Multi-Carrier Technologies for Wireless Communication

Multi-Carrier Technologies for Wireless Communication

MULTI-CARRIER TECHNOLOGIES FOR WIRELESS COMMUNICATION

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MULTI-CARRIER TECHNOLOGIES FOR WIRELESS COMMUNICATION

KLUWER ACADEMIC PUBLISHERS

NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: 0-306-47308-9

Print ISBN: 0-792-37618-8

©2002 Kluwer Academic Publishers

New York, Boston, Dordrecht, London, Moscow

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Created in the United States of America

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AUTHOR BIOGRAPHIES

Carl R Nassar received his Bachelor’s, Master’s and Ph.D degrees all from

McGill University, Montreal, Canada, in 1989, 1990, and 1997 respectively.Between 1991 and 1992, he worked as a design engineer at CAE Electronics

In 1997, upon completion of his doctorate, Carl accepted a position as

assistant professor at McGill University In the fall of 1997, he headed for themountains of Colorado when he accepted an assistant professorship atColorado State University Since that time, Carl has founded the RAWCom(Research in Advanced Wireless Communications) laboratory at CSU He hasbeen working on the development of multi-carrier technologies for thewireless world (the topic of this book) He has authored numerous journalarticles, conference proceedings, and is also the author of the textbook

Telecommunications Demystified.

Bala Natarajan received his B.E degree in Electrical and Electronics

Engineering with distinction from Birla Institute of Technology and Science,Pilani, India in 1997 Since August 1997, he has been at the department ofElectrical and Computer Engineering, Colorado State University, where hewill complete his Ph.D in the spring of 2002 His current research interestsinclude multiple access techniques, estimation theory, multi-user detectionand channel modeling

“I am extremely grateful to my parents for the sacrifices they have made andfor imparting the values and morals that guide my life I would like to express

my gratitude and love to sister Bharathi and her wonderful family for their

support and encouragement Thanks to all the wonderful people in my lab

who have shared their joy with me and helped me live in that spirit of joy.Thank you, Carl, for being a good friend and an understanding advisor,helping me grow academically as well as spiritually Thank you God, forbeing with me, around me and in me.” – Bala Natarajan

Zhiqiang Wu received his B.S in Wireless Telecommunication from Beijing

University of Posts and Telecommunications in 1993, his M.S in ComputerSignal Processing from Peking University in 1996, and his Ph.D at ColoradoState University in Telecommunications in 2001 Between 1996 and 1998, Dr

Wu worked as a research engineer at the Software Center in China’s

Academy for Telecommunication Technology, Beijing He is co-author of thenetwork management standard for DS-CDMA in China.

“It is with great pleasure that I thank my dearest sister, Zhijin Wu, and myparents, Yuanqian Wu and Hong Xu, for their consistent and loving support.”– Zhiqiang Wu

David A Wiegandt received his Bachelor of Science degree in Electrical

Engineering from New Mexico State University in December 1999 Sincethat time, he has been pursuing a Ph.D as a graduate research assistant in theRAWCom Laboratory of Colorado State University’s Department ofElectrical and Computer Engineering Research interests are centered aroundOFDM and WLAN enhancement Work experience includes communicationlink design, channel estimation, and programmable signal processing withNew Mexico State University and Sandia National Laboratories

“I would like to extend my sincere gratitude to my parents Karl and ElizabethWiegandt Thank you for your guidance and your help, but most importantly,thank you for truly being my best friends To my sister Jennifer, I love you

To Carl and my extended RAWCom family, a special thanks for sharing thetears and the laughs It has genuinely been a pleasure.” – David Wiegandt

S Alireza Zekavat received his Bachelor’s and Master’s degrees from Shiraz

University and Sharif University of Technology, respectively He is currently

a Ph.D candidate at Colorado State University, Fort Collins, CO, U.S.A, andwill be receiving his Ph.D in the summer of 2002 His research interests areWireless Communications, Statistical Modeling, Radar Systems and NeuralNetworks

“My professional career has benefited greatly from the guidance and support Ireceived from the following wonderful people Dr H Hashemi introduced me

to the spirit of wireless communications and statistical modeling through thecourses he taught Dr Carl R Nassar supervised me during the challenges of

a Ph.D degree He is a key part of my life and career Dr D Lile’s supportwas also key to my successful academic career Fatemeh and Maryam, mywife and daughter, prepared a lovely space in my house and in my heart Myfather and mother provided unique and wonderful guidance and love Withoutthe support of all these people, throughout my life, I could not have achieved

my current level of success I love them all.” – S Alireza Zekavat

vi

Arnold Alagar has over 15 years experience in communications and software

engineering Mr Alagar co-founded Idris Communications, Inc., a researchcompany dedicated to investigating the practical applications of quantuminterferometry to communication systems In addition, Mr Alagar has over 12years experience with the transfer of technology from R&D environments topractical use At the San Diego Supercomputer Center, Mr Alagar wasinvolved with optimizing circuit simulation and design automation tools foruse on Cray supercomputers At BDM Federal and Lucent, Mr Alagar gainedextensive experience in the development and deployment of hardware andsoftware systems used for communications in mission critical operations such

as air traffic control and telecommunications

Steve Shattil holds an ME in EE from the University of Colorado, an MS in

Physics from Colorado School of Mines, and a BS in Physics from RensselaerPolytechnic Institute He serves as the co-founder, Chief Scientist and PatentCounsel at Idris Communications Inc Prior to founding Idris, he led softwaredevelopment for aviation-related information systems Mr Shattil was a

founder of Genesis Telecom and worked as a research scientist at the National

Institute of Standards and Technology He also led T Tauri Consulting, anoptical-systems design firm whose clients included Ball Corporation andOphir Corporation

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This book is a journey to the cutting edge of research in the field ofwireless telecommunications Many other books take you on a similar butaltogether different journeys: books on space-time coding, turbo-coding,OFDM, and the like Our work takes the best of what is out there today, looks

at where the wireless world wants to go, and then advances the best of thecurrent work to reach those future goals For this reason, my co-authors and Ibelieve this book will take you for the ride of your life

In many ways, as we telecommunication engineers discover time andtime again, the world of wireless telecomm is still in its infancy stages In theearly 1980’s we were humbled when it was shown that a simple merging ofchannel coding and modulation achieved large performance gains withoutbandwidth expansion (trellis coded modulation) A few years later, we weresurprised (even resistant) when we learnt how a simple iterative algorithm

could revolutionize the performance of channel coders (turbo coding) Then, a

few years back, a simple procedure was developed for locating differentcoded bits on different antennas - it dramatically improved performance(space-time codes) When ideas that are, in hinsight, so simple, yet they

radically improve the wireless world, we are forced to come to terms with a

simple realization: we are still far from making maximal use of the wirelessresource

In this book, we present you with yet another simple yet dramatic

means of better exploiting the wireless medium It is based on “smarter”

signal processing It involves the abandonment of time-based processing suchthe beloved equalizer structure and RAKE receiver It replaces these old toolswith new ones performing frequency based processing, breathing new life intoold classics such as the FFT and IFFT

We are not the first to suggest the use of frequency domainprocessing Far from it Indeed, in today’s wireless world, OFDM and MC-CDMA, both based on frequency processing, find themselves in the limelight

However, no one, to the best of our knowledge, has gone as far as thisbook does in explaining and promoting the benefits of frequency-basedprocessing We demonstrate how TDMA, DS-CDMA, OFDM, and MC-CDMA can all share a common hardware platform based on a multi-

carrier/frequency-based implementation We show how the benefits of the

proposed frequency based processing lead to a doubling in throughput ornumbers of users without cost in other system parameters and with GAINS inprobability-of-error performance The key is “smarter” frequency-basedsignal processing.

We understand that the ideas presented in this introduction mayappear controversial We only ask that you read this book with an open mind

We are confident that a careful read of this book will help you rethink the way

signal processing is performed in a world gone wireless

About this Book

Chapter 1 is a brief introduction to wireless world: where it is today,where we believe it is headed, and the role the technology outlined in thisbook can play in the evolutionary process

Chapter 2 is a key chapter, as it provides an overview of thetechnology proposed in this book Specifically, it first recaps existing multi-

carrier technologies (emphasizing OFDM and MC-CDMA), explaining the

reasons underlying their growing popularity, and summarizes how ourtechnology can lead the way toward a multi-carrier revolution

Chapters 3, 4, 5, and 6 detail how the proposed technology enhancesMC-CDMA, TDMA, DS-CDMA, and OFDM respectively Each chapterprovides the necessary background, the underlying signaling scheme, thetransmitter and receiver models, and the key performance results

Chapter 7 introduces a novel manner in which antenna array systemsmay be implemented alongside multi-carrier systems to create gains in both

performance and network capacity

We hope that you enjoy the read, and are glad to have you join us onthis ride through a new world of multi-carrier communications

x

Excellent work is a direct outcome of excellent people workingtogether I attribute the excellence this book brings to the excellent people thathave blessed my life

On the technical side of things, my thanks to my co-authors First toSteve Shattil, who four long years ago approached me with this crazy idea ofreplacing all time-based signal processing with its frequency-basedcounterpart, and helped me see his vision of a frequency-processed wireless

world Next, thanks to Arnold Alagar, who had the wisdom (or was that

daring) to bring our techie-vision to the business community

Staying on the technical end of things, my thanks to my four Ph.D.students whose hard work made this book a reality: to Bala Natarajan forjoining me on both a technical and a spiritual journey; to Zhiqiang “Jong” Wufor his relentless work ethic and uncanny ability to find new researchdirections on a near daily basis; to David Wiegandt, for his ability to

understand the relevance of our research and help us plant our seeds in the

“real-world”; and to Reza Zekavat, for his attention to detail, commitment to

hard work, and big heart

On the personal side of things, I’d like to thank my sweet wifeGretchen, who has helped me reclaim the best of who I am, and who hasgiven up so much time with me that I might pursue the endeavors that fill thisbook And what acknowledgements page would be complete without words ofgratitude to the people that brought me here in the first place, my sweet mom,Mona, and gentle dad, Rudy (and of course, sister Christine) Thanks for allthe loving

And to all those of you who have joined me on the journey and havenot found your names on this page thank you, one and all

Warmly

Carl

Dr Carl R Nassar

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2.3.1 The CI Signal2.3.2 Orthogonality Properties of the CI Signal2.3.3 Pseudo- Orthogonality Properties of CI Signals2.4 CI/MC-CDMA: The Application of the CI Signal to

MC-CDMA2.5 CI/TDMA: Multi-Carrier Implementations of TDMA

and the Demise of the Equalizer2.6 CI/DS-CDMA: A Multi-Carrier Implementation of

DS-CDMA and the Demise of the RAKEreceiver

2.7 CI/OFDM: Increasing Performance and Throughput in

OFDM and Eliminating the PAPR Problem

2.8 Summary

3 High-Performance High-Capacity MC-CDMA for Future

Generations: The CI Approach

12

1616172021

23

24

29

3337

41

4244

49

3.4 Receiver Structures

3.5 Performance Results

3.5.1 Perfect Synchronization3.5.2 Phase Jitter

3.5.3 Frequency Offset3.6 Crest Factor Considerations in CI/MC-CDMA

3.6.1 Downlink Crest Factor3.6.2 Uplink Crest Factor3.6.3 CF Reduction Technique3.7 Conclusions

Appendix 3A: Determining the Phases Minimizing Root

Mean Square CorrelationAppendix 3B: How to Generate Correlated Rayleigh

Envelopes for Use in SimulationsAppendix 3C: Derivation of MMSE Combiner in

4.2.1 Essentials4.2.2 CI Pulse Shapes for Doubling Throughput4.2.3 Bandwidth Efficiency of CI/TDMA4.3 Channel Model

7878

808181828387

89

9091

5.2.1 Introduction5.2.2 DS-CDMA Transmit and Receive Signal

5.3 Novel Multi-carrier Chip Shapes and Novel

Transmitters for DS-CDMA

5.4 Novel Receiver Design for CI/DS-CDMA

5.5 High-capacity DS-CDMA via Pseudo-Orthogonal

CI Chip Shaping

5.6 High Performance, High Capacity via a Second

Pseudo-Orthogonal Chip Shaping

5.7 Channel Model

5.8 Characterizing Performance Gains and Network

Capacity Improvements in CI/DS-CDMA

5.9 Conclusions

6 High-Performance, High-Throughput OFDM with Low

PAPR via Carrier Interferometry Phase Coding

6.1 Introduction

6.2 Novel CI Codes and OFDM Transmitter Structures

6.2.1 CI/OFDM & CI/COFDM6.2.2 Addition of Pseudo-Orthogonality to CI/OFDM

& CI/COFDM6.3 Novel OFDM Receiver Structures

6.4 Channel Modeling

6.5 Performance Results

6.6 Peak to Average Power Ratio Considerations

6.6.1 PAPR in OFDM and CI/OFDM6.6.2 PAPR in PO-CI/OFDM

6.7 Conclusions

7 The Marriage of Smart Antenna Arrays and

Multi-Carrier Systems: Spatial Sweeping, Transmit Diversity,

and Directionality

7.1 Smart Antennas with Spatial Sweeping

7.1.1 Proposed Antenna Array Structure7.1.2 Receiver Design for Smart Antenna with SpatialSweeping

7.1.3 Theoretical Performance7.1.4 Simulated Performance

xv

9193

97101

105

108114

116122

125

125127127

131

134

136137

158159162

7.2 Channel Modeling for Spatial Sweeping Smart Antennas:

Establishing the Available Transmit Diversity

7.2.1 Channel Model Assumptions7.2.2 Linear Time Varying Channel Impulse ResponseModeling

7.2.3 Evaluation of Coherence Time7.2.4 Updates to the Channel Impulse Response:

Antenna Array Factor and Phase7.3 Innovative Combining of Multi-Carrier Systems and

Smart Antennas with Spatial Sweeping

7.3.1 The Transmit Side7.3.2 The Receiver Side7.3.3 Simulated Performance

7.4 Conclusion

Index

xvi

162164

165169

170

177179181190

193

197

be expected that new discoveries and advances in technology will change and,perhaps, radically transform communication theory.

At the beginning of the last century, the inability of classical physics

to adequately describe our universe led to the development of quantumphysics This sparked a new age of understanding and technologicaldevelopment

At the beginning of this century, the inadequacy of classical access protocols used for wireless communications is driving the development

multiple-of Carrier Interferometry (CI) In an analogy to the developments in physics,

CI is based on quantum-interferometry principles that provide multiple-accessprotocols with unsurpassed improvements in capacity, signal quality, range,and power efficiency More importantly, CI provides the building blocks (i.e.,the underlying signal architecture) to build any wireless multiple-access

protocol Rooted in recent telecommunications history, CI can be understood

as a giant leap in the arena of multi-carrier technology, building on the recentsuccesses of OFDM and MC-CDMA

1.2 Unification

The capacity, reliability, and versatility of communication systemscontinues to grow as people, businesses, and government organizationsperceive a growing need for information services A global communicationnetwork known as the Internet is enabling new businesses and new ways ofdoing business The utility of the Internet ultimately depends on connectivity.This is driving the development of technologies that connect more users,provide faster connections, and simplify design of new networks But a rapid

outgrowth of technology is resulting in different wireless communication

systems that are simply not compatible with each other The time to unifywireless systems is at hand

The term “wireless communications” has come to describe a largenumber of systems and applications that service a wide variety ofcommunication needs Different transmission protocols and frequency bandscharacterize different communication markets These markets are encumbered

by technology fragmentation resulting from competitors who have a vestedinterest in promoting their own proprietary transmission protocols and signal-processing technologies This fragmentation impedes compatibility betweendifferent applications and systems, reduces bandwidth efficiency, increasesinterference, and limits the usefulness of wireless services Thus, there is anoverwhelming need to improve and unify these technologies

The idea of unifying wireless technologies is similar to some of themotives behind developing quantum physics Throughout history, the quest to

a unified understanding of natural phenomena has focused on discovering theelementary components of the universe In theory, true elementarycomponents lead to unification of the laws of physics Knowledge offundamental elements facilitates an understanding of complex combinations

of those elements, enabling a unified understanding of “everything” Inwireless telecommunications, CI can serve as a “fundamental element”,enabling all systems to be recreated by novel combining of this one

“element”, thereby unifying the field

CI provides a common signal architecture for different multiple-access techniques, in addition to vastly improving the performance of those techniques One advantage of CI development is that it enables a common network infrastructure forall types of communications Thus, resources, such as spectrum and signal power, can

be used more efficiently and without the interference problems that arise when

3separate communication systems respond to interference by simply increasing signalpower levels CI also enables a universal communication device that cancommunicate with networks that each use different multiple-access protocols.Ultimately, CI may be realized as a technology that helps people use and enjoy thefull potential of the Internet, and the full power of communicating with one another.

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In addition to the interest in multi-carrier communications, there isalso a growing interest in creating a single architecture for wireless devices:engineers envision a simple piece of software capable of switching mobilesfrom TDMA (time division multiple access) to DS-CDMA (direct sequencecode division multiple access) to MC-CDMA to OFDM, while maintaining acommon hardware platform.

In this chapter, we demonstrate how to advance existing multi-carriertechnologies to bring the vision of a common hardware platform to immediatereality, bringing the future to life today In the opening section, we review thepopular multi-carrier technologies of OFDM and MC-CDMA, explaining thereasons that underlie their growing importance In the sections that follow, weexplain how a common multi-carrier platform can be designed for TDMA,DS-CDMA, MC-CDMA and OFDM We demonstrate how, in each and everyscenario, a proposed multi-carrier platform is able to reduce complexity andoutperform existing receiver structures in multipath fading channels, due to

better exploitation of the channel diversity and a minimization of the MAI(multi-access interference) Furthermore, we demonstrate how to use theproposed multi-carrier technologies to increase network capacities (measured

by numbers of users) The mathematical justification and detailed “how-to” isnot presented in this chapter, but rather is the stuff that fills the remainingchapters of this book

2.2 Multicarrier Technologies: Past and Present

The seeds of the multicarrier revolution were first planted decadesago, but it has only been in the past several years that these seeds havebloomed

2.2.1 OFDM

Leading the charge is OFDM, short for orthogonal frequency divisionmultiplexing, first proposed in the 50’s, and only now, with substantialadvancements in DSP (digital signal processing) technology, becoming animportant part of the telecommunications landscape Some examples of therapidly growing use of OFDM include its adoption as a standard for theEuropean wireless data link known as HYPERLAN, as well as its adoption inthe US by the well-known IEEE 802.11 Perhaps of even greater importance

is the emergence of this technology as a competitor for future 4G wirelesssystems These systems, expected to emerge by the year 2010, promise to atlast deliver on the wireless Nirvana of anywhere, anytime, anythingcommunications Should OFDM gain prominence in this arena, andcompanies such as Motorola are banking on just this scenario, then OFDMwill become the technology of choice in most wireless links worldwide

The beauty of OFDM lies in its simplicity In OFDM, an incomingdata stream, most likely with a high data rate, enters at the transmitter side Asseen in Figure 1, this incoming data enters a serial to parallel converter,mapping the high rate data stream into N lower rate (parallel) data streams.Each data stream is then placed on its own carrier, and carrier spacing iscarefully selected to ensure orthogonality, i.e., to ensure that carriers can beperfectly separable one from another at the receiver side The N carriers arenext added together, modulated up to the transmit frequency, and finally sentout across the channel One trick-of-the-trade that makes these transmitterslow cost is the ability to implement the mapping of bits to unique carriers viathe use of an inverse FFT (fast Fourier transform)

The benefit of OFDM is best understood when considering the

transmission over the channel If the original high-rate data stream had been

sent “as is” across the channel (i.e., if the original data stream were simplymapped to the carrier frequency and sent over the channel), the wide

bandwidth of the transmit signal would lead to frequency selectivity That is,

because the transmitted signal would demonstrate a large frequencybandwidth (due to its high bit rate), different frequencies would experiencedifferent gains as they traveled over the wireless channel As a result, areceiver with a large computational complexity, perhaps one based on anequalizer structure, would be required The OFDM transmitter simplifies thechannel effects, and as a result the receiver design, as explained in the nextparagraph

In OFDM, the data stream is not sent out “as is”, but rather is serial toparallel converted prior to transmission This leads to N low-rate data streams,each demonstrating a narrow bandwidth (and each sent on its own carrier) As

a result, when sent over the channel, each low-rate data stream experiences aflat fade, i.e., the gain is constant over all the frequencies that make up onelow-rate data stream Here, no equalizer structure is required at the receiver

At the receiver side in OFDM, the incoming data stream is firstreturned to baseband by use of an appropriate mixer, as seen in Figure 2.Next, the incoming data stream is separated into its N low-rate data streamsby: to extract the ith low-rate data stream, apply the ith carrier’s frequencyfollowed by a low pass filter (implemented using an integrator) Once the datastreams have been separated one from another, a simple decision device isapplied (Receiver implementation can be greatly simplified by use of anFFT.)

2.2.2 Coded OFDM

Unfortunately, OFDM, when implemented as described in section2.2.1, conies with a severe drawback that limits its applicability In short,when implemented as shown in Figures 1 and 2, the performance of OFDM,measured in terms of probability of error, is very poor

The reason for the poor performance follows In each narrow bandcarrier, the low-rate data stream experiences a single gain or attenuation.While this is good from the standpoint of simplifying receiver complexity, it

is quite unfortunate when it comes to receiver performance Specifically, intimes of deep fade, i.e., in times when one of the low-rate data streamsexperiences a large attenuation, the data is effectively lost, and can not berecovered at the receiver side Since data communication typically requires aprobability of error in the order of or (one error in every 100,000 orevery 1,000,000), OFDM systems can not be used as is

To improve OFDM such that it achieves the desired performancebenchmarks, coded OFDM, or COFDM for short, was introduced The ideaunderlying coded OFDM is shown in Figure 3 Here, the incoming datastream first enters a convolutional coder, typically of rate ½ and constraintlength 7 This maps every incoming bit into two outgoing bits, with the extra

bit added to enable the receiver to detect and correct bit errors Following theconvolutional coder is an interleaver, which reorders the incoming bits.(Specifically, the interleaver spaces bits such that the 2 bits output from theconvolutional coder (for each input bit) are NOT sent on adjacent carriers, butare sent out on carriers that are far apart from one another.) Next, the usualOFDM transmitter is employed, following the description outlined in Figure 1and Subsection 2.2.1

At the receiver side (Figure 4), the received bits are returned tobaseband using an appropriately selected mixer, and the low-rate data streamsare separated from one another by application of the appropriate carrier and

an integrator After separation, the decision device of Figure 2 is replaced by:(1) a deinterleaver, which realigns the information bits in correct order (itsorder prior to interleaving), and (2) a soft-decision Viterbi decoder, whichperforms error correction and outputs corrected data bits

The benefits of COFDM (over OFDM), in terms of performanceimprovement, are two-fold First, and most apparent, is the benefit that theconvolutional channel coding brings This channel coding allows the receiver

to correct for errors in transmission The second performance benefit comesvia the interleaver, which creates a diversity benefit The interleaver ensuresthat the 2 bits output by the channel coder (for each incoming bit) are sent oncarriers that are far apart from one another This leads to a frequency diversitybenefit Specifically, since each of the 2 bits output from the channel coder ispositioned at a very different carrier, each bit experiences a unique gain (aunique fade) It is unlikely that both these bits are experiencing a deepattenuation (although one of them may be), and as a result one of the two bits(representing an initial incoming bit) is likely to make it to the receiver intact

As a direct result, probability of error performance is improved

11

2.2.3 MC-CDMA

If OFDM is the flag bearer for the multicarrier nation, leading thecharge toward a multi-carrier world, then MC-CDMA is its star athlete,

generating a second surge of interest in multi-carrier technologies

Before proceeding, a word of caution is in order The term CDMA, short for multi-carrier code division multiple access, has been used to

MC-represent three different technologies Following the notation laid out by

Ramjee Prasad, we separate the three multi-carrier technologies labeled CDMA using the naming conventions of MC-CDMA, MC-DS-CDMA, andMT-CDMA, and we focus on MC-CDMA as defined by Prasad (detailednext)

MC-MC-CDMA was first proposed in 1993 Since its inception, it has

garnished international attention, with hundreds of research articles writtenabout its promise

MC-CDMA refers to a technique for the transmission of multiple

users’ data over a set of N narrowband carriers Specifically, the problem thatMC-CDMA poses and then answers is simply this: If I divide my available

channel bandwidth into N orthogonal carriers, and I have N users who want tosend information simultaneously over these carriers, how do I go aboutallowing users to send their information over carriers?

There are many answers to this question The classic answer is to giveeach of the N users one of the N carriers, and there we have the classictechnology known as FDMA (frequency division multiple access) MC-CDMA presents a more elegant answer, one that enables significant

performance improvement relative to FDMA

In MC-CDMA, each user sends his data on all N carriers That is,

user j sends the exact same data (his own data) on all N carriers

simultaneously Another user, user k, sends his own data at the same timeover the same N carriers The problem, of course, is that the data from user jand the data from user k “collide” We must provide some way to make thedata from user j and the data from user k separable from one another at the

receiver side

To make this possible, user j applies a unique code to the N carriers(typically a series of +1 and –1 values), and user k applies a different code toall N carriers These codes are carefully selected to make the users separable

at the receiver Typically, these codes correspond to well-known spreading

codes such as Hadamard-Walch codes

Specifically, consider the transmitter for user k shown in Figure 5.Here, each information bit is split into N replicas, and each replica is put onone of the N carriers Next, a spreading code is applied to the N carriers,where this spreading code is unique to user k and typically corresponds to aset of values made up of +1 or –1 terms The carriers, each containing thesame bit, are then combined together, and this signal is modulated up to thecarrier frequency and sent out over the channel

Typically, the wireless channel effects the transmitted MC-CDMAsignal as follows Each of the N carriers is narrow in its bandwidth, and, as aresult, each experiences a flat fade (i.e., a single gain effects all thefrequencies in one carrier) However, when considering the entiretransmission bandwidth, made up of N of these narrow band carriers, we have

a wide frequency band Over this entire bandwidth, the channel is frequencyselective, meaning different carriers will experience different gains Anexample of the channel effect is illustrated in Figure 6

The MC-CDMA receiver, built to detect user k’s data, is shown inFigure 7 Here, the incoming signal is first returned to baseband byapplication of a mixer Next, the received signal is divided up into its carriercomponents by: to extract carrier i, the ith carrier frequency is appliedfollowed by a low pass filter implemented as an integrator With the receivedsignal separated into its carrier components, the carriers are next “despread”:The spreading code applied to user k is removed by application of theappropriate “despreading code” Next, the signals (one per carrier) are applied

to a combiner The combiner performs a weighted addition of the carrierterms such that it: (1) minimizes (or completely eliminates) the presence ofthe other users’ signals; (2) maximizes the frequency diversity benefit, i.e., theperformance benefit achievable by sending the information simultaneouslyover all the N carriers; and/or (3) minimizes the presence of the noise.Possible combiner techniques include the EGC (equal gain combiner), ORC(orthogonality restoring combiner), or the MMSEC (minimum mean squarederror combiner)

MC-CDMA demonstrates a number of benefits when compared to thewidely adopted DS-CDMA system The primary benefit is an improvement interms of probability of error performance, which arises from the two primaryreasons outlined next The discussion that follows assumes an understanding

First, MC-CDMA systems are capable of better exploiting the energyspread introduced by the channel That is, when one considers a RAKEreceiver used in DS-CDMA systems, these RAKE receivers typically attempt

to detect and separate the 3 or 4 highest-energy paths introduced in thechannel However, the energy is (in reality) spread out over far more pathsthat these 3 or 4, and hence the energy spread onto the other paths iscompletely lost at the DS-CDMA RAKE receiver In MC-CDMA, on theother hand, the equivalent effect to multipath (in the time domain) isfrequency-selectivity (in the frequency domain), which is completely resolved

DS-CDMA, where a time domain processing is applied, one has no control

over where the paths arrive As a result, it is not possible to effectively

separate paths Here, the SIR on each branch of the RAKE receiver is low

(relative to that in MC-CDMA carrier branches) Specifically, consider theDS-CDMA RAKE receiver, which attempts to separate paths, and assume for

a moment that there are four dominant paths the RAKE receiver is attempting

to separate When writing the output equation for each branch of the RAKEreceiver, one finds that there exists a large number of interfering terms Mostsignificant of all is the term representing interference from all N users present

on the three other paths This path-interference term demonstrates a large

power, and causes the branch terms output from the RAKE receiver todemonstrate a low SIR (i.e., large interference) By contrast, consider MC-CDMA Here, rather than attempting to separate paths in the time domain to

exploit path diversity, there is an attempt to separate narrow-band carriers in

the frequency domain to achieve frequency diversity At the transmitter side,these carriers were selected with a frequency spacing that ensured

orthogonality, and it is easily shown that carriers still remain almost perfectly

separable at the receiver side Hence, each carrier branch experiences a highSIR (low interference), and as such the MC-CDMA receiver can significantly

outperform its DS-CDMA counterpart

2.2.4 Recap

In short, OFDM and its COFDM cousin are promising technologiesdelivering high-performance and reduced receiver complexities over thewireless link, all the while supporting very high data rates MC-CDMA is apowerful multi-carrier multiple access technology, capable of significantlyoutperforming its DS-CDMA counterpart For these reasons, and many more

to be introduced next, we believe we sit at the frontier of a multi-carrier

revolution, and believe that multi-carrier technologies can be designed to

support the needs of next-generation wireless and beyond, all the whileproviding a uniform hardware platform which enables true low-cost softwareradio

2.3 The Carrier Interferometry (CI) Approach

Using a technique referred to as the Carrier Interferometry (CI)Approach, the scope and power of multi-carrier technologies is significantlyenhanced Specifically, with CI, all varieties of signals are implemented viamultiple carriers, and all multiple-access schemes, from TDMA to DS-CDMA, are implemented as multi-carrier technology

From the perspective of an outside observer, the time-domain datatransmission in CI appears unchanged (relative to today’s systems), making

CI systems backward compatible with legacy systems But by employing the

CI multi-carrier implementations at the transmitter side with simple changes

in the receiver technology, the performance (measured in terms of probability

of error) and network capacity (measured in terms of numbers of users

sharing the system, or, equivalently in terms of throughput per user) aresignificantly enhanced

2.3.1 The CI Signal

At the heart of Carrier Interferometry technology lies the signalreferred to as the Carrier Interferometry (CI) signal The CI signaldemonstrates both excellent frequency resolution and excellent timeresolution That is, the CI signal is composed of multiple narrowband carriersthat allow it to be resolved into its frequency components Additionally, whenobserved in the time domain, the CI signal is very narrow, enabling it (1) to beeasily separated from other CI signals, and (2) to resolve the channel’smultipath profiles

The CI signal, denoted c(t), is, conceptually, very simple The CI

signal is the addition of N carriers, each equally spaced by frequencyseparation All carriers are in-phase, with a zero phase offset This isillustrated in the frequency domain in Figure 8 The linear combining of thesecarriers leads to the time domain signal whose envelope is shown in Figure 9.Here, we see a periodic signal with a period each period consists of amainlobe of duration followed by times of sidelobe activity, each ofduration Within one period, the CI signal has the appearance of apulse shape

Placing this in the context of traditional communication signals, the CI signal

is a frequency sampled version of the sinc( ) waveform, whose well known

frequency-time properties are illustrated in Figure 10 That is, the CI signal is

an approximation to the sinc( ) waveform generated by frequency sampling the sinc( ) waveform using N equally spaced samples Of course, frequency

sampling leads to time repetition, which explains the periodic nature of the CIsignal

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2.3.2 Orthogonality Properties of the CI Signal

A CI signal positioned with a mainlobe centered at time 0 is

waveforms can be applied to represent information symbols locatedsequentially in time, without creating inter-symbol interference

There exists an important alternative representation to the statement:

“a CI signal positioned with a mainlobe centered at time 0 is orthogonal to a

CI signal with a mainlobe positioned at time

This alternative is explained in the next paragraph

An offset in the time domain corresponds to a linearly increasingphase offset in the frequency domain With that in mind, we note the

following equivalence A CI signal with a mainlobe positioned at time 0 is

equivalent to a CI signal with carrier 1 to carrier N exhibiting phase offsets

Correspondingly, a CI signal with time offset

is equivalent to a CI signal with carrier 1 to carrier N exhibiting

illustrated in Figure 11 Hence, the orthogonality between CI signals can beunderstood as either: (1) CI signals with an appropriate time separation

are orthogonal to one another, or (2) CI signals,

with carriers coded with an appropriate “complex spreading sequence”,namely

are orthogonal to one another

orthogonal to a CI signal with its mainlobe positioned at time whenever is

2.3.3 Pseudo-Orthogonality Properties of CI Signals

Consider two sets of CI signals:

Set l:

These sets of CI signals are illustrated in Figure 12 (with N = 8) Referring tothe discussion of the previous subsection, the CI signals in set 1 areorthogonal to one another, and the CI signals in set 2 are orthogonal to oneanother However, the CI signals in set 1 are not orthogonal to the CI signals

in set 2 We seek the value of that minimizes the mean squared value of theinterference between the signals of set 1 and set 2 A mathematical derivationconfirms the intuitively pleasing result: select pictorially, this isshown in Figure 12, and conceptually, this corresponds to the rather simple

notion of placing the second set of signals in the “middle” of the first set ofsignals

Of particular interest is the following result: with the

interference between the signals of set 1 and the signals of set 2 is small(characterized in future chapters)

Expressing this result in terms of phase offsets, we can state thefollowing (by simply recognizing the equivalence between shifts in the time

domain and linearly-increasing phase offsets in the frequency domain)

Consider two sets of CI signals:

Set 1:

where

CI signal with carriers {1,2, ,N} demonstrating phase offsets

Set 2:

where

CI signal with carriers {1,2, ,N} demonstrating phase offsets

The CI signals in set 1 are orthogonal to one another, as are the CIsignals in set 2 The CI signals in set 1 and set 2 are not orthogonal to oneanother, but demonstrate a minimal amount of interference when

This is equivalent to the earlier statement, with shifts in the time domainreplaced by offsets in the frequency domain

2.4 CI/CDMA: The application of the CI signal to CDMA

MC-The MC-CDMA transmitter (for user k) is illustrated in the earlier

Figure 5 Here, the input signal is first split into N branches, and the signal oneach branch is modulated onto one of N carriers Each carrier is then coded

with user k’s spreading code; a recombining and modulation to the passbandoccurs; and the signal is sent out over the channel Of particular relevance tothis subsection is the spreading code applied to user k Typically, itcorresponds to well-known codes, where each code value is either +1 or –1,e.g., the Hadamard-Walsh spreading codes or Gold codes

To apply the CI concept to MC-CDMA, we simply replace the usual

spreading codes (e.g., (+1, -1,+1, ,-1)) with the “complex spreading codes”

that make up the CI signal That is, the spreading codes for user k are now

application of these spreading codes, each user’s code now corresponds to one

of the CI signals shown in the solid line of Figure 12

With this selection of CI codes, N users (k=l,2, ,N) can besupported orthogonally, with each user receiving one of the CI signals shown

in the solid line of Figure 12 If, however, additional users wish to besupported by the MC-CDMA system, these users can be introduced (in apseudo-orthogonal manner) by assigning user the spreading code