

parallel interference cancellation

PLL

phase lock loop

pmf

probability mass function

PN

pseudo-noise/phase noise

PR

phase rotation

PSD

power spectral density

PSK

phase shift keying

PSS

primary synchronization signal

QAM

quadrature amplitude modulation

QPSK

quadrature phase shift keying

RA

random access

RAS

receive antenna selection

RC

raised cosine

RE

resource element

RF

radio frequency

RHS

right-hand side

RNN

recurrent neural network

RPE

relative prediction error

RRC

root raised cosine

Rx

receiver

SBL

sparse Bayesian learning

SC-FDMA

single-carrier frequency division multiple access

SE

spectral efficiency

SFFT

symplectic finite Fourier transform

SFO

sampling frequency offset

SFT

symplectic Fourier transform

SGD

stochastic gradient descent

SIMO

single-input multiple-output

SINR

signal-to-interference plus noise ratio

SISO

single-input single-output

SMS

short message service

SNR

signal-to-noise ratio

SOC

system-on-chip

SSS

secondary synchronization signal

STC

space-time coding

TA

timing advance

Tbps

terabits per second

TD

time domain

TDL

tapped delay line

TDM

time domain modulation

TDMA

time division multiple access

TEP

timing error probability

TF

time-frequency

TFRE

time-frequency resource element

THP

Tomlinson–Harashima precoding

THz

terahertz

TSNR

transmit SNR

Tx

transmitter

UAV

unmanned aerial vehicle

UE

user equipment

UL

uplink

UT

user terminal

V2I

vehicle-to-infrastructure

V2V

vehicle-to-vehicle

V2X

vehicle-to-everything

VLSI

very large-scale integration

VB

variational Bayes

VP

vector perturbation

WiFi

wireless fidelity

WiMAX

worldwide interoperability for microwave access

ZC

Zadoff-Chu

ZF

zero forcing

ZP

zero padding

ZT

Zak transform

1Introduction

Cellular mobile communication technology which came into being in the late 1970s has witnessed numerous advances and innovations in the last few decades and has been evolving rapidly. It started with an objective to make large-scale mobile radio service affordable to a sizable segment of the public through efficient use of a limited block of frequency spectrum [1]. A key element that played a crucial role in achieving this objective is the cellular concept, driven by its underlying frequency reuse philosophy [2]. Over these decades, the fraction of global population that has access to mobile communication services has increased tremendously. Present-day cellular mobile communication infrastructure has become a key driving force behind many new-age industries that provide several new services and products. Cellular systems have advanced from being voice service driven in the first generation (1G) in the early 1980s to being data services driven in the fifth generation (5G) now, and likely to be artificial intelligence (AI) driven in the upcoming sixth generation (6G) and beyond in the future. Starting from the early 1980s, the cellular industry has witnessed a new generation of cellular standard replacing its predecessor, once in about every decade. By that count, we are in the midst of a 5G standard which is deployed and operational, and a 6G standard which is in the making for possible deployment in the 2030s.

In the evolution from 1G to 5G, huge strides have been made in enhancing the capabilities of cellular systems through several theoretical advances and technological innovations. This flow of advances has also transformed the teaching of wireless communications [3–8]. Among the several advances and innovations that characterize the evolution of one generation to the next, physical layer waveform design stands out as a crucial enabler to achieve substantially enhanced capabilities across multiple generations. Such capabilities are often in terms of achieving increased data rate, spectral efficiency, energy efficiency, reliability, and robustness to adverse channel characteristics, to name a few. Some of the physical layer advances that distinguished different generations in the past include the following:

adoption of efficient modulation schemes (e.g., moving from analog modulation to digital modulation),

use of spread spectrum and multicarrier modulation techniques (to mitigate the effects of adverse channel characteristics),

use of higher-order modulation (to improve rate and spectral efficiency),

use of multiple antennas (to improve rate, spectral efficiency, reliability, and energy efficiency),

use of capacity achieving codes (to achieve ultra-reliable communication),

use of cooperative relaying (to increase range and improve coverage),

operation in higher and higher frequency bands (to acquire more bandwidth to increase rate),

and the list continues to grow. We can see several new physical layer techniques emerging in the technological horizon as we look for promising possibilities beyond 5G. Some of them include non-orthogonal multiple access (NOMA), reconfigurable intelligent surfaces (RIS), waveform design for robust communication in rapidly time-varying channels, integrated radar sensing and communication, cell-free communication, and millimeter wave (mmWave) and Terahertz (THz) communications.

1.1 Cellular Mobile Evolution

1G technology, called advanced mobile phone system (AMPS), provided primarily voice services using analog switching of frequency-modulated (FM) voice signals, operating in the 800–900 MHz radio frequency (RF) band. Frequency division multiple access (FDMA) technology was used to support multiple voice calls/users requiring a one-way bandwidth of 30 kHz to support a single voice call. Though a revolutionary telecommunication technology at the time, 1G suffered from inconsistent voice quality and coverage, and fared low on size, energy consumption, and security, leaving a lot of room for improvement, innovation, and growth. Following the success of 1G, second generation (2G) systems were introduced in the early 1990s, incorporating several advancements compared to 1G. Foremost among the advancements is the change in the communication waveform used, viz., a digital modulation waveform replacing the analog counterpart in 1G. The digital nature of the information signal in 2G enabled encrypted voice calls with better security. It also enabled packet transmission for data services. Being the first digital cellular standard, the data rate in 2G was quite modest, viz., about 10 kbps digitally encoded voice or data. Error correcting capability for reliable transmission was added through channel coding of information bits. The way different users are multiplexed was also changed, from FDMA in 1G to a more efficient time division multiple access (TDMA) in 2G. In Global System for Mobile communication (GSM) [3, 4