Multi-Carrier Technologies For Wireless Communication

MULTI-CARRIER TECHNOLOGIES FOR WIRELESS COMMUNICATION

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MULTI-CARRIER TECHNOLOGIES FOR WIRELESS COMMUNICATION

by

Carl R. Nassar, B. Natarajan, Z. Wu D. Wiegandt, S. A. Zekavat Colorado State University

S. Shattil

Idris Communications

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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 the mountains of Colorado when he accepted an assistant professorship at Colorado State University. Since that time, Carl has founded the RAWCom (Research in Advanced Wireless Communications) laboratory at CSU. He has been working on the development of multi-carrier technologies for the wireless world (the topic of this book). He has authored numerous journal articles, 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 of Electrical and Computer Engineering, Colorado State University, where he will complete his Ph.D. in the spring of 2002. His current research interests include multiple access techniques, estimation theory, multi-user detection and channel modeling.

“I am extremely grateful to my parents for the sacrifices they have made and for 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, for being 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 Computer Signal Processing from Peking University in 1996, and his Ph.D. at Colorado State 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 the network management standard for DS-CDMA in China.

“It is with great pleasure that I thank my dearest sister, Zhijin Wu, and my parents, 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. Since that time, he has been pursuing a Ph.D. as a graduate research assistant in the RAWCom Laboratory of Colorado State University’s Department of Electrical and Computer Engineering. Research interests are centered around OFDM and WLAN enhancement. Work experience includes communication link design, channel estimation, and programmable signal processing with New Mexico State University and Sandia National Laboratories.

“I would like to extend my sincere gratitude to my parents Karl and Elizabeth Wiegandt. 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 the tears 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, and will be receiving his Ph.D. in the summer of 2002. His research interests are Wireless Communications, Statistical Modeling, Radar Systems and Neural Networks. “My professional career has benefited greatly from the guidance and support I received from the following wonderful people. Dr. H. Hashemi introduced me to the spirit of wireless communications and statistical modeling through the courses 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 support was also key to my successful academic career. Fatemeh and Maryam, my wife and daughter, prepared a lovely space in my house and in my heart. My father and mother provided unique and wonderful guidance and love. Without the 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 research company dedicated to investigating the practical applications of quantum interferometry to communication systems. In addition, Mr. Alagar has over 12 years experience with the transfer of technology from R&D environments to practical use. At the San Diego Supercomputer Center, Mr. Alagar was involved with optimizing circuit simulation and design automation tools for use on Cray supercomputers. At BDM Federal and Lucent, Mr. Alagar gained extensive experience in the development and deployment of hardware and software 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 Rensselaer Polytechnic Institute.. He serves as the co-founder, Chief Scientist and Patent Counsel at Idris Communications Inc. Prior to founding Idris, he led software development 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, an optical-systems design firm whose clients included Ball Corporation and Ophir Corporation.

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PREFACE

This book is a journey to the cutting edge of research in the field of wireless telecommunications. Many other books take you on a similar but altogether 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 the current work to reach those future goals. For this reason, my co-authors and I believe this book will take you for the ride of your life. In many ways, as we telecommunication engineers discover time and time again, the world of wireless telecomm is still in its infancy stages. In the early 1980’s we were humbled when it was shown that a simple merging of channel coding and modulation achieved large performance gains without bandwidth expansion (trellis coded modulation). A few years later, we were surprised (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 different coded 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 wireless resource. 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 such the beloved equalizer structure and RAKE receiver. It replaces these old tools

with new ones performing frequency based processing, breathing new life into old classics such as the FFT and IFFT. We are not the first to suggest the use of frequency domain processing. Far from it. Indeed, in today’s wireless world, OFDM and MCCDMA, both based on frequency processing, find themselves in the limelight. However, no one, to the best of our knowledge, has gone as far as this book does in explaining and promoting the benefits of frequency-based processing. We demonstrate how TDMA, DS-CDMA, OFDM, and MCCDMA can all share a common hardware platform based on a multicarrier/frequency-based implementation. We show how the benefits of the

proposed frequency based processing lead to a doubling in throughput or numbers of users without cost in other system parameters and with GAINS in probability-of-error performance. The key is “smarter” frequency-based signal processing. We understand that the ideas presented in this introduction may appear 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 this book can play in the evolutionary process. Chapter 2 is a key chapter, as it provides an overview of the technology proposed in this book. Specifically, it first recaps existing multicarrier technologies (emphasizing OFDM and MC-CDMA), explaining the

reasons underlying their growing popularity, and summarizes how our technology can lead the way toward a multi-carrier revolution. Chapters 3, 4, 5, and 6 detail how the proposed technology enhances MC-CDMA, TDMA, DS-CDMA, and OFDM respectively. Each chapter provides the necessary background, the underlying signaling scheme, the transmitter and receiver models, and the key performance results. Chapter 7 introduces a novel manner in which antenna array systems may 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 on this ride through a new world of multi-carrier communications.

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ACKNOWLEDGEMENTS

Excellent work is a direct outcome of excellent people working together. I attribute the excellence this book brings to the excellent people that have blessed my life.

On the technical side of things, my thanks to my co-authors. First to Steve Shattil, who four long years ago approached me with this crazy idea of replacing all time-based signal processing with its frequency-based counterpart, 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 for joining me on both a technical and a spiritual journey; to Zhiqiang “Jong” Wu for his relentless work ethic and uncanny ability to find new research

directions 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 wife Gretchen, who has helped me reclaim the best of who I am, and who has given up so much time with me that I might pursue the endeavors that fill this book. And what acknowledgements page would be complete without words of gratitude 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 all the loving. And to all those of you who have joined me on the journey and have not found your names on this page...thank you, one and all. Warmly Carl Dr. Carl R. Nassar

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CONTENTS

1

2

3

Introduction

1

1.1 Multi-Carrier Technology and Carrier Interferometry: A Quantum Leap? 1.2 Unification

1 2

Overview of Multi-Carrier Technologies

5

2.1 Introduction 2.2 Multi-Carrier Technologies: Past and Present 2.2.1 OFDM 2.2.2 Coded OFDM 2.2.3 MC-CDMA 2.2.4 Recap 2.3 The Carrier Interferometry (CI) Approach 2.3.1 The CI Signal 2.3.2 Orthogonality Properties of the CI Signal 2.3.3 Pseudo- Orthogonality Properties of CI Signals 2.4 CI/MC-CDMA: The Application of the CI Signal to MC-CDMA 2.5 CI/TDMA: Multi-Carrier Implementations of TDMA and the Demise of the Equalizer 2.6 CI/DS-CDMA: A Multi-Carrier Implementation of DS-CDMA and the Demise of the RAKE receiver 2.7 CI/OFDM: Increasing Performance and Throughput in OFDM and Eliminating the PAPR Problem 2.8 Summary

5 6 6 8 12 16 16 17 20 21

23 24 29 33 37

High-Performance High-Capacity MC-CDMA for Future Generations: The CI Approach

41

3.1 Introduction 3.2 CI/MC-CDMA Signaling and Transmitter Model 3.3 Channel Model

42 44 49

3.4 Receiver Structures 3.5 Performance Results 3.5.1 Perfect Synchronization 3.5.2 Phase Jitter 3.5.3 Frequency Offset 3.6 Crest Factor Considerations in CI/MC-CDMA 3.6.1 Downlink Crest Factor 3.6.2 Uplink Crest Factor 3.6.3 CF Reduction Technique 3.7 Conclusions

50 52 52 53 55 58 60 60 62 64

Appendix 3A: Determining the Phases Minimizing Root Mean Square Correlation Appendix 3B: How to Generate Correlated Rayleigh

65

Envelopes for Use in Simulations

4

5

66

Appendix 3C: Derivation of MMSE Combiner in CI/MC-CDMA Receeiver

69

High Performance, High Throughput TDMA via Multi-Carrier Implementations

75

4.1 Introduction 4.1.1 Overview of TDMA and GSM 4.1.2 Overview of the CI Approach 4.1.3 Introducing CI to TDMA 4.2 CI Pulse Shaping in TDMA 4.2.1 Essentials 4.2.2 CI Pulse Shapes for Doubling Throughput 4.2.3 Bandwidth Efficiency of CI/TDMA 4.3 Channel Model 4.4 CI/TDMA Receiver 4.5 Performance Results 4.6 Conclusions

75 75 77 77 78 78 80 81 81 82 83 87

High-Perfomance, High-Capacity DS-CDMA via Multicarrier Implementation

89

5.1 Introduction 5.2 Review of DS-CDMA

90 91

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5.2.1 Introduction 5.2.2 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/COFDM 6.2.2 Addition of Pseudo-Orthogonality to CI/OFDM & CI/COFDM 6.3 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/OFDM 6.6.2 PAPR in PO-CI/OFDM 6.7 Conclusions

7

The Marriage of Smart Antenna Arrays and MultiCarrier Systems: Spatial Sweeping, Transmit Diversity, and Directionality 7.1 Smart Antennas with Spatial Sweeping 7.1.1 Proposed Antenna Array Structure 7.1.2 Receiver Design for Smart Antenna with Spatial Sweeping 7.1.3 Theoretical Performance 7.1.4 Simulated Performance xv

91 93 97 101 105 108 114 116 122

125 125 127 127

131 134 136 137 140 141 144 147

151

153 154

158 159 162

7.2 Channel Modeling for Spatial Sweeping Smart Antennas: Establishing the Available Transmit Diversity 7.2.1 Channel Model Assumptions 7.2.2 Linear Time Varying Channel Impulse Response Modeling 7.2.3 Evaluation of Coherence Time 7.2.4 Updates to the Channel Impulse Response: Antenna Array Factor and Phase 7.3 Innovative Combining of Multi-Carrier Systems and Smart Antennas with Spatial Sweeping 7.3.1 The Transmit Side 7.3.2 The Receiver Side 7.3.3 Simulated Performance

162

164 165 169 170 177 179 181 190 193

7.4 Conclusion

197

Index

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Chapter 1 INTRODUCTION

1.1 Mutli-Carrier Technology and Carrier Interferometry: A Quantum Leap? The field of wireless radio communications is a young one, dating back only 100 years or so. In many ways, wireless communications is still in its stages of early development, its “primitive stage”. Thus, at this time, it can 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 quantum physics. This sparked a new age of understanding and technological development. At the beginning of this century, the inadequacy of classical multipleaccess protocols used for wireless communications is driving the development of Carrier Interferometry (CI). In an analogy to the developments in physics, CI is based on quantum-interferometry principles that provide multiple-access protocols 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

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protocol. Rooted in recent telecommunications history, CI can be understood as a giant leap in the arena of multi-carrier technology, building on the recent successes of OFDM and MC-CDMA.

1.2 Unification The capacity, reliability, and versatility of communication systems continues to grow as people, businesses, and government organizations perceive a growing need for information services. A global communication network known as the Internet is enabling new businesses and new ways of doing 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 unify wireless systems is at hand. The term “wireless communications” has come to describe a large number of systems and applications that service a wide variety of communication needs. Different transmission protocols and frequency bands characterize different communication markets. These markets are encumbered by technology fragmentation resulting from competitors who have a vested interest in promoting their own proprietary transmission protocols and signalprocessing technologies. This fragmentation impedes compatibility between different applications and systems, reduces bandwidth efficiency, increases interference, and limits the usefulness of wireless services. Thus, there is an overwhelming need to improve and unify these technologies. The idea of unifying wireless technologies is similar to some of the motives behind developing quantum physics. Throughout history, the quest to a unified understanding of natural phenomena has focused on discovering the elementary components of the universe. In theory, true elementary components lead to unification of the laws of physics. Knowledge of fundamental elements facilitates an understanding of complex combinations of those elements, enabling a unified understanding of “everything”. In wireless 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 for all types of communications. Thus, resources, such as spectrum and signal power, can be used more efficiently and without the interference problems that arise when

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

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Chapter 2 OVERVIEW OF MULTI-CARRIER TECHNOLOGIES Past, Present, and Future

2.1 Introduction In the rapidly growing world of wireless telecommunications, a number of trends are gaining widespread popularity. Among these is the explosion of interest in multi-carrier communications, and its application to wireless multiple-access. In particular, there has been a great deal of research and development of late in areas of OFDM (orthogonal frequency division multiplexing) and MC-CDMA (multi-carrier code division multiple access). In addition to the interest in multi-carrier communications, there is also a growing interest in creating a single architecture for wireless devices: engineers envision a simple piece of software capable of switching mobiles from TDMA (time division multiple access) to DS-CDMA (direct sequence code division multiple access) to MC-CDMA to OFDM, while maintaining a common hardware platform. In this chapter, we demonstrate how to advance existing multi-carrier technologies to bring the vision of a common hardware platform to immediate reality, bringing the future to life today. In the opening section, we review the popular multi-carrier technologies of OFDM and MC-CDMA, explaining the reasons that underlie their growing importance. In the sections that follow, we explain how a common multi-carrier platform can be designed for TDMA, DS-CDMA, MC-CDMA and OFDM. We demonstrate how, in each and every scenario, a proposed multi-carrier platform is able to reduce complexity and outperform existing receiver structures in multipath fading channels, due to

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better exploitation of the channel diversity and a minimization of the MAI (multi-access interference). Furthermore, we demonstrate how to use the proposed multi-carrier technologies to increase network capacities (measured by numbers of users). The mathematical justification and detailed “how-to” is not presented in this chapter, but rather is the stuff that fills the remaining chapters of this book.

2.2 Multicarrier Technologies: Past and Present The seeds of the multicarrier revolution were first planted decades ago, but it has only been in the past several years that these seeds have bloomed. 2.2.1 OFDM

Leading the charge is OFDM, short for orthogonal frequency division multiplexing, first proposed in the 50’s, and only now, with substantial advancements in DSP (digital signal processing) technology, becoming an important part of the telecommunications landscape. Some examples of the rapidly growing use of OFDM include its adoption as a standard for the European wireless data link known as HYPERLAN, as well as its adoption in the 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 wireless systems. These systems, expected to emerge by the year 2010, promise to at last deliver on the wireless Nirvana of anywhere, anytime, anything communications. Should OFDM gain prominence in this arena, and companies such as Motorola are banking on just this scenario, then OFDM will become the technology of choice in most wireless links worldwide.

The beauty of OFDM lies in its simplicity. In OFDM, an incoming data stream, most likely with a high data rate, enters at the transmitter side. As seen 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 is carefully selected to ensure orthogonality, i.e., to ensure that carriers can be perfectly separable one from another at the receiver side. The N carriers are next added together, modulated up to the transmit frequency, and finally sent out across the channel. One trick-of-the-trade that makes these transmitters low cost is the ability to implement the mapping of bits to unique carriers via the 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

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sent “as is” across the channel (i.e., if the original data stream were simply mapped 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 frequency bandwidth (due to its high bit rate), different frequencies would experience different gains as they traveled over the wireless channel. As a result, a receiver with a large computational complexity, perhaps one based on an equalizer structure, would be required. The OFDM transmitter simplifies the channel effects, and as a result the receiver design, as explained in the next paragraph.

In OFDM, the data stream is not sent out “as is”, but rather is serial to parallel 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 a flat fade, i.e., the gain is constant over all the frequencies that make up one low-rate data stream. Here, no equalizer structure is required at the receiver. At the receiver side in OFDM, the incoming data stream is first returned 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 streams by: to extract the ith low-rate data stream, apply the ith carrier’s frequency followed by a low pass filter (implemented using an integrator). Once the data streams have been separated one from another, a simple decision device is applied. (Receiver implementation can be greatly simplified by use of an FFT.)

8

2.2.2 Coded OFDM

9

Unfortunately, OFDM, when implemented as described in section 2.2.1, 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 band carrier, 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, in times of deep fade, i.e., in times when one of the low-rate data streams experiences a large attenuation, the data is effectively lost, and can not be recovered at the receiver side. Since data communication typically requires a probability of error in the order of or (one error in every 100,000 or every 1,000,000), OFDM systems can not be used as is. To improve OFDM such that it achieves the desired performance benchmarks, coded OFDM, or COFDM for short, was introduced. The idea underlying coded OFDM is shown in Figure 3. Here, the incoming data stream first enters a convolutional coder, typically of rate ½ and constraint length 7. This maps every incoming bit into two outgoing bits, with the extra

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

At the receiver side (Figure 4), the received bits are returned to baseband using an appropriately selected mixer, and the low-rate data streams are 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 (its order prior to interleaving), and (2) a soft-decision Viterbi decoder, which performs error correction and outputs corrected data bits. The benefits of COFDM (over OFDM), in terms of performance improvement, are two-fold. First, and most apparent, is the benefit that the convolutional channel coding brings. This channel coding allows the receiver to correct for errors in transmission. The second performance benefit comes via the interleaver, which creates a diversity benefit. The interleaver ensures that the 2 bits output by the channel coder (for each incoming bit) are sent on carriers that are far apart from one another. This leads to a frequency diversity benefit. Specifically, since each of the 2 bits output from the channel coder is positioned at a very different carrier, each bit experiences a unique gain (a unique fade). It is unlikely that both these bits are experiencing a deep attenuation (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.

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2.2.3 MC-CDMA If OFDM is the flag bearer for the multicarrier nation, leading the charge 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 MCCDMA, short for multi-carrier code division multiple access, has been used to represent three different technologies. Following the notation laid out by

Ramjee Prasad, we separate the three multi-carrier technologies labeled MCCDMA using the naming conventions of MC-CDMA, MC-DS-CDMA, and MT-CDMA, and we focus on MC-CDMA as defined by Prasad (detailed next). MC-CDMA was first proposed in 1993. Since its inception, it has

garnished international attention, with hundreds of research articles written about 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 that MC-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 to send information simultaneously over these carriers, how do I go about allowing users to send their information over carriers? There are many answers to this question. The classic answer is to give each of the N users one of the N carriers, and there we have the classic technology known as FDMA (frequency division multiple access). MCCDMA 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 time over the same N carriers. The problem, of course, is that the data from user j and the data from user k “collide”. We must provide some way to make the data 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 to all 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.

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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 on one 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 a set of values made up of +1 or –1 terms. The carriers, each containing the same bit, are then combined together, and this signal is modulated up to the carrier frequency and sent out over the channel.

Typically, the wireless channel effects the transmitted MC-CDMA signal as follows. Each of the N carriers is narrow in its bandwidth, and, as a result, each experiences a flat fade (i.e., a single gain effects all the frequencies in one carrier). However, when considering the entire transmission bandwidth, made up of N of these narrow band carriers, we have a wide frequency band. Over this entire bandwidth, the channel is frequency selective, meaning different carriers will experience different gains. An example of the channel effect is illustrated in Figure 6.

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The MC-CDMA receiver, built to detect user k’s data, is shown in Figure 7. Here, the incoming signal is first returned to baseband by application of a mixer. Next, the received signal is divided up into its carrier components by: to extract carrier i, the ith carrier frequency is applied followed by a low pass filter implemented as an integrator. With the received signal separated into its carrier components, the carriers are next “despread”: The spreading code applied to user k is removed by application of the appropriate “despreading code”. Next, the signals (one per carrier) are applied to a combiner. The combiner performs a weighted addition of the carrier terms such that it: (1) minimizes (or completely eliminates) the presence of the other users’ signals; (2) maximizes the frequency diversity benefit, i.e., the performance benefit achievable by sending the information simultaneously over 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 squared error combiner). MC-CDMA demonstrates a number of benefits when compared to the widely adopted DS-CDMA system. The primary benefit is an improvement in terms of probability of error performance, which arises from the two primary reasons outlined next. The discussion that follows assumes an understanding

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of multipath fading and its duality in the frequency domain, frequencyselective fading.

In MC-CDMA, performance benefits are achieved by combining across carriers to maximize frequency diversity benefits. In contrast, in DSCDMA, performance benefits are achieved by combining across paths in the multipath communication channel (typically using a RAKE receiver). Since the multipath effect is the dual of frequency-selectivity, the path diversity achieved via DS-CDMA should, one would imagine, be identical to the frequency diversity available in MC-CDMA. As it turns out, this is not the case, with MC-CDMA capable of significantly outperforming its DS-CDMA counterpart. There are two reasons for this, the latter being far more important than the former. First, MC-CDMA systems are capable of better exploiting the energy spread introduced by the channel. That is, when one considers a RAKE receiver used in DS-CDMA systems, these RAKE receivers typically attempt to detect and separate the 3 or 4 highest-energy paths introduced in the channel. However, the energy is (in reality) spread out over far more paths that these 3 or 4, and hence the energy spread onto the other paths is completely lost at the DS-CDMA RAKE receiver. In MC-CDMA, on the other hand, the equivalent effect to multipath (in the time domain) is frequency-selectivity (in the frequency domain), which is completely resolved

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by the multiple carriers and can be fully exploited by the cross-carrier combiner at the MC-CDMA receiver side (Figure 7).

More importantly, when the MC-CDMA receiver separates carriers (Figure 7), one observes little to no inter-carrier interference. That is, the SIR (signal to interference ratio) on each carrier branch (Figure 7) is very large. In 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 the DS-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 RAKE receiver, one finds that there exists a large number of interfering terms. Most significant 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 to demonstrate a low SIR (i.e., large interference). By contrast, consider MCCDMA. 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 high SIR (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 technologies delivering high-performance and reduced receiver complexities over the wireless link, all the while supporting very high data rates. MC-CDMA is a powerful multi-carrier multiple access technology, capable of significantly outperforming 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 while providing a uniform hardware platform which enables true low-cost software radio.

2.3 The Carrier Interferometry (CI) Approach

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

From the perspective of an outside observer, the time-domain data transmission 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) are significantly enhanced. 2.3.1 The CI Signal

At the heart of Carrier Interferometry technology lies the signal referred to as the Carrier Interferometry (CI) signal. The CI signal demonstrates both excellent frequency resolution and excellent time resolution. That is, the CI signal is composed of multiple narrowband carriers that allow it to be resolved into its frequency components. Additionally, when observed in the time domain, the CI signal is very narrow, enabling it (1) to be easily separated from other CI signals, and (2) to resolve the channel’s multipath profiles. The CI signal, denoted c(t), is, conceptually, very simple. The CI signal is the addition of N carriers, each equally spaced by frequency separation All carriers are in-phase, with a zero phase offset. This is illustrated in the frequency domain in Figure 8. The linear combining of these carriers 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 a mainlobe of duration followed by times of sidelobe activity, each of duration Within one period, the CI signal has the appearance of a pulse shape.

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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 CI signal.

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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 orthogonal to a CI signal with its mainlobe positioned at time whenever is a value in the set This property assures us that CI waveforms can be applied to represent information symbols located sequentially 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 increasing phase 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 phase offsets This is illustrated in Figure 11. Hence, the orthogonality between CI signals can be understood 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.

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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 to the discussion of the previous subsection, the CI signals in set 1 are orthogonal to one another, and the CI signals in set 2 are orthogonal to one another. 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 the interference between the signals of set 1 and set 2. A mathematical derivation confirms the intuitively pleasing result: select pictorially, this is shown in Figure 12, and conceptually, this corresponds to the rather simple

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

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 the following (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

Set 2:

phase offsets

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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 CI signals in set 2. The CI signals in set 1 and set 2 are not orthogonal to one another, but demonstrate a minimal amount of interference when This is equivalent to the earlier statement, with shifts in the time domain replaced by offsets in the frequency domain.

2.4 CI/MC-CDMA: The application of the CI signal to MCCDMA 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 on each 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 passband occurs; and the signal is sent out over the channel. Of particular relevance to this subsection is the spreading code applied to user k. Typically, it

corresponds 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 selected as the set By 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 be supported orthogonally, with each user receiving one of the CI signals shown in the solid line of Figure 12. If, however, additional users wish to be supported by the MC-CDMA system, these users can be introduced (in a pseudo-orthogonal manner) by assigning user the spreading code where In this way, an additional N pseudo-orthogonal users (users are supported by assigning, to these users, codes corresponding to CI signals pseudo-orthogonal to the original N user’s CI signals. This is seen in Figure 12, where the dotted CI signals represents the new users’ codes

24 in accordance with minimizing the mean squared MAI (multi-access interference)).

This CI/MC-CDMA system demonstrates “flexibility with elegance”: when N users or less are to be supported, the CI/MC-CDMA system supports these users orthogonally; when additional users request service, these users are supported in a pseudo-orthogonal manner.

Most impressive of all is the performance curve of MC-CDMA when multi-carrier codes correspond to CI signals. Applying the complex spreading codes associated with CI signals, performance curves typified by Figure 13 result. From this curve, it is evident that with 2N=64 users occupying an MCCDMA system with CI codes, the performance is effectively identical to that of an MC-CDMA system supporting only N=32 users with Hadamard-Walsh spreading codes. In MC-CDMA, CI codes are capable of supporting twice as many users, doubling network capacity, without performance degradation.

2.5 CI/TDMA: Multicarrier Implementations of TDMA & The Demise of the Equalizer

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The Carrier Interferometry approach in general and the CI signal in particular are easily extended to TDMA systems with impressive results in terms of both performance and network capacity.

Consider Figure 14, a conceptual representation of the modulator used in TDMA. In modern-day communication systems, the pulse shape p(t) used to modulate the data is either the sinc( ) pulse shape or the root raised cosine pulse shape. Since the CI signal c(t) represents a sampled version of the sinc( ) pulse shape, and satisfies the same Nyquist criteria for zero ISI, we apply Carrier Interferometry to TDMA by setting the pulse shape p(t) to the CI signal c(t). While this appears to be a minor revision, it creates a dramatic improvement in terms of both performance and network capacity, as outlined next. First, we demonstrate the performance improvement, based on a redesigning of the receiver. Typically in TDMA, upon transmission over a wireless link, the channel introduces a multipath effect, representing a major roadblock to successful data detection. In order to overcome this roadblock, TDMA receivers are built with equalizers, which (in essence) attempt to undo the multipath effect by approximating a filter which inverts the multipath effect. The equalizer effectively aligns (in time) the multiple paths, and linearly recombines them, allowing the receiver to benefit from the energy spread among the many paths. Although many equalizer structures are available, the most popular among these is the DFE (differential feedback equalizer).

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In CI/TDMA, i.e., TDMA where the pulse shaping filter is matched to the CI signal c(t), the equalizer is abandoned, replaced by a frequency recombining receiver structure shown in Figure 15. Recall that the CI signal c(t) is decomposable into its N frequency components. The first task implemented by the receiver is the breakdown of the CI signal into its N frequency components. While frequency selective fading exists over the entire transmit bandwidth, the N narrowband frequency components of the CI signal allow it to be resolved into N bands each experiencing a flat fade. A combiner is then applied which, much like that in the CI/MC-CDMA receiver, serves to (1) maximize the frequency diversity benefit available across the frequency selective channel, (2) minimize any inter-bit interference introduced by the channel, and/or (3) minimize the additive noise.

When TDMA receivers employ frequency domain processing, they easily outperform traditional TDMA with equalizer processing in the time domain. This is shown in Figure 16. Here, probability of error performance versus SNR is demonstrated over a Hilly Terrain fading channel. Over l0dB performance gain is available at probability of errors of (with gains increasing at lower probability of errors).

Next, we demonstrate a significant throughput benefit, trading in a small percentage of our performance gain for dramatic increases in TDMA throughputs. For quite some time now, CDMA has held one very significant benefit over its TDMA counterpart: CDMA can support not only orthogonal codes, but pseudo-orthogonal codes as well. As a result, CDMA system promise increased network capacity (as measured by numbers of users) or throughput (measured by bits/sec/user). However, with CI/TDMA, TDMA can now claim the same benefit, i.e., TDMA can also increase its throughput in much the same way as CDMA, not with pseudo-orthogonal codes, but with pseudo-orthogonal pulse shapes. Returning to the presentation of CI signals and their properties, it was shown that, given N orthogonal carriers, frequency separated by N orthogonal CI signals can be located at positions Additionally, an extra set of N CI signals can be introduced pseudoorthogonally at times This was shown pictorially in Figure 12. In terms of the current TDMA discussion, this corresponds to: In a length N TDMA burst, locate N information bearing pulses at the usual times and place an additional set of N information bearing pulses at times This leads to a total of 2N information bearing pulses in a length-N burst, which doubles throughput. The cost, of course, is a degradation in probability of error performance because we are introducing a carefully-controlled amount of ISI (intersymbol interference) at the transmitter side.

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The probability of error performance is evaluated for a TDMA transmitter sending 2N information symbols in a packet that would typically hold N orthogonal symbols, and with a receiver designed based on frequency recombining principles of Figure 15. The performance is plotted in Figure 17, where we see that doubling the throughput leads to a degradation in performance relative to the CI/TDMA system operating with only N symbols

per burst. However, CI/TDMA with 2N symbols per burst still outperforms tradition TDMA (with the usual N symbols per burst and using a DFE equalizer) by 9 dB at a probability of error of In short, by application of the CI pulse shape in TDMA, we are able to construct a new receiver which performs a frequency recombining. This receiver enables CI/TDMA to significantly outperform TDMA systems operating with a usual equalizer-based receiver. We can trade off small amounts of performance improvement for a doubling of throughput (based on pseudo-orthogonal placement of CI pulse shapes). This enables CI/TDMA to double throughput while notably outperforming TDMA with equalizer-based receivers.

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2.6 CI/DS-CDMA: A Multi-Carrier Implementation of DSCDMA and The Demise of the RAKE Receiver The Carrier Interferometry principle in general, and the CI signal in

particular, can be applied to DS-CDMA, offering significant benefits in terms

of performance and network capacity. The application of the CI signal to DS-CDMA is similar to its application in TDMA. Specifically, in TDMA, the key upgrade took place at the transmitter side, where the usual sinc( ) and raised cosine pulse shapes were replaced by the CI signal c(t), i.e., the pulse shape p(t)=c(t) This same principle applies to chip shaping in DS-CDMA.

Specifically, in DS-CDMA, each user’s code consists of a spreading sequence (a sequence of values typically +1 or –1 each) applied to N chip

shapes, each separated in time by chip duration This code generation at the transmitter side is illustrated in Figure 18. Now, we update the chip shaping in DS-CDMA to create CI/DS-CDMA. Specifically, we replace the usual chip shaping filter at the code generator (Figure 18) with a chip shaping filter

matched to the CI signal c(t). This enables improvements in performance and network capacity as outlined next.

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Typically, when a DS-CDMA signal is transmitted over a wireless link, the major channel impairment is the multipath effect. The DS-CDMA receiver attempts to turn this impairment to its advantage by use of a RAKE receiver, which, to the best of its ability, separates the multiple paths, realigns them, then recombines them in a way to optimizes receiver performance. However, the RAKE receiver’s performance, as discussed earlier, is limited by its inability to effectively separate paths from one another. When DS-CDMA is used with CI chip shapes, i.e., in CI/DS-CDMA, the RAKE receiver is abandoned, and in its place a receiver based on frequency decomposition and recombining is applied. Specifically, at the receiver side, each chip is separated into its N frequency components and recombined in a manner that enables (1) optimal frequency diversity benefits, (2) minimal inter-chip interference, and (3) a reduction in additive noise power. Upon frequency recombining of each chip, the DS-CDMA spreading codes are applied to the chips to separate users one from another (in the usual DS-CDMA manner). The details of this receiver structure and its implementation is the stuff of a later chapter. Impressive performance benefits are available via the new frequencybased DS-CDMA receiver, which replaces the traditional RAKE receiver when CI chips shapes are used at the transmitter side. Figure 19 plots a typical

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performance comparison, showing probability of error versus SNR for a fully loaded DS-CDMA system with a processing gain of 32. Here, the performance of a typical DS-CDMA RAKE receiver levels off at a high probability of error due to the damaging effects of (large) inter-path interference. The CI/DS-CDMA system, on the other hand, demonstrates a probability of error performance that continues to improve as SNR increases. At probability of errors of a 14 dB performance improvement is evident. This gain results from the frequency processing benefit discussed when comparing MC-CDMA with DS-CDMA, namely: the carriers which make up the frequency decomposable CI chip are orthogonal to one another, allowing carriers to be separated and recombined in a manner optimizing diversity gain without interference from other diversity channels.

Some of the performance improvement of CI/DS-CDMA can be traded in for an increase in network capacity, much like in the CI/TDMA case. Specifically, in CI/DS-CDMA, rather than place N CI-shaped chips in a system with processing gain N, we place 2N CI-shaped chips in the same time duration and bandwidth. The result is inter-chip interference introduced at the transmitter side, which leads to a performance degradation at the receiver. The benefit, of course, is the ability to locate twice as many users on 2N chips as were possible when only N chips were available. Specifically, in CI/DS-CDMA, N chips are located at the usual positions, i.e., N chips correspond to and the other N chips are located at the mid-positions between these chips, i.e., the other N chips correspond to This concept is illustrated in Figure 12, with the first set of chips represented by the solid line, and the second set of chips corresponding to the dotted line. The 2N CI-based chips demonstrate the same occupancy in the time domain and frequency domain as a typical N-chip shape system (i.e., the same total time duration and frequency bandwidth), while supporting twice as many users as an N-chip system. The cost is performance degradation due to the introduction of interchip interference at the transmitter side. The performance of the CI/DS-CDMA system with 2N CI-based chips per bit, i.e., capable of supporting 2N users, is shown in Figure 20. This is compared with the performance of the typical DS-CDMA system with N chips per bit and a RAKE receiver. All systems demonstrate an identical bandwidth occupancy. It is apparent that by application of CI principles to DS-CDMA, we can double the network capacity of DS-CDMA while maintaining performance improvements.

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2.7 CI/OFDM: Increasing Performance & Throughput in OFDM and Eliminating the PAPR Problem Another system of prominence in the wireless world is OFDM. As discussed earlier, OFDM is a multi-carrier system where (1) an incoming high-rate data stream is mapped to N low rate data streams by a serial to parallel converter; (2) each low rate data stream is modulated onto its own orthogonal carrier, and finally (3) the carriers are combined together and sent out over the channel. The poor probability of error performance of some of the low-rate data links led to the development of coded OFDM, where each bit is mapped to two bits by a convolutional coder, and each of these two bits is sent over it’s own unique carrier. The Carrier Interferometry approach enabled performance and network capacity improvements in MC-CDMA, TDMA, and DS-CDMA. It can do the same for OFDM. Specifically, to apply the CI approach to OFDM, we make a simple decision: we will not send each bit over its own carrier. Instead, we will send each bit over all N carriers simultaneously. That is, the N bits are sent out at the same time, and each of these N bits occupies the same set of N carriers. To enable bits to be separated from one another at the receiver side, we code each bit with a CI spreading code: that is, the N carriers labeled (1,2,...,N) are all used to send the bit and they experience the respective phase offsets This is illustrated in Figure 21.

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At the receiver side, bit k is extracted as shown in Figure 22. First, the N orthogonal carriers are separated from one another; next the phase offsets applied to the carriers for bit k are removed; and finally, a combiner is applied which combines the signal across carriers to exploit the available frequency diversity, minimize inter-bit interference, and reduce the additive noise power. In this way, each bit benefits from the full frequency diversity benefit available over the frequency selective channel, dramatically improving performance. A typical performance benefit of the proposed CI/OFDM relative to OFDM is illustrated in Figure 23. Here, we see a 10 dB performance benefit over OFDM at a probability of error of Additionally, CI/OFDM, which offers the same throughput as OFDM, can be compared to coded OFDM (COFDM), where a reduction in throughput by a factor of 2 has been introduced by a convolutional coding. CI/OFDM demonstrates only a 4dB degradation relative to COFDM while demonstrating twice the throughput. (Of course, as shown in a later chapter, coded CI/OFDM can be constructed which notably outperforms coded OFDM.)

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CI/OFDM can trade off some of its performance benefit for significant gains in the throughput of OFDM systems. This is achieved by allowing 2N bits to simultaneously occupy the N orthogonal OFDM carriers. Specifically, we allow 2N bits to be sent over all N carriers simultaneously. We ensure bits are separable from one another (as best as possible) at the receiver side by applying a unique CI spreading sequence to each of the 2N bits. Specifically, for bit k, we assign the following phase offsets to bit k’s carriers:

This corresponds to what was referred to as set 1 and set 2 in the original discussion of Carrier Interferometry signals and their properties (subsection 2.3.3). Figure 24 presents a typical probability of error performance curve for CI/OFDM with 2N bits on its N carriers (labeled PO-CI OFDM). It is evident from this curve that CI/OFDM, with twice as many bits on its N carriers, can still significantly outperform OFDM. If we introduce a coded

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CI/OFDM, where a rate ½ coding reduces the bit rate to that of the original OFDM system, we see that coded CI/OFDM offers the same throughput as original OFDM with the performance of coded OFDM. In other words, with Carrier Interferometry, we get the best of both worlds. In the case of OFDM, yet another powerful benefit emerges in the CI approach: the elimination of the PAPR (peak to average power ratio) problem. The peak to average power ratio problem, described next, limits the practicability of OFDM. In OFDM, the N independently modulated carriers combine in-phase at times, resulting in sudden peaks in transmit power, and at other times combine out-of-phase, leading to times of low transmit power. This creates problems for linear amplifiers, which are now required to demonstrate large ranges of linear operation. In CI/OFDM, on the other hand, where each bit is carefully phase coded onto all the carriers, it is easily shown that when one bit’s energy is at a maxima, the other bits’ energies are at minima. This eliminates peaks in transmit power, which in turn eliminates the PAPR problem. Details are found in Chapter 6.

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2.8 Summary In summary, multi-carrier technologies are emerging as a considerable force in the wireless world. OFDM charges ahead, with MCCDMA close behind. However, as this chapter demonstrates, multi-carrier technologies are not limited to OFDM and MC-CDMA. By application of the Carrier Interferometry (CI) approach, we have demonstrated that we can create CI/TDMA and CI/DS-CDMA, i.e., multi-carrier implementations of existing TDMA and DS-CDMA technologies. These implementations enable significant improvements in both performance (measured in terms of probability of error) and network capacity (measured in terms of numbers of users or throughput per user). Specifically, we double the network capacity of existing TDMA and DS-CDMA systems and simultaneously outperform these systems’ current implementations. Of course, the benefits of Carrier Interferometry are not limited to TDMA and DS-CDMA: It also significantly improves the existing MC-CDMA and OFDM multi-carrier systems. What emerges is a very powerful technology indeed! Through the application of Carrier Interferometry, we create a common multi-carrier architecture for DS-CDMA, TDMA, OFDM, and MC-CDMA, bridging the

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hardware gap between the world’s most promising technologies. But that is only the tip of the iceberg. The technology that bridges the gap also improves all the systems it comes into contact with, enhancing network capacity and probability of error performance of DS-CDMA, TDMA, OFDM and MCCDMA.

References: [1] B. Natarajan, C.R. Nassar, S. Shattil, M. Michelini, Z. Wu “High-Performance MC-CDMA via carrier interferometry codes”, accepted for publication in IEEE Transactions on Vehicular Technology. [2] Carl R Nassar, Bala Natarajan, and Steve Shattil, “Introduction of carrier interference to spread spectrum multiple access ,” IEEE Emerging Technologies Symposium, Dallas, Texas,

12-13 Apr 1999. [3] B. Natarajan, C. R. Nassar, and V. Chandrasekhar, “Generation of correlated Rayleigh fading envelopes for spread spectrum applications,” IEEE Communications Letters, Vol. 4, No. l, Jan. 2000, pp. 9-11.

[4] Carl R Nassar, Bala Natarajan, and V Chandrasekar, “Generation of Correlated Rayleigh Random Variables with Spread Spectrum Application,” IEEE Radio and Wireless Conference, Denver, CO, Aug. 1-4, 1999, pp.45-48. [5] B. Natarajan and C.R. Nassar, “Introducing novel FDD and FDM in MC-CDMA to enhance

performance,” IEEE Radio and Wireless Conference, Denver, CO, Sept. 10-13, 2000, pp. 2932.

[6] B. Natarajan, C.R. Nassar, and S. Shattil, “High Performance TDMA in wireless channels via innovations in pulse shaping,” accepted for publication in IEEE Communication Letters. [7] B. Natarajan, C.R. Nassar, and S. Shattil, “Exploiting frequency diversity in TDMA through carrier interferometry,” Wireless 2000: The 12th Annual International Conference on Wireless Communications, Calgary, Alberta, Canada, July 10-12, 2000, pp. 469-476. [8] B. Natarajan, C.R. Nassar, and S. Shattil, “Throughput enhancement in TDMA through carrier interferometry pulse shaping,” 2000 IEEE Vehicular Technology Conference, Boston,

MA, Sept. 24-28, 2000, pp. 1799-1803. [9] C.R. Nassar and Z. Wu, “High performance broadband DS-CDMA via carrier interferometry chip shaping,” 2000 International Symposium on Advanced Radio Technologies, Boulder, CO, Sept. 6-8, 2000, proceeding available online at http://ntai.its.bldrdoc.gov/meetings/art/index.html.

[10] Z. Wu, C.R. Nassar, and S. Shattil, “Capacity enhanced DS-CDMA via carrier interferometry chip shaping,” IEEE 3G Wireless Symposium, May 30 – June 2, 2001, San Francisco, CA.

[11] Z. Wu and C.R. Nassar, “MMSE frequency combining for CI/DS-CDMA,” IEEE Radio and Wireless Conference, Denver, CO, Sept. 10-13, 2000, pp. 103-106. [12] Zhiqiang Wu, Carl R. Nassar, “Next Generation High Performance DS-CDMA via Carrier Interformetry”, The 13th International Conference on Wireless Communications, Calgary,

Canada, July 9-11, 2001, pp. 564-569 [13] Zhiqiang Wu, Balasubramaniam Natarajan , Carl R. Nassar “High-Performance, High-

Capacity MC-CDMA via Carrier Interferometry”, The 12th IEEE International Symposium on Personal, Indoor and Mobile Radio Communication, San Diego, Sep 30-Oct 3, 2001 [14] D. A. Wiegandt and C. R. Nassar, “High performance OFDM via carrier interferometry,” accepted for presentation at 3Gwireless’01 IEEE International Conference on Third Generation Wireless and Beyond.

[15] D. A. Wiegandt and C. R. Nassar, “High-throughput, High-performance OFDM via pseudo-orthogonal carrier interferometry coding,” IEEE PIMRC 2001 IEEE International Symposium on Personal, Indoor and Mobile Radio Communication.

39 [16] D. A. Wiegandt, C. R. Nassar, and Z. Wu, “Overcoming peak-to-average power ratio issues in OFDM via carrier interferometry codes,” IEEE VTC 2001 (Atlantic City, NJ). [17] D. A. Wiegandt, and C. R. Nassar, “Peak-to-average power reduction in highperformance, high-throughput OFDM via pseudo-orthogonal carrier interferometry coding,” IEEE PACRIM 2001 (Victoria, Brittish Columbia).

[18] D. A. Wiegandt, and C. R. Nassar, “High-Performance 802.11a wireless LAN via carrier interferometry orthogonal frequency division multiplexing at 5 GHz,” IEEE Globecom 2001 (San Antonio, TX). [19] D. A. Wiegandt, and C. R. Nassar, “High-performance wireless ATM via application of

carrier interferometry to OFDM,” WOC ‘01 (Banff, Alberta, Canada).

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Chapter 3

HIGH PERFORMANCE, HIGH CAPACITY MC-CDMA FOR FUTURE GENERATIONS The CI Approach

CDMA (Code Division Multiple Access) has emerged as a very popular multiple acess technique for wireless communications. The benefits offered by CDMA include the ability to combat hostile frequency selective channels and the ability to support higher network capacities

relative to the conventional access techniques of TDMA and FDMA. Multi-carrier modulation schemes such as OFDM have also gained a lot of attention of late due to the demand for high data rate transmission in mobile radio environments. Desire is the mother of invention. The desire to combine the benefits of CDMA and OFDM gave birth to the idea of Multi-Carrier CDMA (MCCDMA) in 1993 [1]. MC-CDMA demonstrates many desirable qualities including: overcoming drawbacks of frequency selective channels, exploiting frequency diversity, and the handling of diverse multimedia traffic [2]. This chapter reviews the features of traditional MC-CDMA and discusses the benefits of incorporating Carrier Interferometry (CI) spreading codes in MC-CDMA. Section 3.2 presents CI signaling and the

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transmitter model. This section also introduces the notion of pseudoorthogonal CI spreading codes to increase network capacity with zero cost in bandwidth. Section 3.3 discusses the channel model, and Section 3.4 presents receiver design architectures. Section 3.5 introduces performance results assuming perfect synchronization as well as in the presence of phase and frequency jitters. We address crest factor issues in MC-CDMA with CI spreading codes in Section 3.6. Conclusions follow in Section 3.7.

3.1.

Introduction

Since its introduction in the winter of 1993, MC-CDMA has been the focus of research and development efforts (e.g., [3-8]) and has emerged as a powerful alternative to conventional direct sequence CDMA (DSCDMA)[9] in mobile wireless communications. In MC-CDMA, each user’s data symbol is transmitted simultaneously over N narrowband subcarriers, with each subcarrier encoded with a –1 or +1 (as determined by an assigned spreading code). Multiple users are assigned unique, orthogonal (or pseudo-orthogonal) codes. That is, while DSCDMA spreads in the time domain, MC-CDMA applies the same spreading sequences in the frequency domain.

The most common question one is confronted with is “Can MCCDMA be better than DS-CDMA in terms of performance - after all, time and frequency domain processing are dual of each other?”. The answer follows. When perfectly orthogonal code sequences are transmitted synchronously over slow, flat fading channels with perfect synchronization, the performance of DS-CDMA and MC-CDMA is equivalent. Here, the orthogonal multi-user interference vanishes completely in both MC-CDMA and DS-CDMA [10]. However, in reality, wideband CDMA signals are sent over multipath channels, and these signals experience more severe channel distortions. The resulting channel dispersion (i.e., frequency selectivity) erodes the orthogonality of CDMA signals. In such cases, it turns out to be far more beneficial to harness the signal energy in the frequency domain (as in MC-CDMA) than in the time domain (as in DS-CDMA) [9], [11]. Specifically, MC-CDMA receivers exploit frequency diversity in the frequency selective channel by separating carriers and then carefully recombe them, while DS-CDMA RAKE receivers use correlators to resolve multiple paths and create path diversity. The primary reason MCCDMA receivers outperform their DS-CDMA counterparts is: (1) in

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DS-CDMA RAKE receivers, large interference results on each diversity branch (each path) due to the presence of other users’ signals from other paths as well as one’s own signal from other paths; (2) in MC-CDMA, where carriers are separated from one another, receivers can perfectly separate the carrier components by performing an FFT operation (since carriers are designed to be orthogonal to one another). In other words, the SIR (Signal to Interference Ratio) on each diversity branch in MCCDMA is much higher than the SIR on diversity branches in DS-CDMA. For this reason (primarily) MC-CDMA demonstrates performance gains relative to DS-CDMA. To further improve MC-CDMA, we turn our attention to the principle of Interferometry. Interferometry [12], a classical method in experimental physics, refers to the study of interference patterns resulting from the superpositioning of waves. The ideas underlying interferometry extend naturally to multiple access applications in telecommunications. For example, in antenna arrays supporting space division multiple access, EM waves are emitted simultaneously from multiple antenna elements, and initial phases are chosen to ensure that interference patterns create a peak at the desired user location, and nulls at the position of other users. We can apply the principles of interferometry to create a novel spreading code set for MC-CDMA. The idea here is that one user transmit his bit simultaneously on the N carriers of MC-CDMA, with carefully chosen phase offsets (a spreading code) that ensure a periodic mainlobe in the time domain (with sidelobe activity at intermediate times). When the superpositioning of one user’s carriers creates a mainlobe in time, all other users are at the times of sidelobe activity (and, by careful positioning, can be made strictly orthogonal or pseudo-orthogonal to the user transmitting a mainlobe).

In this proposed innovation to MC-CDMA, we are replacing the use of spreading codes identical to those in DS-CDMA with spreading codes which create interferometry patterns among carriers. Hence, we call our proposed spreading codes Carrier Interferometry codes (CI codes)

and our proposed scheme Carrier Interferometry/MC-CDMA (CI/MCCDMA). Already, there has been tremendous interest in the development of spreading codes (e.g., for DS-CDMA see [13]-[16], and see [17] for an overview of MC-CDMA codes). In [13] a general set of complex valued spreading codes for DS-CDMA are proposed that provide a better compromise between auto and cross correlation properties relative to binary spreading codes. However, codes of length N support

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a maximum of only users. In [14] and [15], a novel spread signature CDMA system is introduced where the length of the spreading code is far greater than the symbol duration. This technique is best suited to exploit temporal diversity in fast fading environments. Addi-

tionally, in [16], a multivalued set of orthogonal codes are constructed using wavelet and subband transform theories. In [17], a thorough analysis and comparison of existing MC-CDMA codes is presented: specifically, [17] examines the use of Hadamard Walsh, Gold, Orthogonal Gold and Zadoff Chu sequences in MC-CDMA systems. However, the DSCDMA codes ([13]-[16]) and MC-CDMA codes [17] are designed to be either orthogonal, supporting N users (where N is the processing gain or code length), or pseudo-orthogonal, supporting greater than N users, at the cost of degraded performance. Furthermore, N, is limited to or The CI spreading codes of length N introduced in this paper have a unique feature which allows the CI/MC-CDMA system to (1) support N users orthogonally; (2) then, as system demand increases, codes can be selected to accommodate up to an additional N users pseudo-orthogonally. Additionally, there is no restriction on the length N of the CI code making it more robust to the diverse requirements of wireless environments.

The following sections demonstrate the flexibility and the performance improvement achievable through CI/MC-CDMA.

3.2.

CI/MC-CDMA Signaling and Transmitter model

The transmitter for the in Figure 3.1. Here, the

user in a CI/MC-CDMA system is shown user's spreading code corresponds to Specifically, the input data symbol is where n denotes the bit interval and k denotes the user. It is assumed that takes on values -1 and +1 with equal probability. The transmitted signal corresponding to the input is

where and is defined to be a Nyquist pulse for the bit in the interval 0 to As with traditional MC-CDMA, the are selected such that the carrier frequencies are orthogonal to each other, typically where is the bit duration.

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The transmitted signal can also be expressed as

where is refered to as user k’s code and corresponds to the superpositioning of N equally spaced carriers, i.e.,

User k’s code,

corresponds to a cosine waveform with frequency and envelope

Figure 3.2 plots the envelope for carriers, and This demonstrates a code that is : (1) periodic with period (2) the nth period contains a mainlobe of duration the mainlobe positioned at time (3) each period contains sidelobes of duration where th the l side lobe has maximum amplitude (normalized with respect to mainlobe amplitude) of

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The Cross Correlation (CC) between user k’s signature waveform (created using the spreading sequence and user j’s signature waveform (created via the spreading sequence

can be shown to be

where demonstrates N – 1 equally spaced zeros at

These N – 1 zeros indicate that a CI/MC-CDMA system can simultaneously support N orthogonal users by use of N codes where

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Next, consider introducing a fixed phase offset to all user’s phases. That is, replace in equation (3.8). All users remain orthogonal. That is, the cross correlation between spreading codes remains zero, as is evident from (3.6), where depends only on the difference There exist N orthogonal codes for any selection of where

namely

The orthogonal set of N codes described in equation (3.7) and (3.8) (constructed with and the orthogonal set of N codes described via equations (3.9) and (3.10) (constructed with demonstrate a non-zero cross correlation with one another. We select in (3.10) to minimize the cross-correlation between the two sets of N orthogonal codes (those in (3.7) and (3.8), and those in (3.9) and (3.10)). Let refer to the cross correlation between the jth code in orthogonal code group 1 (constructed with and the kth code in orthogonal group 2 (constructed with Also let

represent the root-mean-square cross correlation that exists between codes in group 1 and group 2. We seek to find the value for that minimizes Now, it is easily shown that

It is also easy to show that

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That is, the total cross correlation between the kth code in orthogonal group 2 and all the codes in group 1 is identical to the cross-correlation between the code in orthogonal group 2 and all codes in group 1. Using equation (3.13), we can rewrite equation (3.11) as

and using equation (3.12), this becomes

We now determine the selection of the root-mean-square correlation, To do this, we select

for code group 2 that minimizes between the two code groups.

The solution to this equation is derived in Appendix 3A (found at the

end of this chapter), and corresponds to Hence, if we have one set of N orthogonal CI codes, and we want to increase system capacity by introducing a second set of N orthogonal CI codes: To best do that, in a minimum mean squared interference sense, introduce the second set of CI codes with phases offset by with respect to the first set of CI codes. That is, for 2N users on the system, each user should be assigned the spreading code where,

In this way, CI/MC-CDMA doubles network capacity. The total transmitted signal with a full 2N users is

where

are selected as shown in equation (3.18) and (3.19).

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Viewing the CI codes based on equation (3.17),(3.18) and (3.19) in the time domain leads to Figure 3.3 (with N = 8). Here, the solid lines correspond to the first orthogonal set of CI codes (based on equation (3.18)). These CI codes can be thought of (conceptually) as orthogonal because when one code is at a time of mainlobe (peak energy) all other codes codes are at a time of sidelobe activity (very low energy). The second set of orthogonal codes (based on equation (3.19)) are shown by the dotted line. These codes minimize root-mean-square correlation between code sets (conceptually) because the mainlobes of these CI codes lies right between the mainlobes of the first orthogonal set. It is important to note that even though CI codes correspond to easy-to-understand waveforms in the time domain (namely interferometry patterns), it is their frequency decomposibilty that will serve us well in the receiver processing.

3.3.

Channel Model

The transmitted signal in (3.20) is sent out across the channel, and, with that in mind, the channel model becomes the next focus of attention. We assume synchronicity between users, typically characteristic of the downlink in a mobile communication system. However, more and more wireless communication systems are being proposed with syn-

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chronous uplink channels, as recent efforts in 3G have focused on the creation of synchronous uplinks (e.g., [18][19]). For example, in [19], the China Wireless Telecommunication Standard (CWTS), time division is introduced to support synchronous CDMA uplinks. The channel model studied here is of course valid for both this category of uplinks as well as downlinks. We assume a slowly varying frequency-selective Rayleigh fading channel, typical of the wideband channels for MC-CDMA systems. Frequency selectivity refers to the selectivity over the entire bandwidth of transmission, and not over each subcarrier transmission; that is [20]

where is the coherence bandwidth of the channel (defined as the bandwidth over which fade correlation is above 0.5) and BW is the total bandwidth of the multicarrier system. In this work, we examine frequency selectivity resulting in L fold frequency diversity over the entire bandwidth (typically, With N carriers residing over the entire bandwidth, BW, each carrier undergoes a flat fade, with the correlation between the subcarrier fade and the subcarrier fade characterized by [21]

Generation of correlated fades for simulation purposes is discussed in [22],[23] and a recap of this work is found in Appendix 3B (at the end of this chapter).

3.4.

Receiver Structures

Assuming the transmitted signal in equation (3.20), and the channel model of section 3.3, the received signal corresponds to

where is the gain and the phase offset in the carrier due to the fade; K is the total number of users utilizing the system; and represents additive white gaussian noise (AWGN). The CI/MC-CDMA receiver for user k is shown in Figure 3.4. Here, the received signal is first projected onto the N orthonormal carriers

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that make up the transmitted signal. This leads to the output where

Here, is a Gaussian random variable with mean 0 and variance and exact phase and frequency synchronization has been assumed in determining (3.24). Next, a suitable combining strategy is used to linearly combine the terms and create a decision variable, D. In a flat fading channel (i.e., a simple addition, i.e., leads to the elimination of the second term (whenever codes and are orthogonal) and maximizes the SNR. However, in frequency selective channels of interest here, different combining methods may be used: minimum mean square error combining (MMSEC) produces the best performances in terms of MC-CDMA probability of error[9]. Employing MMSEC in CI/MC-CDMA results in the decision variable (see Appendix 3C)

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where to

is a known constant for a given K and carrier i and corresponds

It is important to note that, by constructing a receiver that processes the signal in the frequency domain rather than in the time domain, we circumvent the need for sub chip synchronism.

3.5.

Performance Results

We now characterize the performance of a wireless system where: (1) MC-CDMA transmitters are constructed using CI codes as shown in Figure 3.1 and equations (3.17)-(3.20); (2) channels are slow, frequency selective fading channels characterized in Section 3.3; and (3) receivers are constructed as shown in Figure 3.4 and described in Section 3.4.

3.5.1

Perfect Synchronization

Figure 3.5 presents the average bit error rate (BER) versus number of users for carriers and Results are presented for a frequency selective Rayleigh fading channel with (supporting diversity over the entire bandwidth). In Figure 3.5, two benchmark MC-CDMA system curves are also provided. The first MC-CDMA benchmark assumes orthogonal HadamardWalsh (HW) codes of length 32 (dashed line) and the second assumes Gold codes (solid line) - here, length 31 Gold codes support 33 users, with a second set of Gold codes used to support additional users. Additionally, a flat dotted line is drawn which represents the matched filter lower bound (performance of a single user system exploiting the available diversity through MRC)[24]. The BER for our proposed CI/MC-CDMA is shown on the dotted line. It slightly outperforms MC-CDMA (using HW codes) up to 32 users. While orthogonal MC-CDMA can not support additional users,

CI/MC-CDMA accommodates an additional 32 users (up to 64 users) by using a second set orthogonal set of codes. If MC-CDMA is pre-selected to support additional users, by use of pseudo orthogonal Gold codes, it results in significant performance degradation relative to

CI/MC-CDMA as shown by the solid line. In fact, at a BER of 0.005, the CI/MC-CDMA system supports 64 users, 4 times the number of

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users supported by the pseudo-orthogonal MC-CDMA system.

It is observed that with a total of 64 users (32 orthogonal and 32 pseudo orthogonal), CI/MC-CDMA systems offer an average performance comparable to that of MC-CDMA employing Gold codes with 16 users or MC-CDMA employing HW codes with 32 users. Hence, CI/MC-CDMA enjoys approximately 300% more capacity relative to pseudo orthogonal MC-CDMA methods and 100% more relative to MCCDMA with HW codes. Furthermore, the CI/MC-CDMA system is implemented using FFT’s and IFFT’s similar to MC-CDMA, resulting in comparable complexities.

3.5.2

Phase Jitter

The channel introduces the phase offset on the carrier (see equation (3.23)), which may be tracked and accounted for at the receiver using, e.g., a phase locked loop (PLL). Tracking loops are not perfect and hence a degradation in performance may result due to phase jitter. If is the estimate of the phase using a PLL, then the carrier phase error, has the Tikhonov probability density function (pdf)

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[25],

Here, is a parameter related to the tracking loop SNR and is the modified Bessel function of the first kind. For first order tracking loops, is the loop SNR and for second order loops, is approximately the loop SNR for sufficiently large values [26].

After demodulating the received signal using phase on the carrier, the received signal component (see Figure 3.4, and shown in (3.23) with perfect synchronization) is now given by

where As in Section 3.4, these signal components are then combined across carriers using the MMSEC of equation (3.25). The performance of CI/MC-CDMA with phase jitter is illustrated in Figure 3.6. This figure represents simulation results under conditions identical to those used to achieve Figure 3.5, with the exception of phase jitters corresponding to and 100 (i.e., rms phase jitters of 18.7°, 10° and 5° respectively). CI/MC-CDMA demonstrates graceful performance degradation, even as phase jitters grow

very large. This results because the spreading sequence of user k is while user j’s spreading sequence is and hence, even if the value of is close to (e.g., the phase spacing between the ith spreading sequence elements is which is large for large values of i. Thus the CI/MC-CDMA system is more robust to phase jitters than one might expect at initial glance.

Figures 3.7 and 3.8 compare the effect of phase jitters on the CI/MCCDMA proposed in this chapter and benchmark MC-CDMA with HW and Gold codes. Figure 3.7 shows the performance with phase jitter corresponding to and Figure 3.8 shows results. It is observed that relative performance does not change significantly for high values of As decreases (i.e., as tracking loop SNR degrades), the CI/MC-CDMA degrades at a slightly more rapid rate than its MCCDMA counterpart, but still offers comparable benefits to those outlined in subsection 3.5.1.

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3.5.3

Frequency Offset

Multi-carrier transmission schemes including traditional MC-CDMA and the newly introduced CI/MC-CDMA are particularly susceptible to

56

performance degradations from carrier frequency offset. Two major factors are at the root of such carrier frequency offsets : (1) Doppler spread caused by a high-speed mobile and (2) offsets between the oscillator at the transmitter and that of the receiver. Frequency offsets caused by less than perfect synchronicity between the transmitter and the receiver oscillators are present to the same degree all carriers. On the other hand, offsets due to Doppler spreads are different on each carrier (a function of the carrier’s location in the spectrum). However, for mobile communication systems operating at a typical carrier frequency of e.g., 2 GHz and occupying a characteristic 1 MHz bandwidth, the maximum difference in Doppler spread among 32 carriers is in the range of 0-5 Hz, which is negligible when compared to subcarrier spacings of about 30 KHz [27]. Hence, we treat frequency offsets as a phenomenon with identical characteristics in all subchannels. Frequency offsets in the proposed CI/MC-CDMA system results in two key adverse effects. First is the reduction of desired signal amplitude and second is the loss of carrier orthogonality which leads to the introduction of intercarrier interferences.

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If is the normalized frequency offset (defined as the ratio of the actual frequency offset to the subcarrier separation ), the decision variable D (see Figure 3.4 and equation (3.25)) is given by (analogous to [28], [29]),

where the five components correspond to

Here, denote the desired signal, the multi- access interference, the intercarrier interference generated from within the user’s CI code, and the intercarrier interference generated from the CI codes of the other users. Figure 3.9 plots the performance of the proposed CI/MC-CDMA in the presence of frequency offsets and 0.2. It is observed that CI/MC-CDMA is immune to 10% frequency offset while a degradation is visible for a 20% offset level. Figures 3.10 and 3.11 compare the impact of frequency offset on CI/MC-CDMA and traditional MC-CDMA with HW codes. Both systems are degraded by a comparable amount, demonstrating that CI/MC-CDMA is no more susceptible to frequency

offsets than its traditional MC-CDMA counterpart.

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3.6.

Crest Factor Considerations in CI/MC-CDMA

One concern regarding the use of MC-CDMA with CI codes is the peak-to-average power ratio (PAPR) as well as increased signal dynamic range relative to single carrier schemes. This concern arises because, in the time domain, these codes create a periodic mainlobe with sidelobe activity at intermediate times (see Figure 3.2). The correspondingly

59

large PAPR leads to a reduced efficiency of the power amplifier, and an increased signal dynamic range requires power amplifiers with higher range of linearity. To measure the signal compactness of the CI/MC-CDMA signal, we employ the crest factor (CF). For a multi-carrier signal s(t) [30]

where is the largest positive and is the most negative value of s(t). Eeff represents the total amount of energy contained in s(t) and equals i.e., the rms value of s(t). It is clear from (3.35) that a sine wave has a crest factor of Another common approximation found in the literature [31] relates crest factor to PAPR:

where corresponds to the maximum absolute value of s ( t ) In the following discussion, we provide exact CF values in accordance with (3.35) as well as values (see (3.36)) for CI/MC-CDMA.

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3.6.1

Downlink Crest Factor

In the MC-CDMA downlink, all K user’s signals are bundled together prior to transmission, leading to

This equation is shown in greater detail in (3.20) (with

The crest factor of is dependent on the binary antipodal data symbols of the users, equally likely to be or . The crest factor is therefore a Gaussian distributed random variable [32] [33]. Assuming carriers and users, the probability density functions of CF and for are plotted in Figures 3.12 and 3.13 respectively. These results were obtained using computer-based simulation of the transmitted signal with random binary data, followed by evaluation of the CF values based on (3.35) and (3.36). It is observed that and where E[.] refers to the numerical mean. These values are well within tolerable levels of power amplifiers. The probability of is less than 4%, indicating that the variance of CF is low, i.e., CF rarely ventures far above its mean of 1.85. This low CF can be attributed to simultaneous transmission of all users’ signals. That is, even though the signature waveform of Figure 3.2 appears to have a poor CF, the combined signal, with all signature waveforms and data symbols on them, actually improves the CF tremendously. An example of this phenomenon is shown in Figure 3.14: when bits are ’1’ for all users the combined signal (solid line) is seen to demonstrate small values of PAPR and CF.

3.6.2

Uplink Crest Factor

We now turn our attention to the CF in the CI/MC-CDMA uplink. The signal transmitted by user k in the uplink is (see equation (3.1) and Figure 3.2 for details). The crest factor of sup(t) is shown in Table 3.1 where it is apparent that CF and increase with increasing N. These values were calculated analytically, since the uplink CI/MC-CDMA signal envelope has a fixed maximum, minimum and rms value that does not depend on the transmitted data. Systems built to accommodate such crest factor values would be extremely inefficient as high CF would cause the power amplifier to ‘backoff’ (reduce average transmission power) to avoid non-linear distortions. Hence, we employ a CF reduction technique that enables the CI/MCCDMA system to demonstrate desirable CF values in the uplink.

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3.6.3

CF Reduction Technique

In a multi-carrier signal such as the CI/MC-CDMA code of Figure 3.2 and equation (3.3), the crest factor is a function of the phase angles of

the carriers. Schroeder [34] proposed a powerful, easy-to-implement rule for phase angle adjustment that creates a multi-carrier signal with a low CF: the rule for creating low CF is effective in cases when the carriers are concentrated in a small frequency band (small relative to the center frequency), as in the case in CI/MC-CDMA . In this section, we apply Schroeder’s technique to reduce CF in the CI/MC-CDMA uplink. (It is important to note that there are other techniques of phase angle adjustments ([35],[36]) that can alternatively be employed in CI/MC-CDMA systems to reduce CF). Refering to [34], the CF is reduced in the uplink of CI/MC-CDMA by introducing a phase offset into each carrier at the transmitter side, i.e., the code for the uplink of CI/MC-CDMA is updated from equation (3.3) to

where are determined as follows. We start with a random phase for the first carrier, and calculate the phases for the

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remaining carriers

using [34]

The CF for the signal in (3.38) (with these phase offsets from (3.39)) is computed and stored. Starting with a new random value for we repeat equation (3.39) to determine a new The CF for the signal in (3.38) with the new phase offsets are again computed. This procedure is repeated approximately 1000 times and the CF values computed are inspected to determine the that minimized CF. Alternately, in [34], a second method is provided where we restrict such that Here, the phase offsets are computed using

where [x] indicates the largest integer not larger than x. The CF and of CI codes in (3.38) with generated using the Schroeder methods are presented in Table 3.2 and Table 3.3. These results were obtained for a CI/MC-CDMA system uplink employing and 32 carriers. From Table 3.2, we observe (using Shroeder’s method to determine ) CF values of CI codes are reduced from 4.9 to 1.6 when Even after limiting the phase offsets such that we observe an improvement from 4.9 to 1.8. Similar improvements are also seen in values. Specifically, the CF of the uplink is now reduced to values close to that of a single sine wave (CF of sine Hence, the CF problem of uplink CI/MC-CDMA is efficiently solved. Finally, it is also important to note that the signature waveforms and in a CI/MC-CDMA system are simply time shifted versions of one other. Hence, it suffices to calculate one set of phase offsets to reduce the CF and this set can be applied to all the users’ spreading codes (as in (3.38)). (In MC-CDMA systems applying e.g., Gold codes or Hadamard Walsh codes, the same phase offsets cannot be used for all users’ spreading codes).

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One attractive feature of these CI codes results by extending the use of (from Schroeder’s method) to enhance security. Specifically, one can envision a CI system where the transmitter updates the set of phases it applies to the CI code (equation (3.38)). Here, the CI signal is constantly changing shape (from one low PAPR shape to another), making unwanted detection and decryption near to impossible.

3.7.

Conclusions

In this chapter, CI/MC-CDMA , an innovation in code design for MCCDMA, was introduced. In synchronous frequency selective Rayleigh fading channels, CI/MC-CDMA’s performance matches that of orthogonal MC-CDMA using Hadamard-Walsh codes up to the MC-CDMA user limit; moreover, CI/MC-CDMA provides the added flexibility of supporting (up to ) users by adding users with pseudo orthogonal codes. CI/MC-CDMA also provides added flexibility in the choice of N versus making it more robust to the wide range of mobile system applications. The CI/MC-CDMA system was tested in the presence of phase jitters and frequency offsets and was found to demonstrate very graceful degradations in performance at high levels of synchronization errors. This chapter also addressed PAPR concerns in CI/MC-CDMA. An analysis of the CI/MC-CDMA downlink shows that PAPR is well within

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tolerable levels for today’s power amplifiers. On the other hand, the CI/MC-CDMA uplink suffers from high (poor) PAPR values. However, applying Schroeder’s CF reduction technique, we demonstrate that the uplink CF is easily brought to very low values (close to that of a pure sine wave). The application of CI codes to MC-CDMA enables MC-CDMA systems to take yet another leap ahead, advancing the multi-carrier revolution that promises to reshape the wireless world: CI enables gains in performance and network capacities, all the while maintaining low complexity designs via FFTand IFFTpiiimplementation, R and keeping PAPR values to a minimum. For additional reading, please see our earlier publications [41]-[44].

APPENDIX 3A : Determining the Phases minimizing Root-Mean-Square Correlation We seek to determine the value of that minimizes the (root mean square correlation) between codes of set 1 (equation (3.7) and (3.8)) and codes of set 2 (equation(3.9) and (3.10)), i.e., to seek the value of that satisfies

Using (3.14),

where

Now,

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Hence, when we have and, therefore from equation (3.42), Seeking to determine which are maxima and which are minima, we calculate the second order partial derivative at and determine:

Hence, corresponds to a maxima and minima. Selecting we choose as our minima.

provides

APPENDIX 3B : How to Generate Correlated Rayleigh Envelopes for Use in Simulations It is well known that Rayleigh random variables are closely related to complex Gaussian random variables. To illustrate this point, consider N complex Gaussian signals where

67

and are independent zero mean Gaussian random variables with variance The envelopes of labeled and corresponding to

are Rayleigh distributed.

Assume we want to generate N Rayleigh envelopes with a normalized covariance matrix

The idea underlying this work is to generate N complex Gaussian random variables with a corresponding normalized Covariance matrix

such that creation of the desired solute values of

results by taking ab-

The generation of given is based on the following realization : the value the th element of (representing the correlation coefficient between is determined exclusively by the absolute value of the th element of (the magnitude of the correlation coefficient between and For simplicity in presentation and algorithm implementation, we assume that the elements of are real, and consequently the value is determined exclusively by (and vice-versa). The exact analytical relationship relating [37]

and

is given by

where denotes the complete elliptic integral of the second kind with modulus In [22], the lack of a direct closed form solution to

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the equation is resolved by the use of numerical methods, namely polynomial approximation (to evaluate the elliptical integrals). While the results of [22] may be used to relate to (using an intermediate variable a new method is provided here which offers an immediate, simple, one-to-one relationship between and Given (1) create pairs of complex Gaussian samples with correlation from pairs of uncorrelated samples by employing Cholesky Decomposition [38]; (2) numerically evaluate the correlation among the envelopes of Gaussian samples with correlation coefficient this provides (3) In this way, a look-up table of values relating and is available. Table 3.4 and Figure 3.15 show a table and corresponding plot relating and The table and figure may be used as a quick reference to evaluate given (using linear interpolation).

In this way, all elements of _ can be mapped to corresponding elements in Once is determined, the N correlated Gaussian samples are generated by Cholesky Decomposition [38], and the desired are created by evaluating the envelopes of the N complex Gaussian samples.

The procedure for generating the N correlated Rayleigh fading signals is summarized by the following algorithm Algorithm The starting point is the desired covariance matrix of the Rayleigh envelopes given by

1. Normalize this matrix to create the normalized covariance matrix

where 2. For each cross correlation coefficient compute the corresponding by (a) using Table 3.4 (and linear interpolation) or (b) relating

69

and as discussed earlier. 3. Form the normalized covariance matrix of complex Gaussian samples:

4. Generate N uncorrelated complex Gaussian samples each with variance then, determine the coloring matrix L corresponding to (the coloring matrix L is the lower triangular matrix such that where represents the transpose of L) and generate correlated complex Gaussian samples using 5. The N envelopes of the Gaussian samples in W correspond to Rayleigh random variables with normalized covariance matrix and equal variance [20]

6. Create the desired Rayleigh envelopes samples by evaluating

from the where

APPENDIX 3C : Derivation of MMSE Combiner in CI/MC-CDMA Receiver

The minimum mean square error combining method approximates the transmitted symbol from the N-length vector

70

(see Figure 4) by using the linear sum :

Based on the MMSEC criterion, the estimation error must be orthogonal to all the baseband components of the received subcarriers [39]. That is,

The solution to equation (3.56) as obtained from Weiner filter theory corresponds to [40] where and where E{.} denotes the expected value. This operation, when applied to the in CI/MCCDMA (equation(3.21)) yields

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Substituting (3.58) and (3.59) in (3.57) we obtain the weights for MMSEC:

and; hence, from (3.55),

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nications system based on orthogonal multi-carrier SSMA,” Wireless Personal Communications 2, pp. 121-144, 1995. [4] T.Mueller, K.Brueninghauss, and H.Rohling, “Performance of coherent OFDMCDMA for broadband mobile communications,” Wireless Personal Communications 2, pp. 295-305, 1996. [5] N.Yee, J.P.Linnartz,“Controlled Equalization of multi-carrier CDMA in an Indoor Rician Fading Channel,” Proc. of VTC ‘94, pp. 1665-1669, Stockholm 1994. [6] K.Fazel, “Performance of CDMA/OFDM for mobile communication systems,” ICUPC ;93, pp. 975-79, 1993.

[7] L.Vanderdorpe,“Multitone spread spectrum multiple access communications system in a multipath Rician fading channel,” IEICE Tran. Commun., Japan, vol. E77-B, pp. 900-904, July 1994. [8] D.N.Kalofonis and J.G.Proakis, “Performance of the multi-stage detector for a MC-CDMA system in a Rayleigh fading channel,” Globecom ‘96, pp. 1784-88, 18-22 November 1996, London, UK. [9] S. Hara and R. Prasad, “Overview of multi-carrier CDMA,” IEEE Communications Magazine, vol.35, no. 12, Dec. 1997, pp. 126-133. [10] Ramjee Prasad, Universal Wireless Mobile Personal Communications, Artech House, 1998. [11] S.Zhou,G.B.Giannakis, A.Swami,“Comparison of digital multi-carrier with direct

sequence spread spectrum in the presence of multipath,” Proc. of ICASSP 2001, vol. IV, pp. 2225-2228, May 7-11, Salt Lake City, 2001.

[12] W.H.Steel, Interferometry. Cambridge: Cambridge University Press, 1st ed., 1967. [13] I.Opperman and B.S.Vucetic, “Complex Spreading sequences with a wide range

of correlation properties,” IEEE Transactions on Communications, vol. 45, no. 3, March 1997. [14] G.W.Wornell, “Spread-Signature CDMA: Efficient Multi-user Communication in the presence of fading,” IEEE Trans. on Information Theory, vol.41, no.5, Sept 1995. [15] G.W.Wornell, “Emerging Applications of Multirate Signal Processing and Wavelets

72 in Digital Communications,” Proceedings of the IEEE, vol. 84, no.4, April 1996. [16] Ali N.Akansu al., “Wavelet and Subband Transforms: Fundamentals and Communication Applications,” IEEE Communications Magazine, December 1997. [17] B.M.Popovic, “Spreading Sequences for Multicarrier CDMA systems,” IEEE Transactions on Communications, vol.47, no.6, June 1999. [18] F.Kleer, S.Hara and R.Prasad, “Detection Strategies and cancellation schemes in a MC-CDMA system,” CDMA Techniques for Third Generation Mobile Systems, pp. 185-215, Kluwer Acad. Publishing, 1st ed. 1999. [19] TS C101 V3.0.0 - China Wireless Telecommunications Standard (CWTS) ; Physical Layer - General Description, 1999. [20] J.Proakis, Digital Communications. New York: McGraw-Hill, 3rd ed., 1995. [21] W.Xu and L.B.Milstein, “Performance of Multicarrier DS CDMA Systems in the presence of correlated fading,” IEEE 47th Vehicular Technology Conference, Phoenix, AZ, May 4-7, 1997, pp. 2050-4 [22] R.B.Ertel and J.H.Reed, “Generation of Two Equal Power Correlated Rayleigh fading envelopes,” IEEE Communication Letters, vol.2, no. 10, Oct. 1998, pp. 276278

[23] B.Natarajan,C.R.Nassar and V.Chandrasekhar, “Generation of Correlated Rayleigh fading envelopes for Spread Spectrum Applications,” IEEE Communications Letters, vol.4, no.l, January 2000.

[24] M.K.Simon and M.S.Alouini, Digital Communication over Fading Channels - A Unified Approach to Performance Analysis, Wiley-Interscience, New York,2000. [25] H.Leib and S.Pasupathy,“Trellis-Coded MPSK with Reference Phase Errors,” IEEE Tran. on Communications, vol. COM-35, no.9, September 1987. [26] W.C.Lindsey and M.K. Simon, Telecommunication Systems Engineering, Prentice Hall, Inc., New York, NY, 1973. [27] G.Malmgren , Impact of Carrier Frequency Offset, Doppler Spread and Time Synchronization [28] Y.Kim, S.Choi, C.You and D.Hong, “Effect of Carrier Frequency Offset on the performance of an MC-CDMA system and its countermeasure using pulse shaping,” Proceedings of IEEE International Conference on Communications, vol.1, pp. 167171, Vancouver, June 1999.

[29] P.H.Moose,“A Technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Transactions on Communications, vol.42, no.10, pp.29082914, October 1994. [30] Edwin Van der Ouderaa, J.Schoukens and J.Renneboog, “Peak factor minimization of input and output signals of linear systems,” IEEE Transactions on Instrumentation and Measurement, vol.37, no.2, pp. 207-212, June 1988. [31] B.M.Popovic,“Synthesis of power efficient multitone signals with flat amplitude spectrum,” IEEE Tran. on Communications, vol.39, pp. 1031-1033, July 1991.

[32] R.V.Nee and R.Prasad, OFDM for Wireless Multimedia Communications,Aitech House, Boston, 2000. [33] K.Fazel and S.Kaiser, “Analysis of non-linear Distortions on MC-CDMA, ” Proceedings of International Conference on Communications 98, vol.2, pp. 1028-1034, 1998. [34] M.R.Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Tran. on Information Theory (Corresp.), vol.IT-16, pp. 85-89, Jan 1970. [35] A. Van den Boss, “A new method for synthesis of low-peak-factor signal,” IEEE Transactions on Acoust., Speech, Signal Processing, vol. ASSP-35, no.l,pp. 120-122,

73 Jan1987. [36] V.Aue and G.P.Fettweis,“Multi-carrier spread spectrum modulation with reduced dynamic range,” in Proc. VTC ’ 96, Atlanta, April/May 1996, pp. 914-917. [37] W.C.Jakes, Ed., Microwave Mobile Communications. New York; IEEE Press, 1974. [38] E.Kreyszig, Advanced Engineering Mathematics, John Wiley & sons, 8th ed.,1998. [39] Leon-Garcia, Probability and Random Processes for Electrical Engineering, Addison Wesley, 2nd ed., May 1994. [40] S.Haykin, Adaptive Filter Theory, 2nd ed.,Prentice Hall, 1991. [41] C.R.Nassar, B.Natarajan, S.Shattil, “Introduction of Carrier Interference to Spread Spectrum Multiple Access,” Proceedings of the IEEE Emerging Technologies Symposium on Wireless Communications and Systems, April 12-13, Dallas, 1999. [42] B.Natarajan, C.R.Nassar, S.Shattil, M.Michelini, Z.Wu,“High Performance MCCDMA via Carrier Interferometry Codes,” accepted for publication in IEEE Transactions on Vehicular Technology. [43] Z.Wu, B.Natarajan, C.R. Nassar and S.Shattil,“High Performance, High Capacity MC-CDMA via Carrier Interferometry,” to be published in the proceedings of IEEE Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2001, September 30 - October 3, San Diego, 2001. [44] B.Natarajan and C.R.Nassar, “Crest Factor Considerations in MC-CDMA with Carrier Interferometry Codes,” Proceedings of IEEE Pacific-Rim Conference on Communications, Computers and Signal Processing, vol. 2, pp. 445-448, August 26-28,

Victoria, Canada, 2001.

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Chapter 4

HIGH PERFORMANCE, HIGHTHROUGHPUT TDMA VIA MULTICARRIER IMPLEMENTATIONS The CI Approach

This chapter demonstrates how multi-carrier implementations of TDMA, based on the CI approach, lead to dramatic benefits in terms of probabilityof-error performance, throughput and network capacity.

4.1. 4.1.1

Introduction Overview of TDMA and GSM

Time division multiple access (TDMA) is a transmission protocol that allows users to share a communication link by assigning unique time slots to each user. Specifically, in TDMA, time is segmented into time slots that are assigned to individual users. In fixed assignment TDMA, each user transmits in one or more predetermined time slots that occur periodically. Dynamic assignment, or packet switching, assigns time slots

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at the time of transmission.

The Global System for Mobile Communications (GSM)[1], which was

the most widespread digital cellular architecture in the world in the days of 2G, is based on TDMA. In typical GSM systems, each user’s time slot holds 148 bits. The transmission bit rate is 270.8 kbps. Thus the bit duration and the time slot duration A guard interval of is used between slots. GSM systems use binary Gaussian minimum shift keying (GMSK) modulation. Here, information is conveyed by the phase of the transmitted signal (characterized by a constant envelope and narrow bandwidth). Specifically, the information bits of user p are first differentially encoded, producing an NRZ (nonreturn-to-zero) symbol stream

next this symbol stream excites a transmit filter h(t) with a Gaussian impulse response. The waveform at the output of the Gaussian filter may be expressed as

where

Here, m(r) is the rectangular waveform of the NRZ pulse and h(t) is the Gaussian pulse defined by

B is the 3dB bandwidth and 2.668. Finally, the Gaussian filter output is integrated, resulting in and this serves as the phase of the transmitted waveform. The complex baseband representation of the output signal corresponds to

Typically, the non-linear baseband GMSK signal is approximated by a linear modulation[2] to aid in system analysis, receiver design and simulation.

GSM, like most TDMA systems, suffers from intersymbol interference (ISI) resulting from multipath. Thus, GSM receivers commonly employ

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a decision feedback equalizer (DFE) . DFE’s significantly reduce receiver complexity while only slightly compromising performance compared to maximum likelihood sequence estimators [3].

4.1.2

Overview of the CI Approach

CI achieves the benefits of both narrowband and wideband processing. Narrowband processing is simpler than wideband processing. For example, wireless channel distortions in a narrow band signal can be characterized by a single attenuation and phase offset. Additionally, array processing, such as phased array and adaptive beam forming techniques, are more effective and more easily performed with narrowband signals. This is important as array processing enables frequency reuse via spatial division multiple access, which greatly increases network capacity.

Wideband processing, on the other hand, can provide benefits of path or frequency diversity. Path diversity exploits the short symbol length of a wideband signal relative to multipath delay. Path diversity processing, such as RAKE reception, coherently combines multiple reflections of a desired signal to improve receiver performance. Frequency diversity, a frequency domain counterpart to path diversity, enables the processing of the reflected energy more efficiently in the frequency domain, further increasing receiever performance.

4.1.3

Introducing CI to TDMA

Carrier Interferometry (CI) may be applied to TDMA . Here, the usual TDMA pulse shape is replaced by the CI signal described in Chapters 2 and 3. That is, each pulse in the TDMA burst corresponds to a linear combining of N carriers (i.e., an N point frequency sampling of the usual sinc(•) pulse shape). The resulting system is refered to as CI/TDMA (e.g, [4]-[6]).

This small change in the transmitter architecture leads to more dramatic changes at the receiver side, which in turn generates very significant performance and throughput benefits. Specifically: the TDMA receiver is constructed to perform a frequency decomposition of the pulse shape followed by a recombining which minimizes ISI while optimizing frequency diversity. Such a frequency based combining significantly outperforms the time based equalizer structures with limited number of taps.

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Moreover, some of the more than 10 dB performance gains achieved in CI/TDMA can be traded off for a doubling of throughput. Specifically, introducing the concept of pseudo-orthogonal pulse positioning in TDMA we fit 2N bits in a burst that typically holds N bits; burst time and system bandwidth are held constant, so a controlled amount of ISI results at the transmit side with 2N bits per N-bit burst. Even with the doubling in throughput, CI/TDMA systems still outperform TDMA with traditional pulse shapes and DFE equalizers. Hence, we have a new TDMA system simultaneously offering doubling in throughput and dramatic performance benefits. The details follow.

4.2. 4.2.1

CI Pulse Shaping in TDMA Essentials

Figure 4.1 illustrates how a CI signal is generated (for use as a TDMA pulse shape). Here, it is observed that a CI pulse is created from a superposition of N carriers equally spaced in frequency by (the N corresponds to the number of bits per slot, e.g., 148 in GSM, and is the TDMA slot duration, e.g., Hence, the CI pulse shape used in TDMA systems corresponds to

or equivalently using properties of summation and sinusoids

Here, refers to the rectangular function that extends over a slot duration and is a constant that ensures a pulse energy of unity. In a CI/TDMA system that complies with GSM specifications, corresponds to the GSM slot duration of and is the number of bits per GSM slot. The total bandwidth of the CI/TDMA system is which is the same bandwidth used by a typical GSM system. However, the frequency domain characteristics of CI/TDMA signal differ substantially from the frequency domain characteristics of a typical GSM system. Figure 4.2 plots the pulse shape h(t). Very similar in time to a typical sinc(•) pulse shape, the CI shape peaks at the time of the intended data

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bit and demonstrates sidelobes for the remainder of the TDMA slot (the remainder of To transmit a burst of bits, the kth bit in a user’s burst is modulated by the CI shape creating the total transmitted signal

It is important to note that the time shifted pulses are orthogonal to one another, i.e., the Nyquist criterion is satisfied at the transmit side:

This pulse shaping strategy creates TDMA signals which are made up of N separable frequency components (equation (4.5)). That is, consider Figure 4.3(a) and (b) - Figure 4.3(a) shows a typical TDMA frequency

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response with traditional pulse shaping, while Figure 4.3(b) shows the TDMA frequency response with CI pulse shaping. It is apparent from these figures that CI-TDMA will allow receivers to separate the wideband signal into frequency components (to create frequency diversity).

4.2.2

CI Pulse Shapes for Doubling Throughput

CI pulse shapes can be used to replace traditional pulse shaping strategies with N pulses per TDMA burst. However, to increase throughput, CI pulse shapes can be applied in TDMA in a manner doubling throughput. The details follow. Consider N orthogonal pulse shapes,

in a TDMA burst. This leads to the N-bit per burst transmission

Next, consider a second set of N pulse shapes time offset from the first set by i.e., consider Pulses in this second set are orthogonal to one another, but pseudoorthogonal to the first orthogonal set. We seek the value of that minimizes the average root mean square intersymbol interference between pulses of set 1 and 2. In a manner analogous to that shown in Chapter 3, we determine that the value of minimizing average rms ISI is This suggests placing 2N symbols in a TDMA burst corresponding to

Notice that 2N symbols have been positioned in the same slot duration

by separating pulses by duration

rather than the usual

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4.2.3

Bandwidth Efficiency of CI/TDMA

A TDMA system using Nyquist root raised cosine pulse shaping with a roll-off factor has a total RF bandwidth A CI signal with equivalent bandwidth (and a carrier-frequency spacing of has carriers in bandwidth In these N´ carriers, we can co-locate N´ orthogonal and N´ pseudo-orthogonal pulses. The total throughput of CI/TDMA is therefore expressed by:

For (sine shapes), CI/TDMA provides a 100% increase in throughput. For (an example of a raised cosine pulse), throughput is increased by 300%.

4.3.

Channel Model

The TDMA burst of equation (4.7) or (4.10) experiences the fading channel taken from the COST-207 GSM system standard[7]. Three basic multipath channel models which represent different radio propagation environments are considered: the hilly terrain (HT) model, the typical urban (TU) model and the rural area (RA) model. These models are

defined as transversal filters with time varying coefficients whose average power is determined by the multipath power delay profiles (PDPs) given in Table 4.1. For realistic vehicle speeds, the coherence time of these channels is greater than the duration of a time slot - hence, the channel is considered constant during the transmission of a burst (but varies from one burst to the next). In typical GSM/TDMA simulations, the PDPs characterize the ISI introduced by the channel. In CI/TDMA, where pulse shapes consist of multiple carrier transmissions which will be frequency separated at

the receiver (next section), the channel must be characterized by the coherence bandwidth (defined here as the bandwidth over which the frequency correlation function is above 0.5). This can be computed from a multipath PDP by using the approximate relationship [8]

where

is the rms delay spread and is computed according to

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Here, is the power of the multipath component arriving at delay This leads to the following coherence bandwidth results (using Table 4.1): for HT , for and for TU, For HT and TU channels the values satisfy

where BW is the total bandwidth of the TDMA system. Equation(4.16) indicates that the HT and TU channels are frequency selective over the entire bandwidth of transmission, but not over each subcarrier (of the CI

pulse shape) [9]. Specifically, with N carriers creating the CI pulse shape, i.e., N carriers residing over the entire bandwidth, BW , each carrier undergoes a flat fade, with the correlation between the ith subcarrier fade and the jth subcarrier fade characterized by [10]

where indicates the frequency separation between the ith and the th j subcarriers. Generation of fades with correlation has been discussed in [11] and briefly presented in Chapter 3.

4.4.

CI/TDMA Receiver

We assume we are transmitting 2N bits per burst (equation (4.10)) and each frequency component making up the CI/TDMA pulse shape experiences a different fade (Section 4.3). That is, the received signal is characterized by

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where is the gain and the phase offset in the carrier of the CI pulse shape (due to the channel fade) and is additive white gaussian noise (AWGN). To simplify the analysis, exact phase synchronization is assumed. Figure 4.4 illustrates the CI/TDMA receiver’s detection of the symbol. Here, the symbol residing on the CI pulse shape, is separated into its N component frequencies (implementable via an FFT). This results in a decision vector where is the ith carrier component and corresponds to

The second term represents the presence (in the other bits in a user’s burst.

carrier) of the

A suitable strategy must be found to combine the Orthogonality restoring combining (ORC) involves the scaling of each by (creating and a summing of the terms (creating This enables the minimization of the second term, but can result in substantial noise enhancement. Minimum mean square error combining (MMSEC) is a powerful alternative which attempts to jointly minimize the second term and the noise term. In our case, employing MMSEC results in the decision variable R given by the linear sum

Note that for small the gain becomes small to avoid the excessive noise amplification, while for large it becomes proportional to the inverse of the subcarrier envelope, in order to recover the orthogonality among pulse shapes. A hard decision device provides the final output

4.5.

Performance Results

Figures 4.5,4.6 and 4.7 present bit error probability (BER) versus SNR performance curves for the hilly terrain (HT), rural area (RA) and

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typical urban (TU) channels respectively. The dotted line (marked with

circles) represents the CI/TDMA system results (with symbols per burst) and the dashed line (marked with stars) represents a GSM system employing Gaussian pulse shaping with a DFE (6,4) receiver (and symbols per burst) [1]. Both systems have identical slot duration, throughput, and bandwidth. The new CI/TDMA scheme achieves more than 8dB gain in the HT channel at probabilty of errors in the order of In the TU channel, gains in the order of 5dB are achieved at probability of errors of The performance benefit in the RA case is not as noticeable as in the

HT and TU environments. This is because in RA channels, coherence bandwidth is large (delay spread is small), meaning the channel models are closely approximated by a flat fading channel. In this case, there is little frequency diversity benefit for CI/TDMA to exploit. Figures 4.8 and 4.9 present bit error probability (BER) versus SNR

performance curves for a CI/TDMA system operating with pseudoorthogonal bits in a burst. The dotted line marked with circles represents the performance of the CI/TDMA system with orthogonal pulses. The dashed line marked with stars demonstrates the performance of the CI/TDMA system with double throughput (296 symbols per burst) via pseudo-orthogonal positioning. Relative to the CI/TDMA system with symbols per slot, the novel CI/TDMA architecture demonstrates degradations of 1-2 dB, resulting from the ISI introduced at the transmitter side. This performance degradation is small when compared to the doubling in throughput. Moreover, with 296 bits per

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slot, the CI/TDMA system achieves close to 6.5 dB gain relative to GSM with 148 bits per burst, Gaussian pulse shaping and a DFE(6,4) receiver at BER of in a HT chanel. In the TU channel, gains in the order of 4 dB are achieved at probability of errors in the order of These results were obtained with no increase in bandwidth, or burst duration, and with no change in modulation formats.

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These results show that the performance degradations that result due to limited number of taps in a digital matched filter and DFE (6,4) equalizer are overcome by a receiver which employs a frequency based processing. As the number of taps in the equalizer is increased, the performance of the equalizer structure can be significantly improved. However, this comes at a significant cost in complexity. Here, without cost in bandwidth, throughput or slot duration, CI/TDMA provides an efficient low cost way of achieving high performance and high-throughput

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by exploiting the frequency domain through pulse shaping. Since it retains all the features of a TDMA system, all higher protocol levels currently in use for TDMA are applicable to CI/TDMA as well.

4.6.

Conclusions

In this chapter we introduced Carrier Interferometry to TDMA systems in the form of a novel pulse shape. The resulting CI/TDMA system is bandwidth efficient, significantly enhances performance, and has the ability to double throughput by positioning CI pulse shapes pseudoorthogonally in time. Even when throughputs are doubled, performance still exceeds that of traditional TDMA systems. By application of the multi-carrier approach found in OFDM and MC-CDMA, and by using the pseudo-orthogonality concept that has found widespread use in DS-CDMA, TDMA systems can now benefit from significant gains in performance and throughput.

References [1] Bjorn A.Bjerke, J.G.Proakis, M.K.Lee and Z.Zvonar, “A comparison of Decision feedback equalization and data directed Estimation technique for the GSM system,” IEEE 6th International conference on Universal personal communications, 1997. [2] P.A.Laurent, “Exact and approximate construction of digital phase modulations

88 by superposition of amplitude modulated pulses,” IEEE Trans. on Communication, pages 150-160, Feb.1986. [3] G.D.Aria, R.Piermarini and V.Zingarelli, “Fast Adaptive Equalizers for narrow-

band TDMA Mobile Radio,” IEEE Trans. on Vehic. Tech., pg 392-404, May 1991. [4] B.Natarajan, C.R.Nassar, S.Shattil, “Innovative Pulse Shaping for High Performance Wireless TDMA,” accepted for publication in IEEE Communication Letters [5] B.Natarajan, C.R.Nassar and S.Shattil, “Exploiting Frequency Diversity in TDMA through Carrier Interferometry,” Proceedings of Wireless 2000. vol. 2, pp. 469-476, Calgary, Canada, July 10-12, 2000. [6] B.Natarajan, C.R.Nassar and S.Shattil, “Throughput Enhancement in TDMA through

Carrier Interference Pulse Shaping,” Proceedings of IEEE Vehicular Technology Conference, vol.4, pp. 1799-1803, Fall 2000, Boston. [7] COST-207: “Digital land mobile radio communications,” Final report of the COST-Project 207, Commission of the European Community, Brussels, 1989. [8] T.S.Rappaport, Wireless Communications - Principles and Practice. New Jersey: Prentice Hall, 1st ed.,1996. [9] J.Proakis, Digital Communications. New York: McGraw-Hill, 3rd ed., 1995. [10] W.Xu and L.B.Milstein, “Performance of Multicarrier DS CDMA Systems in the

presence of correlated fading,” IEEE 47th Vehicular Technology Conference, Phoenix, AZ, May 4-7, 1997, pp. 2050-4 [11] B.Natarajan,C.R.Nassar & V.Chandrasekhar, “Generation of Correlated Rayleigh

Fading envelopes for spread spectrum applications,” IEEE Communication letters, vol.4, no.l, pp 9-11, January 2000. [12] J.Proakis, “Adaptive equalization for TDMA digital mobile radio,” IEEE Tran. on Vehicular Technology, vol. 40, pp. 333-341, May 1991. [13] J.Tellado-Mourelo, E.Wessel, and J.M. Cioffi, “Adaptive DFE for GMSK in indoor radio channels,” IEEE Tran. on Communications Systems, vol.14, pp. 492-501, April 1996. [14] T.K.Ohno and F.Adachi, “GMSK frequency detection using decision feedback equalization,” Electronics Letters, vol. 23, no.25, pp. 1350-1351. Dec 1987. [15] M.Rahnema, “Channel Equalization for the GSM System,” IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC ’96, pp. 878-882, October 15-18, 1996.

[16] D.C.Cox, “Universal digital portable radio communications,” Proc. IEEE, vol. 75, no.4, April 1987. [17] R.D’Avella, L.Moreno and M.Sant’ Agostino, “An adaptive MLSE receiver for

TDMA digital mobile radio,” IEEE Journal on Selected Areas in Communications, SAC-7, 122-129, 1989. [18] B.Glance and L.J.Greenstein, “Frequency selective fading effects in digital mobile radio with diversity combining,” IEEE Tran. on Communications, vol. COM-31, pp. 1085-1094, Sept. 1983. [19] G.K. Kaleh, “Channel equalization for block transmission systems,” IEEE Journal on Selected Areas in Communications, pp. 110-121, Jan 1995. [20] R.Steele, Mobile Radio Communications, Pentech Press, 1992.

Chapter 5 HIGH-PERFORMANCE, HIGH-CAPACITY DSCDMA VIA MULTICARRIER IMPLEMENTATION

This chapter introduces powerful new multi-carrier technologies to existing DS-CDMA (direct sequence code division multiple access) platforms: these improve both the probability of error performance and network capacity (measured by number of users per cell) of today’s DSCDMA systems. Specifically, this chapter introduces Carrier Interformetry (CI) chip shaping, a novel multi-carrier chip shaping scheme for DS-CDMA systems. By using CI chip shaping, DS-CDMA systems significantly improve upon their BER performances and increase their network capacity (i.e., the number of users supported).

Specifically, in the proposed DS-CDMA systems with CI chip shapes, each chip is created via a linear combining of N carriers (where N is the processing gain). At the receiver, a novel detection strategy is employed whereby each chip is decomposed into its N frequency components and optimally recombined to create large frequency diversity benefits. Simulations performed over Rayleigh fading channels indicate the new chip shaping and detection strategy outperforms conventional DS-CDMA with RAKE reception by as much as 14 dB at low bit error rates. Moreover, CI chip shapes may be positioned both orthogonally as well as pseudo-orthogonally (in time), allowing the novel system to support many more chips per symbol duration and unit bandwidth (than traditional DS-CDMA). More chips correspond to more users per cell per unit bandwidth. Simulations performed over Rayleigh fading channels indicate the new chip shaping (and corresponding detection strategy) enables a doubling

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of DS-CDMA network capacity (i.e., doubling in terms of number of users) without any loss in performance. With the exception of chip shape and receiver design, this new system retains all the features of a conventional DSCDMA system.

5.1 Introduction DS-CDMA (direct sequence code division multiple access) has emerged as a dominant player in the world of wireless telecommunications [114]. Among DS-CDMA’s successes is its adoption as the standard of choice in 3G wireless (see, e.g., [15][16]). However, DS-CDMA is not without its drawbacks, including limits to the probability of error performance and network capacity.

With regard to performance, DS-CDMA systems use RAKE receivers [1-14] in an attempt to exploit path diversity and improve probability of error performance. However, it is difficult for the DS-CDMA RAKE receiver to fully benefit from the path diversity and make efficient use of the received signal energy scattered in the time domain because (1) the multi-path effect that induces path diversity also causes a loss of user orthogonality (this leads to large inter-path interference and hence lowered SIR), and (2) only a limited number of taps are available to the RAKE receiver.

One system that has emerged recently, capable of outperforming DSCDMA, is MC-CDMA (multi-carrier code division multiple access) [17-27]. As detailed in Chapter 3, MC-CDMA employs receivers which offer frequency diversity benefits instead of path diversity benefits to enhance performance in a multipath channel. Here, carefully designed MC-CDMA receivers make efficient use of the received signal energy in the frequency domain, demonstrating significant performance improvements over DSCDMA with RAKE receivers (e.g., [5]). In this work, we demonstrate the power of multi-carrier chip shaping in DS-CDMA: by replacing the usual sinc and raised cosine chip shapes with the CI (carrier interferometry) chip shapes, we bring the performance benefits of MC-CDMA to DS-CDMA, bridging the gap between DS-CDMA and MCCDMA performances. Specifically, by employing CI chip shaping in DSCDMA, we introduced an exploitable frequency diversity at the DS-CDMA receiver and enable DS-CDMA receivers to make full use of the received signal energy.

Another key concern in DS-CDMA systems is network capacity as measured by the number of users per cell. In current DS-CDMA systems, designers choose between (1) orthogonal spreading codes (Hadamard-Walsh

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codes) where network capacity is hard-limited by the length of the spreading code (processing gain); or (2) pseudo-orthogonal codes where more users may be supported at the cost of increasing the multiple access interference (MAI) (leading to significant degradation in the performance of DS-CDMA systems).

In this chapter, we continue to demonstrate the power of chip shaping in DS-CDMA by introducing the concept of pseudo-orthogonal CI chips to DS-CDMA systems: this doubles network capacity. Specifically, a second set of N CI chips (where N is the processing gain) is sent out with the original DS-CDMA N chip set (the two sets of chips are sent within the same symbol duration). The positioning (in time) of the new N chip set is based on minimum correlation. These 2N chips allow DS-CDMA to support twice as many users per unit bandwidth. In short, we present an innovation in chip shaping which enhances both the performance and network capacity of existing DS-CDMA systems, bringing as much as 14 dB performance gain to today’s DS-CDMA systems, and doubling DS-CDMA’s network capacity. Section 5.2 briefly reviews conventional DS-CDMA systems. Section 5.3 presents the novel Carrier Interferometry (CI) Chip Shaping technique and its application to the transmitter of a DS-CDMA system. Section 5.4 discusses the novel frequency-based receiver structure and the corresponding frequency combining schemes for these DS-CDMA systems. Sections 5.5 and 5.6 introduce pseudo-orthogonal chips and demonstrate how they can be applied to increase DS-CDMA’s network capacity. Section 5.7 discusses channel modeling, and section 5.8 presents computer simulation results when the system is emulated over Rayleigh fading channels.

5.2 Review of DS-CDMA

5.2.1

Introduction

DS-CDMA systems come with a wide range of far-reaching benefits: these include enhanced privacy, inherent resistance to fading, and spectral efficiency in a cellular system. The block diagram representation of today’s DS-CDMA transmitter is shown in Figure 5.1. As is evident from the figure, the DS-CDMA transmitter for user k spreads the original data stream via a

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spreading code applied in the time domain Each user is allocated a unique spreading code (typically orthogonal in the downlink and pseudoorthogonal in the uplink). The ability to suppress multi-user interference is determined by the cross-correlation characteristics of the spreading codes.

After transmission over a frequency selective fading channel (typical of wideband DS-CDMA), the received signal is the superposition of several multipath signals each arriving with different delays (in the time domain). Here, the cross-correlation of different users’ signals on different paths is no longer the cross-correlation of the time-aligned spreading codes. In today’s DS-CDMA receiver (Figure 5.2), a tapped delay line RAKE receiver [1][4][27] improves performance in the presence of mulitpath propagation. That is, assuming L separable multi-paths, the RAKE receiver attempts to provide -order diversity via path separation (of the L paths) and a weighted coherent recombining (typically MRC (maximum ratio combining)). However, the multipath effect causes a loss of orthogonality between different user’s signals (even in the synchronous case) thereby degrading the SIR (signal to interference ratio) on each branch of the RAKE (due to large inter-path interference). As a result, it is difficult for the DSCDMA receivers employing path diversity to make full use of the received signal energy scattered in the time domain.

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5.2.2

DS-CDMA Transmit and Receive Signal

As seen in Figure 5.1, user k’s data bit is spread (in the time domain) by a multiplication with the spreading code This code is composed of N chips per bit, each modulated by either +1 or –1. Mathematically, this corresponds to

where

is the ith element of user k’s spreading code

and is the chip shaping filter. In current DSCDMA systems, the most commonly used spreading code is the HadamardWalsh code (as this maintains the orthogonality between different users’ time aligned signals); the chip shaping is either the usual sinc function or raised cosine function. Including chip code creation at the usual DS-CDMA transmitter side, we can redraw Figure 5.1 in a more detailed manner, as shown in Figure 5.3:

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Thus, in DS-CDMA, the corresponds to (at baseband):

user’s transmitted signal (for one bit)

where A is constant ensuring a bit energy of unity. (Also, BPSK has been assumed for ease in presentation.) The total transmit signal considering all K users’ signals (and assuming downlink or synchronous uplink communications) is:

Transmitted over a multipath fading channel at carrier frequency the signal arriving at the receiver side corresponds to

where L is the total number of paths;

is the fading parameter of the

path;

is the time delay of the path; is the phase offset of the and is the additive white Gaussian noise.

path;

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In current DS-CDMA systems, tapped delay line RAKE receivers (Figure 5.2) are commonly employed to achieve path diversity gains. In a frequency-selective multipath channel with L separable paths, the RAKE receiver attempts to provide up to -order diversity. Specifically, in RAKE receivers, each “finger” extracts one of the multi-paths, and the fingers’ outputs are then combined to exploit path diversity and overcome multi-path effects. That is, for the RAKE receiver of Figure 5.2, the for user k corresponds to

where

finger’s output

is user k’s previous data bit, is user k’s next data bit, and represents the partial cross-correlation of user k and n at time delay

T:

Specifically, when there is no time delay and when orthogonal spreading codes (e.g., Hadamard-Walsh codes) are employed

Assuming orthogonal codes, we rewrite equation (5.6) as

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In RAKE receivers, the decision variables are combined, i.e., the decision variables are combined across paths to exploit the path diversity gain. The final decision statistic for user k corresponds to

Maximum Ratio Combining (MRC) is usually applied, i.e,

A hard decision device follows:

As discussed earlier, the received DS-CDMA signal on each branch of the RAKE receiver suffers from large inter-path interference. This interpath interference is detailed by the second and third terms of equation (5.9). As a result, each diversity component demonstrates a significantly reduced SIR, which limits the performance of the RAKE receiver. Figure 5.4 shows a typical DS-CDMA BER performance versus signal to noise ratio (SNR) curve in the hilly terrain (HT) channel. The processing gain is and the system is fully loaded: the high error floor due to the multipath interference is clearly evident.

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5.3 Novel Multi-Carrier Chip Shapes and Novel Transmitters for DS-CDMA We propose a novel chip shape for DS-CDMA: the chip shape corresponds to the superpositioning of N carriers equally spaced in frequency by (where N corresponds to the processing gain in DS-CDMA and is the symbol duration). This chip shape (implemented using an IFFT) corresponds to [28-33]

where A refers to the constant that ensures a chip energy of 1/N. Figure 5.5 shows the creation of the new chip shape. Figure 5.6(a) plots the chip shape h(t) over symbol duration and Figure 5.6(b) plots h(t) in the frequency

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domain. As evident from Figure 5.6(b), the CI chip shape is simply an Npoint frequency sampling of the sinc chip shape. As a direct consequence, it is important to note that these proposed chips (h(t)'s) satisfy the usual orthogonality condition:

Moreover, considering Figure 5.6(a), the chip shape demonstrates an interferometry pattern in the time domain: hence, the chip shape is referred to as the carrier interferometry (CI) chip shape.

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To generate the DS-CDMA code for user , the value of the spreading sequence, (typically +1 or –1), modulates the CI chip shape filter

where h(t) is as shown in equation (5.13). Correspondingly, user k’s output signal at the transmitter side is

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where is the data bit of the user, and g(t) is a unit amplitude rectangular waveform of duration and is a constant that ensures the symbol energy of user k is unity.

Noting that

we can rewrite equation (5.18) as:

Using equation (5.20), it is evident that the chip

corresponds

to the linear combining of the N carriers as seen in equation (5.13), where now the carrier is phase offset by where

The total transmit signal for K users in a downlink (or synchronous

uplink) is simply:

Figure 5.7(a) presents the block diagram for the DS-CDMA transmitter employing CI chip shapes.

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It is apparent from Figure 5.7 that the transmitter for CI/DS-CDMA is identical to that of traditional DS-CDMA (Figure 5.3) with the one exception of the CI chip shaping filter h(t) replacing usual chip shaping filter As evidenced in Figure 5.6(b), our chip shaping strategy creates DSCDMA signals which are made up of N separable frequency components. That is, the CI chip shape will allow DS-CDMA receivers to separate the incoming wideband signal into frequency components (enabling frequency diversity at the receiver).

5.4 Novel Receiver Design for CI/DS-CDMA The receiver for the novel CI/DS-CDMA system is shown in Figure 5.8 and is similar to the receiver structure for other CI implementations (Chapter 2-4). This receiver is detailed next.

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Assuming a Rayleigh frequency-selective slow fading channel (typical of wideband DS-CDMA), frequency selectivity exists over the entire bandwidth, but not over the individual carriers that make up the CI chip

shape. Hence, each frequency component making up the CI chip shape experiences a unique flat fade. That is, the received signal (assuming the transmit signal in equation (5.22)) is characterized by:

where is the gain and the phase offset in the carrier of the CI chip shape (due to the channel fade), and represents additive white Gaussian noise. To simplify the analysis, exact phase synchronization is assumed. The CI/DS-CDMA receiver shown in Figure 5.8 consists of three main components: (1) the incoming DS-CDMA signal is separated into its N chip components, and each chip is decomposed into its carriers and recombined to exploit frequency diversity and minimize inter-chip interference and noise; (2) the newly recreated CI chips are despread and

linearly combined to eliminate the presence of other users (typical of DSCDMA receivers); and (3) a hard decision device creates the final bit decisions [30-33]. The processing of the chip for user l is detailed in Figure 5.8(b). Here, the chip is separated into its N carrier components by a bank of mixers and integrators. Each carrier contributes one decision variable corresponding to

We can rewrite this equation as

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The first term represents the desired contribution from user l, chip m and carrier n. The second term represents the presence (in the carrier) of the remaining N-1 chips of the same user (user l). The third term represents the presence of other users’ interference due to their chip. The fourth term represents the presence (in the carrier) of the other users' remaining N-1 chips. The fifth term is a zero mean Gaussian random variable with variance It is important to note that the terms are correlated across chips (but not across carriers). The covariance matrix of the vector noise corresponding to a fixed n (carrier number) and a different m (chip number) is:

A suitable frequency combining strategy is employed in Figure 5.8(b) to combine the across carriers. The intention here is to: (1) offer frequency diversity gains when recreating the chip, and (2) remove the second and fourth interference term in equation (5.25) (removing the inter-chip interference) while minimizing noise. Orthogonality Restoring Combining (ORC) refers to the combining where each is scaled by then summed, i.e.,

This enables a perfect elimination of the second term and fourth term (due to the chip orthogonality condition of equation (5.14), while providing optimal frequency diversity combining. However, it can result in substantial noise enhancement, and as a result is only suitable in low noise conditions (high SNR). When SNR is low, Equal Gain Combining (EGC) is a good choice for the combining strategy as it minimizes noise. Here, the N carrier terms for the chip are combined to create:

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A Minimum Mean Square Error Combining (MMSEC) can also be devised, one which jointly minimizes the second term, the fourth term, and the noise, all the while achieving maximum frequency diversity [30]. The MMSE combining across the N carriers of the chip creates the output decision variable:

where

After frequency combining across chips’ carriers, we return to Figure 5.8(a) where a final decision variable for user l is generated by combining across chips in the usual DS-CDMA fashion, eliminating multi-user interference (the third term of equation (5.25)):

That is, the chip decision variable is multiplied by spreading code and the resulting product terms are combined together. The orthogonal cross-correlation between spreading codes of different users enables this combining to minimize multi-user interference in a conventional DS-CDMA manner.

5.5 High Capacity DS-CDMA via Pseudo-Orthogonal CI Chip Shaping

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As seen in section 5.4, the CI chip shaping strategy leads to a new receiver structure based on frequency combining. This will enable significant performance gain in DS-CDMA systems (discussed in section 5.8). However, CI chip shaping not only helps DS-CDMA in terms of probability of error performance, but also allows for increases in network capacity. This forms the focus of this subsection. [33].

We seek to create two sets of CI chip shapes in the symbol duration The first set corresponds to the usual N chips , and the second set corresponds to K

chips

In so doing, N users can be supported on the first set of N chips and an additional K users can be supported on the second set of K chips, leading to a total DS-CDMA network capacity of N+K users (without any increase in bandwidth nor a decrease in throughput per user).

To determine the location of CI chip shapes in the second set of K CI chips, i.e., to determine we study the cross correlation between CI chip shape h(t) and its time delay version This can easily be shown to correspond to (using equation (5.13)):

This cross correlation term demonstrates 2N-3 zeros: •

N-1 equally spaced zeros at the

•

resulting from

term, and

N-2 equally spaced zeros at as a result of the cos(•) term. (The zero at

when N is even is not

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included because it is already included in the first set of zeros. We assume N is even throughout for simplicity in presentation.) The existence of the first set of equally spaced zeros indicates that a DS-CDMA system can simultaneously support N orthogonal CI chips in one data symbol, namely the proposed of earlier section. The existence of the second set of zeros indicates that we can place an additional N-2 chips at highly (but pseudo) orthogonal locations, creating a second set of N-2 CI chips in the same duration corresponding to

With these two sets of CI chips in symbol duration we support (2N-2) users. The first N users employ spreading codes (e.g., HadamardWalsh codes) applied to the N orthogonal chips , i.e.,

The remaining (N-2) users employ spreading codes (e.g., truncated Hadamard-Walsh codes) applied to the (N-2) pseudo orthogonal chips, i.e.,

That is, with all (2N-2) users on the system, the transmitted signal is:

i.e.,

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where

and

After transmission through a frequency selective fading channel, the received signal in the downlink is characterized by:

where is the gain and the phase offset in the carrier of the CI chip (due to the channel fade), and n(t) represents additive white Gaussian noise. Exact phase synchronization is assumed. The receiver structure for CI/DS-CDMA with increased capacity is essentially unchanged from its schematic in Figure 5.8 and its description in section 5.4. The only modification is as follows: Minimum Mean Square Error frequency combining (MMSEC) for DS-CDMA transmission with the codes (t) of equation (5.34) and (5.35) corresponds to

where is shown in equation (5.30) and L is the number of users employing the system (e.g., when fully loaded).

5.6 High Performance, High Capacity via a Second PseudoOrthogonal Chip Shaping In theprevious section, we increased network capacity by positioning a new (N-2)-chip set alongside the original N-chip set (in the same symbol

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duration It is easily shown that this proposed (N-2)-chip set minimizes correlation with respect to the first chip in the original chip set. This is not an optimal criteria. In this section, we take advances in DS-CDMA chip shaping one step further: we introduce two sets of N-chips each into one symbol duration, and we ensure that the total cross correlation (inter-chip interference) between the two sets of chips is minimized. That is, two orthogonal CI chips sets (of length N chips each, where N is the processing gain) are positioned pseudoorthogonally in one symbol duration which allows for a doubling of the number of chips without increasing symbol time or bandwidth. Simulation results over multipath fading channel shows that the novel CI/DS-CDMA system with double capacity still outperforms the conventional DS-CDMA system. When compared to applying pseudo-orthogonal spreading codes into DS-CDMA systems to double network capacity, the proposed CI/DS-CDMA system is shown to support 8 times of the network capacity with the same BER performance. Specifically, let the first set of N CI chips correspond to the usual orthogonal set and let a second set of N CI chip shapes correspond to These N chips are time delayed by with respect to the first N chip set Since the chips in the first set are orthogonal to one another, it is obvious that the chips in the second set are also orthogonal to each other, i.e.,

To double network capacity in DS-CDMA, we propose that the

second set of N orthogonal CI chip shapes be sent out simultaneously with the original N-chip set. With two sets of CI chip shapes, we can support two groups of N users each [34].

The CI chips in the first set and the CI chip shapes in the second set are not orthogonal to one another. There exists a cross correlation between the chip shapes from different sets. We now determine the value in the second CI chips set such that there exists a minimum average cross-correlation th between the sets. Let denote the cross correlation between the j chip

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in chip set 1 Also, let

and the

chip in chip set 2 (constructed with

).

represent the root mean square cross correlation that exists between chip shapes in set 1 and set 2. We seek to find the two sets of chip shapes (i.e., the

value) that minimizes

. Now, it is easily shown that

It is also easily shown that

That is, the total cross-correlation between the chip in orthogonal chip set 2 and all chips in set 1 is identical to the cross-correlation between the chip in chip set 2 and all chips in set 1. Using equation (5.45), we

rewrite equation (5.43) as

and, using equation (5.44), this becomes

We now determine the selection of

, which we refer to as

,

minimizing the root mean square correlation between the two chip sets. To do this, we seek the value that solves

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Now,

where

Now,

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From (5.59), when

we have

and,

therefore, from equation (5.50),

Seeking to determine which

are maxima and

which are minima, we calculate the second order partial derivative at and determine:

Hence, minima. Selecting

corresponds to maxima and we choose

root mean square cross correlation, selection of

as a minima.

provides

as our minima. Figure 5.9 plots the as a function of

, verifying our

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Hence, if we have one set of N orthogonal CI chip shapes, and we want to increase system capacity to 2N users, we can introduce a second set of N orthogonal CI chip shapes. To best do that, in a minimum inter-chip interference sense, introduce a second set of CI chip shapes with phase offset

by

with respect to the first set of CI chip shapes. Remembering that , the selection of

leads to

That is, the second set of CI chip shapes with minimum cross correlation to the original set of CI chip shapes is just the time delayed version of the original set with delay corresponding to a half chip duration delay.

With these two sets of N CI chip shapes each, two groups of N users can be supported simultaneously in the DS-CDMA system. The first group of N users spreads its data bits over the first set of N CI chips and the second

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group uses the second set. The total transmit signal in a CI/DS-CDMA system supporting all 2N users corresponds to

The receiver for detection of this transmit signal is consistent with the receiver structure shown earlier in Figure 5.8, and characterized in section 5.4.

5.7 Channel Modeling In this work, a typical multipath fading channel model is used to characterize the performance benefit of the DS-CDMA with CI chip shapes: the Hilly Terrain (HT) channel model taken from the COST-207 GSM standard [35]. This channel model is defined as a transversal filter with time varying coefficients whose average power is determined by the multipath power delay profile (PDP) given in Table 5.1.

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We assume bandwidth and symbol rate consistent with the GSM standard. That is, we choose chip duration and bit rate=270.8 kbit/s. For such a DS-CDMA system, the HT channel is a two path Rayleigh fading channel (path 1-4 in the HT power delay profile converge to one path, and path 5 and 6 converge to the second path). The average power of the second path is 4.25 dB lower than that of the first. In a DS-CDMA system with CI chip shapes, the chip shapes consist of multiple carrier transmissions (frequency separated at the receiver). In this

case, the channel must be characterized in the frequency domain by the coherence bandwidth (defined here as the bandwidth over which the frequency correlation function is above 0.5). This can be computed from a multipath power delay profile by using the approximate relationship [36]

where

is the rms delay spread and is computed according to

Here,

is the power of the multipath component arriving at delay

This leads to the following coherence bandwidth result: for the HT channel

model of Table I,

This

value satisfies

where is the total bandwidth of the system. Equation (5.69) indicates that the HT and TU channels are frequency selective over the entire

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bandwidth of transmission, but not over each carrier [37]. Specifically, with N carriers residing over the entire bandwidth, BW, each carrier undergoes a flat fade, with the correlation between the subcarrier fade and the subcarrier fade characterized by [37]

where indicates the frequency separation between the and the subcarriers. Generation of fades with correlation has been discussed in Chapter 3 [38].

5.8 Characterizing Performance Gains and Network Capacity Improvements in CI/DS-CDMA CI/DS-CDMA is simulated using the HT channel model of subsection 5.7. Results for a conventional DS-CDMA system with a RAKE receiver are generated to form a benchmark for comparison.

We assume a synchronous downlink channel (or, equvalently, an uplink channel where synchronousity is maintained). To make a fair comparison, we assume the processing gains are 32 for all systems and each uses Hadamard-Walsh codes in all simulations. All simulations are performed with a fully loaded system. Figure 5.10 presents bit error probability (BER) versus SNR performance curves for the HT channel. The line marked with circles represents the CI/DS-CDMA system with MMSE combining at the receiver, and the line marked with stars represents the benchmark DS-CDMA system. From the figure, traditional DS-CDMA’s BER floor, due to inter-path interference in the RAKE receiver branches, severely limits its performance. The proposed CI/DS-CDMA system with MMSEC combining suppresses this floor. By employing frequency diversity, CI/DS-CDMA achieves performance gains on the order of 14 dB at

Figure 5.11 compares the BER results of traditional DS-CDMA with a CI/DS-CDMA system using EGC combining. From the figure we observe CI/DS-CDMA, even with the low complexity EGC combining, achieves much better performances than DS-CDMA.

Figure 5.12 presents the network capacity benefits that can be achieved in CI/DS-CDMA systems using the (2N-2) chips shapes

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characterized in subsection 4.5. Benchmark results are generated using the following systems: (1) a traditional DS-CDMA system with a RAKE receiver using N=32 Hadamard-Walsh codes and (2) a traditional DS-CDMA using pseudo-orthogonal codes where the first 33 users use one set of Gold codes and the next 32 users use a second set of Gold codes (for a total capacity of 65 users). In Figure 5.12(a), the curve marked with asterisks represents the performance of traditional DS-CDMA with Hadamard-Walsh codes, while the curves marked with circles represents the performance of CI/DS-CDMA. In

CI/DS-CDMA, the first 32 users are supported using N=32 orthogonally positioned CI chip shapes and H-W codes, and the next 30 users are supported using N-2=30 pseudo-orthogonal CI chips and truncated H-W codes. For

users, the performance benefits of CI/DS-CDMA over traditional DSCDMA confirms that energy harnessed from a frequency domain combining (creating frequency diversity benefits) provides greater benefit than the time domain combining based on a RAKE receiver. The ability to locate chips

pseudo-orthogonally results in the ability to support an extra 30 users, nearly doubling capacity without extra bandwidth. Without any loss of performance,

capacity increases of 45% can be supported when SNR is 5 dB (Figure 5.12(a)). In traditional DS-CDMA, network capacities are increased by use of

pseudo-orthogonal codes. Figure 5.12(b) shows performance curves for (1) traditional DS-CDMA with K=65 users supported using pseudo-orthogonal Gold codes and (2) CI/DS-CDMA supporting 62 users by use of N=32 orthogonal and N-2=30 pseudo-orthogonal chips in duration It is clearly observed that the use of pseudo-orthogonal CI chips offers a performance far better than that achieved by pseudo-orthogonal codes (for comparable capacity).

118

t

119

120

Figure 5.13 presents the network capacity gain achieved when using the optimally designed 2N CI chips co-located in each symbol duration (as characterized in section 5.6). Here, the curve marked with asterisks represents the performance of traditional DS-CDMA with Gold codes, while the curves marked with circles represents the performance of traditional DS-CDMA with Hadamard-Walsh codes. The curves marked with dots represents the performance of the proposed CI/DS-CDMA system with two chip sets of size N=32 chips each. For users, the performance benefits of CI/DS-CDMA over traditional DS-CDMA again confirms that energy harnessed from a frequency domain combining (creating frequency diversity benefits) provides greater benefit than the time domain combining. The ability to locate the second set of CI chip shapes results in the ability to support an extra 32 users, doubling network capacity without any increase in bandwidth or loss in throughput. Even when doubling the network capacity of the system, the CI/DS-CDMA with two N=32 chip sets still outperforms conventional DSCDMA systems with Hadamard-Walsh codes and RAKE reception. It is apparent from Figure 5.13 that CI/DS-CDMA supporting 64 users provides the same BER performance as a traditional DS-CDMA system with only 16 users.

In traditional DS-CDMA, network capacities can be increased by use of pseudo-orthogonal codes. Referring to Figure 5.13, it is evident that the use

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of pseudo-orthogonal CI chips offers a performance far better than that achieved by use of pseudo-orthogonal codes (for comparable network capacity). The CI/DS-CDMA system supporting 64 users has the same BER performance of a DS-CDMA system using Gold codes and supporting only 6 users.

Figure 5.14 compares the performance of CI/DS-CDMA using the (2N-2) chips per symbol (as described in section 5.5) with the CI/DS-CDMA system using the 2N chips per symbol designed as explained in section 5.6, We refer to these schemes as CI/DS-CDMA-1 and CI/DS-CDMA-2, respectively. From this curve, it is evident that CI/DS-CDMA-2 outerperforms CI/DSCDMA-1, which is no surprise since the CI chip shapes in CI/DS-CDMA-2 were designed based on minimum average inter-chip interference criteria.

In addition to performance and network capacity gains, CI/DSCDMA avoids the complex and expensive RAKE receiver structure (which must operate at chip rate). The CI/DS-CDMA receiver structure maintains low complexity through application of the inverse fast Fourier transform (IFFT) at the transmitter, and application of the FFT at the receiver.

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5.9 Conclusions In this chapter, a novel chip shaping method that involves carrier interferometry is investigated and is shown to support the DS-CDMA architecture with improved performance and increased network capacity. This multi-carrier scheme does not require a RAKE receiver. Instead, using suitable combining strategies at the receiver, the system exploits frequency diversity benefits that are inherent in the proposed multi-carrier chip shaping. Simulation results show dramatically improved BER performance when the new architecture is applied (when compared to a traditional DS-CDMA system). By introducing pseudo-orthogonal chips into the system, we demonstrate increases in the network capacity of the system by 100% while outperforming traditional DS-CDMA.

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Interformetry”, The International Conference on Wireless Communications, Calgary, Canada, July 9-11, 2001, pp. 564-569 [33] Zhiqiang Wu, Carl R. Nassar, “Chip Shaping Advances for High Capacity DS-CDMA”, 2001 International Conference on Third Generation Wireless and Beyond, San Francisco, May 30-June 2, 2001

[34] Zhiqiang Wu, Balasubramaniam Natarajan ,Carl R. Nassar “High-Performance, HighCapacity MC-CDMA via Carrier Interferometry”, The IEEE International Symposium on Personal, Indoor and Mobile Radio Communication, San Diego, Sep 30-Oct 3, 2001 [35] COST-207: “Digital land mobile radio communications”, Final report of the COST-Project 207, Commission of the European Community, Brussels, 1989 [36] T.S. Rappaport, Wireless Communications-Principles and Practice. New Jersey: Prentice Hall, 1996 [37] J. G. Proakis, Digital Communications, Mc-Graw Hill,

ed., 1991.

124 [38] B. Natarajan, C.R. Nassar and V. Chandrasekhar, “Generation of Correlated Rayleigh Fading envelops for spread spectrum applications”, IEEE Communication Letters, Vol. 4. No.l. Jan, 2000, pp9-11

Chapter 6 HIGH-PERFORMANCE, HIGH-THROUGHPUT OFDM WITH LOW PAPR VIA CARRIER INTERFEROMETRY PHASE CODING

6.1 Introduction Experimentation with parallel data transmission techniques began as early as the 1950’s [1], and in the mid 1960’s a multitude of work was emerging on the topic of Frequency Division Multiplexing, or FDM [2]. The basic premise for FDM was to avoid the hazards of the frequency selective fading channel by dividing the band into many smaller bands. Specifically, serial-to-parallel conversion of the incoming information bits, and transmission of each bit upon its own unique carrier, created a data rate per carrier that was a factor of N smaller than the original data rate. Hence, the bandwidth per carrier was only of the overall system bandwidth. As a result, each transmitted bit (one per carrier) experienced a flat fade.

When the ability to avoid the frequency selective fading channel first became possible, the overall bandwidth efficiency was low. Weinstein and Ebert introduced the discrete Fourier transform (DFT) to FDM in 1971 [3], and through this addition to the modulation/demodulation process made it possible to orthogonally overlap the smaller bands. This gave way to Orthogonal Frequency Division Multiplexing (OFDM). Since its first-introduction some four decades ago, advances in digital signal processing, specifically the Fast Fourier Transform (FFT), have led to OFDM’s growing popularity. Applications to date include variable rate

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modems [4], wideband data communications over mobile radio FM channels [5], high data rate subscriber lines [6], digital terrestrial TV broadcasting [7], fixed wireless [8], and wireless ATM [9]. More recently, OFDM has emerged as the standard in a number of high data rate applications: Digital television broadcasting (such as the digital ATV terrestrial broadcasting [10] and European DAB and DVB-T [11]), and numerous wireless local area networks (most notably IEEE 802.11 operating at 5 GHz [12] and ETSI BRAN’s HYPERLAN 2 standards [13]). While the excitement for OFDM continues to grow, and even as OFDM emerges as a possible “platform” technology, it is not without its

drawbacks: problematic bit loss arises due to deep fades, throughput loss results due to “performance-aiding” coding, and peak-to-average power ratio dilemmas have led to questions regarding implementation. In the following sections, we introduce a novel OFDM architecture, one which enables OFDM to overcome its limiations. This architecture,

referred to as Carrier Interferometry OFDM (or CI/OFDM for short), utilizes frequency diversity to increase OFDM performance without bandwidth expansion and without decreased data rate. Specifically, Carrier Interferometry OFDM (1) simultaneously modulates each information bit onto all carriers, and (2) assigns a unique phase code set to the carriers of each bit to assure orthogonality between bits. This creates a frequency diversity benefit for each bit, and leads to high performances. Moreover, in addition to the dramatic performance gains that are possible through the use of CI/OFDM, Pseudo-Orthogonal Carrier Interferometry (PO-CI) codes can be applied to the CI/OFDM systems. Here, (1) each bit is still simultaneously sent over all N carriers, but now (2) each bit’s N carriers are assigned pseudoorthogonal CI codes, making them nearly orthogonal to other bits at the transmitter. By applying pseudo-orthogonal codes to the N carriers of each bit, we can assign 2N bits onto the N carriers, doubling the number of information bits on the original number of carriers, without bandwidth expansion. It will also be shown in section 6.7, that CI/OFDM is capable of not only enhancing probability of error performance and doubling throughput, but also acts to eliminate the peak-to-average power ratio (PAPR) problem inherent in traditional OFDM systems.

Since typical OFDM systems already employ coding to overcome channel degradations, we also present the application of coding to the proposed CI/OFDM system, leading to further performance enhancement. In the resulting CI/COFDM systems, a time interleaving is incorporated to create a time diversity benefit alongside the channel coding gain and the frequency diversity gain inherent in CI/OFDM.

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Sections 6.2 and 6.3 describe the transmitter and receiver models respectively for CI/OFDM and PO-CI/OFDM. The remaining sections of this chapter provide additional information regarding CI and the performance benefits available through its use.

6.2 Novel CI Codes and OFDM Transmitter Structures In today’s OFDM, incoming information bits are mapped into transmit data symbols corresponding to Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK) symbols. To simplify the discussion of this chapter, Binary Phase Shift Keying (BPSK) will be assumed as the mapping (i.e., incoming information bits consisting of 0’s and 1’s are mapped to –1 and +1 respectively). After mapping, the OFDM transmit operation is shown in Figure 6.1 (a). Here, N symbols are serial-to-parallel converted and sent simultaneously over N orthogonal carriers [14]. The data rate per carrier is a factor of N smaller than the original data rate, and hence the bandwidth per carrier is only of the overall system bandwidth. As a result, each transmitted bit (one per carrier) experiences a flat fade. This translates into simple receiver design and a system that drastically reduces inter-symbol interference and avoids multipath in a frequency selective channel. However, there is a very real disadvantage in this OFDM architecture. Since each carrier experiences a flat fade and reaches the receiver with a different amplitude, it is possible, even likely, that some of the N data symbols are completely lost due to deep fades. To account for this, Coded OFDM (COFDM) has been introduced (e.g., [15][16][17][18]). Here, incoming information bits are channel coded prior to serial-to-parallel

conversion. In a rate coder, each bit is effectively sent over n frequency carriers, introducing a frequency diversity benefit and channel coding gain, which overcomes the fading degradation. The draw back is of course a lowered throughput (by a factor of n). The following illustrates the incorporation of the CI phase codes to the OFDM transmitter. This will enable full utilization of the frequency diversity available in the channel.

6.2.1 CI/OFDM & CI/COFDM A typical OFDM transmitter is shown in Figure 6.1 (a), and the novel CI/OFDM transmitter is depicted in Figures 6.1(b) and 6.1(c). In both OFDM

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and CI/OFDM, input bits are serial to parallel converted. However, unlike OFDM, where each bit is modulated onto its own carrier, in CI/OFDM each bit is modulated onto all of the N carriers. To separate bits located on identical carriers, we introduce a phase offset to each of bit k’s carriers. Specifically, is the phase offset applied to the carrier for bit k (Figure 6.1(c)). The set of phases applied to bit k’s carriers, is known as the spreading code for bit k. Careful selection of will lead to spreading codes that ensure orthogonality among the N transmitted bits, even though bits occupy the same carriers at the same time. This notion is very similar to that of MC-CDMA systems [19], where N users occupy all N carriers at the same time, but are separated by spreading codes corresponding to phase offsets.

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The spreading codes used in CI/OFDM, referred to as CI codes, correspond to those used to create user orthogonality in CI/MC-CDMA (Chapter 3): the spreading code for user where Therefore, the spreading codes for

bits defined phase offsets:

in the CI/OFDM system utilizes the following code-

The transmitted signal for the

bit in a CI/OFDM system is:

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where (1) refers to the bit and is assumed to be +1 or –1 with equal probability; (2) and is the bit rate) to assure orthogonality among carriers; (3) is the phase offset used to generate bit k’s spreading code, and ensures orthogonality among the N bits; and (4) ensures a bit energy of unity. Now, over the entire OFDM block of N bits, the transmitted signal in CI/OFDM is:

As mentioned, channel coding is incorporated into most traditional OFDM architectures, leading to coded OFDM (COFDM). In typical COFDM systems, prior to the serial to parallel conversion of Figure l(a), each l input bits (typically ) are channel coded to n output bits (typically Then, in the same serial-to-parallel manner, each bit is transmitted on its own carrier for a total of information bits sent on N carriers. In this way, l information bits are effectively sent on n carriers, enabling frequency diversity benefits at a cost of decreased throughput. In our CI/COFDM system, each set of l input bits are similarly coded to n output bits (e.g. 1 bit to 2 bits). Now, since CI/OFDM already sends each bit on all N carriers (exploiting the full frequency diversity benefit), each set of n coded bits are sufficiently time interleaved to add an nfold time diversity benefit. Figure 6.2 illustrates this interleaving methodology.

Referring to Figure 6.2, it can be seen that for a rate convolutional coder, one bit is input and two coded bits are output, creating “coded output bit 1” (denoted in Figure 6.2 as A) and “coded output bit 2” (denoted in

131 Figure 6.2 as B). These coded output bits are then time interleaved onto two

different CI/OFDM symbols such that one CI/OFDM symbol contains N “ coded output 1 bits” and another CI/OFDM symbol contains the second N “ coded output 2 bits.” In this way, CI/COFDM has the same degree of redundancy (i.e. same throughput) as COFDM, but instead of the redundant bits being transmitted on the carriers at the same time, they are time interleaved. CI/COFDM then, offers the same full frequency diversity benefit of CI/OFDM, and adds an nfold time diversity benefit, all with the same throughput of a COFDM system. 6.2.2 Addition of Pseudo-Orthogonality to CI/OFDM & CI/COFDM CI/OFDM, as presented to date, represents a powerful alternative implementation for OFDM that enables significant gains in performance (via enhanced diversity gains). However, the benefits of CI/OFDM are not limited to performance, as CI/OFDM also creates a doubling in throughput. This benefit is demonstrated in this subsection, where we refer to the CI/OFDM implementation that doubles throughput as PO-CI/OFDM (pseudo-orthogonal CI/OFDM). In PO-CI/OFDM, we transmit 2N data symbols on N carriers; rather than the usual N symbols on N carriers. Specifically, a data stream with twice the usual OFDM throughput is serial to parallel converted into 2N data streams. Each parallel data stream has the same data rate of a traditional percarrier OFDM data stream. Next, just as in CI/OFDM, each bit is modulated onto all of the N carriers. To separate bit k from the (2N -1) other bits located on identical carriers, we again introduce a phase offset to each of bit k’s carriers. Specifically, the carrier for bit k is assigned phase offset In other words, the spreading code is applied to bit k’s carriers, and is referred to as the code-defining phase offset. By careful selection of the code-defining phase offset, the 2N bits can be supported on N orthogonal carriers in a manner that makes them highly (but pseudo) orthogonal. Specifically, we support the first bits on the N carriers by using the usual CI/OFDM code-defining phase offsets (equation (6.1)), i.e.,

To the next set of N bits (bits N, N+1,..., spreading codes with code-defining phase offsets

2N-1), we assign

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The second set of bits are hence assigned code-defining phase offsets that allow them to be orthogonal to one another, but pseudo-orthogonal to the first set. We select such that we minimize the amount of inter-bit interference at the transmitter. The intuitive solution is to select as this creates a second set of code-defining phase offsets equidistant from the original set. This has been proven mathematically to minimize the inter-bit interference (analogous to the derivation in Chapter 3). Hence, the following is used as the second set of code-defining phase offsets:

That is, for CI/OFDM systems incorporating K = 2N bits on N carriers, referenced as bit 0 to bit 2N-1, each bit is applied to all N carriers and assigned spreading code

where

Again, this means the first N bits are orthogonal amongst themselves, the second N bits are orthogonal amongst themselves, but both sets of N bits (for a total of 2N bits) are pseudo-orthogonal to each other. The transmitted signal for the

bit in PO-CI/OFDM is therefore:

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and the PO-CI/OFDM transmitted signal considering the entire OFDM block of 2N bits is thus:

Channel coding, common in OFDM, can also be applied to POCI/OFDM, leading to PO-CI/COFDM. In PO-CI/COFDM, each l input bits (typically are channel coded to n output bits (typically n = 2) prior to the seriako-parallel conversion. COFDM transmits each of the n bits on a

unique carrier, for a total of information bits sent on N carriers. (This introduces frequency diversity and channel coding to OFDM.) POCI/COFDM, on the other hand, transmits information bits on N carriers, and time interleaves each set of n coded bits to create a time diversity benefit in addition to the channel coding gain. Figure 6.3 illustrates the time interleaving in the PO-CI/COFDM architecture. Referring to Figure 6.3, and again for a rate convolutional coder, one bit is input and two coded bits are output, creating “coded output bit 1” and “coded output bit 2.”

In Figure 6.3, for the first set of N “coded output 1” bits and the first set of N “coded output 2” bits are denoted as A and B respectively, and the second set

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of N “ coded output 1” bits and N “ coded output 2” bits are denoted C and D respectively. These blocks of coded output bits are time interleaved onto two PO-CI/OFDM symbols such that one PO-CI/OFDM symbol contains 2N “coded output 1 bits” and another PO-CI/OFDM symbol contains the second N “coded output 2 bits.” When utilizing this strategy, PO-CI/COFDM, offers the same full frequency diversity benefit of PO-CI/OFDM and adds an n-fold time diversity benefit (in addition to the channel coding gain).

6.3 Novel OFDM Receiver Structures In the Carrier Interferometry implementation of OFDM, one major benefit is the receiver’s ability to fully exploit the channel frequency diversity and, as a result, significantly enhance performance. The novel CI/OFDM receivers that achieve large performance gains are the topic of this subsection.

The received signal, assuming the sent signal s(t) in (6.3) or (6.10), is mathematically characterized by the following equation:

Here, K = N if s(t) is based on equation (6.3) and K = 2N if s(t) corresponds to equation (6.10); and are the fade parameter and phase offset, respectively, introduced into the carrier by the frequency selective Rayleigh fading channel; and n(t) is additive white Gaussian noise (AWGN). We will assume perfect phase synchronization, for reasons of simplicity in presentation. The CI/OFDM receiver is depicted in Figure 6.4 for detection of the bit. Here, r(t) is separated into its N orthogonal carriers, and the bit's phase offset is removed from carrier i.

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This lead to the decision vector

where

The second term represents the existence of the (K – 1) other bits on the bit; that is, it represents inter-bit interference. In an AWGN channel, this

term, when combined across carriers (i.e. after performing

sums

to zero due to the orthogonality between bits created by the appropriate choice of . (In the case where bits are pseudo-orthogonal and not orthogonal, i.e., when K = 2N, this term is minimized in an AWGN channel via the combining of

In the frequency selective channel, however, a

simple combining across fails to minimize the presence of the interference term, due to the presence of the carrier dependent fade, . In frequency selective channels, a different combining strategy will be employed in the CI/OFDM receiver, to rebuild our bit from the newly created While numerous combining techniques are possible, it has been shown in the MC-CDMA literature (e.g., [20]) that minimum mean square error combining (MMSEC) offers the best performance. This MMSEC minimizes the inter-bit interference and noise while best exploiting the frequency diversity benefits. This combining corresponds to the following decision variable:

For uncoded CI/OFDM and PO-CI/OFDM, the variable C enters a hard decision device which outputs . In the cases of CI/COFDM and POCI/COFDM, the decision variable C enters a deinterleaver, followed by a soft decision decoding Viterbi Algorithm (VA) employing the Euclidean distance metric.

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6.4 Channel Modeling In order to compare OFDM, CI/OFDM and PO-CI/OFDM, appropriate channel modeling must be employed. The following elaborates on the channel models. Extensive work has been done on the modeling of wireless channels. These models, typically based on measurement data, emulate realistic environments for transmission. Here we focus on the indoor channel models, since many of today’s OFDM systems are intended for this environment. These models characterize environments such as the small office/home office (SOHO), large office, and warehouse type structures. Each of these is characterized by a specific delay spread and path model. As discussed in the literature (e.g., [21]), root mean squared (rms) values of delay spread vary from 20-50 ns for small office/home offices (SOHO) and from 50-100 ns for large office buildings.

The specific models used for simulation are based on the UMTS indoor office and large office models [22]. Specifically, rms delay spreads for these environments correspond to 35 ns and 100 ns respectively (as specified by the UMTS channel model for indoor test environments [22]). The 35 ns and 100 ns delay spreads correspond to a 2.8-fold and an 8.125-fold frequency diversity (respectively), over the entire bandwidth. (This assumes a bandwidth consistent with the IEEE 802.11a standard) We also utilize an “average” channel model with a 4-fold frequency diversity over the entire bandwidth. With this 3 to 8-fold frequency diversity, the channel fades in equation (6.11) are correlated according to [23]:

where is the correlation between carrier fade and carrier is the frequency separation between these two carriers, and channel’s coherence bandwidth.

fade, is the

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6.5 Performance Results Throughout this chapter, we have discussed the promise of CI/OFDM and PO-CI/OFDM in terms of increased performance and throughput. In this section, we demonstrate these benefits via performances and throughput curves. Figure 6.5 illustrates the bit error rate (BER) versus signal to noise ratio for OFDM, COFDM, CI/OFDM, and CI/COFDM. Each system transmits N = 32 bits over N = 32 carriers. We also assume a channel with a 4-fold frequency diversity. In cases of OFDM and CI/OFDM, the N = 32 transmit bits all correspond to information bearing bits; in COFDM and CI/COFDM, only 16 of these N = 32 bits are information bearing (the rest are redundancy bits). Referring to Figure 6.5, the CI/OFDM system offers 10 dB performance gain over OFDM at a BER of This gain is due to the frequency diversity benefit inherent in the CI/OFDM system. It is apparent that the interbit interference due to the second term in (6.12) (reduced by the combining in (6.13)) is more than compensated for by the gain achieved via frequency diversity (sending the same bit over the N =32 carriers). The performance gain is even larger at lower BER’s: for example, at BER of an 18 dB gain is available.

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For the coded systems, we have implemented the coder as a rate convolutional coder with a constraint length of 3, and utilized a soft decision decoding Viterbi Algorithm. Referring once again to Figure 6.5, it is observed that the traditional COFDM system gains approximately 14 dB over OFDM at BER of The substantial benefits of channel coding, in terms of both coding gain and frequency diversity benefit, are apparent, but the cost is high -- in this case a factor of 2 degradation in throughput. Without any coding, and hence without loss in throughput, CI/OFDM offers 10 of COFDM’s 14 dB gain. Moreover, for only a 4 dB performance loss relative to COFDM, CI/OFDM is available without the complexity of a soft decision decoding VA at its receiver. When the identical rate convolutional coding scheme is applied to the CI/OFDM system, creating CI/COFDM, 16 dB gain is achieved over OFDM, and a 2 dB gain is available over COFDM at BER of By BER = 23 dB gains are observed in relation to OFDM and 3 dB gains are achieved relative to COFDM. The performance benefits of CI/OFDM are observed because not only is the full frequency diversity exploited, but in addition, (1) a time diversity benefit is achieved in bit interleaving the channel coded bits, and (2) convolutional decoding using a VA offers welldocumented benefits.

Figures 6.6 and 6.7 illustrate the bit error rate (BER) versus signal to noise ratio for OFDM, COFDM, CI/OFDM, CI/COFDM, PO-CI/OFDM and PO-CI/COFDM. In all cases, N = 32 carriers are employed, and the coding applied to the coded systems is rate with constraint length 3.

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The OFDM, COFDM, CI/OFDM and CI/COFDM systems all transmit N= 32

bits over the N = 32 carriers. In the coded cases only 16 of every 32 bits are information bearing. In PO-CI/OFDM, by application of pseudo-orthogonal codes to each bit, 2N = 64 bits are sent over N = 32 carriers. In the coded cases, 32 of the 64 bits are information bearing. To emulate realistic wireless environments, we assume a 4-fold frequency diversity over the entire bandwidth.

Referring to Figure 6.6, we see that 64-bit, 32-carrier PO-CI/OFDM loses 2 dB relative to 32-bit, 32-carrier CI/OFDM at a BER of and that the 32-information bit, 32-carrier PO-CI/COFDM system loses 2 dB relative to the 16-information bit, 32-carrier CI/COFDM system at a BER of These losses in performance demonstrate the impact of inter-bit interference created by the pseudo-orthogonal spreading codes assigned to the bits. Degradation in performance is a cost paid for the doubling of the throughput. However, CI/OFDM is known to significantly outperform OFDM (Figure 6.5), and the losses in PO-CI/OFDM (relative to CI/OFDM) are small enough that PO-CI/OFDM will still outperform OFDM. Referring to Figure 6.7, the increased capacity 64-bit, 32-carrier POCI/OFDM system offers 8 dB of gain over a 32-bit, 32-carrier OFDM system at a BER of While it loses 6 dB relative to the 16-information bit, 32-

140 carrier COFDM system, PO-CI/OFDM has four times the throughput relative to COFDM over the same 32 carriers (and a less complex receiver design).

Also in Figure 6.7, the 32-information bit, 32-carrier PO-CI/COFDM system demonstrates essentially the same performance as the 16-information bit, 32-carrier COFDM system, and hence the same gain of 14 dB over typical OFDM at a BER of This means that the inter-bit interference in POCI/COFDM, even with pseudo-orthogonal codes applied to the bits, is more then compensated for by the gain achieved via the full frequency diversity (sending the same bit over the N = 32 carriers), the time diversity benefit (induced in time interleaving the channel coded bits), and the VA convolutional decoding. These benefits allow our 32-information bit, 32carrier PO-CI/COFDM system to perform as well as its 16-information bit, 32-carrier COFDM counterpart. Hence, PO-CI/COFDM achieves the performance of COFDM, with the same throughput as in OFDM. We achieve the best of both worlds. The cost, of course, is transmitter and receiver

complexity.

6.6 Peak to Average Power Ratio Considerations Of great concern in OFDM systems is high peak-to-average power ratios (PAPR). Specifically, in OFDM and COFDM, high peaks in power (up to N times the average) are observed, a consequence of using independently modulated carriers. This, in turn, leads to inefficient operation of the transmit power amplifier.

A number of solutions to OFDM’s peak-to-average power ratio (PAPR) problem have been proposed in the literature (i.e., block coding [24], partial transmit sequences [25], selective mapping [26], and clipping [27]). While reducing the PAPR, these schemes typically increase the complexity of the OFDM system. The proposed Carrier-Interferometry OFDM (CI/OFDM) system demonstrates a low PAPR. That is, in CI/OFDM, PAPR is simply not an issue. Specifically, the phase codes applied to the N carriers result in one bit’s power reaching a maximum when the powers of the remaining N-1 bits are at a minimum. Therefore, a stable transmit envelope is observed, and, the PAPR is small.

Pseudo-Orthogonal Carrier-Interferometry OFDM (PO-CI/OFDM) demonstrates even lower PAPR values than those in CI/OFDM. Specifically, as in CI/OFDM, when one bit’s power reaches a maximum, the powers of the remaining 2N-1 bits are at a minimum; and now, because there are twice as

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many bits per N carriers (in PO-CI/OFDM relative to CI/OFDM), an even better averaging of the power across the OFDM symbol is observed. 6.6.1 PAPR in OFDM and CI/OFDM

PAPR is defined as the peak power per OFDM symbol versus the average power per OFDM symbol, i.e.,

The average power in CI/OFDM (and OFDM) is:

where

is the power on one carrier, i.e.,

The OFDM method of serial-to-parallel converting incoming information bits and transmitting each bit on its own unique carrier leads to the potential for high peak power. This is a result of a possible in-phase, coherent addition of all the carriers. In this worst case (WC) senario, where the N carriers combine coherently, OFDM’s peak power is equal to:

In CI/OFDM, as discussed in section 6.2.1, all bits are transmitted simultaneously over all carriers, and an appropriate selection of phase offsets makes bits separable at the receiver. However, these phase offsets have a second benefit: they reduce the peak power. Specifically, they ensure that when one bit’s carriers add coherently, other bit’s carriers do not add coherently. Therefore, is much less than That is, considering worst case scenarios:

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and

Figure 6.8 shows PAPR levels across 10,000 transmit symbols for both OFDM (black) and CI/OFDM (gray), each with N=32 carriers. As seen in Figure 6.8, spurious peaks with PAPR > 7.5 are quite common in OFDM transmissions (arising 2.5% of the time), and even peaks of 15 < PAPR < 20 result at select transmission times. CI/OFDM, on the other hand, displays no peaks with PAPR > 6.5, and displays PAPR < 5 at almost all times. On average, OFDM demonstrates a PAPR of 3.79 while Cl/OFDM’s PAPR is 3.41.

Figure 6.9 demonstrates the standard deviation of the PAPR as a function of increasing number of carriers. With N = 32 carriers, OFDM’s PAPR demonstrates a standard deviation of 1.23 (a variance of 1.5), while CI/OFDM’s standard deviation is only 0.665 (a variance of 0.442).

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Now, referring to Figure 6.10, 98% of the CI/OFDM transmissions demonstrate PAPR < 5, and all transmissions (100%) demonstrate PAPR < 6.5. Meanwhile, only 88% of the OFDM transmissions demonstrate PAPR < 5, and it is not until y = 32 that Pr(PAPR = y) = 100%. Clearly, the PAPR values in CI/OFDM will allow amplifiers at the transmit side to operate with much greater power efficiency.

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6.6.2 PAPR in PO-CI/OFDM

Figure 6.11 illustrates PAPR levels across 10,000 transmit symbols for 32-bit, 32-carrier OFDM (black) and 64-bit, 32-carrier PO-CI/OFDM (gray). Referring to Figure 6.11, OFDM’s PAPR can be characterized as erratic, displaying a mean PAPR of 3.79, and consistently reaching levels exceeding 6 (5% of the time), with some PAPR values exceeding 15 and even 20. PO-CI/OFDM, on the other hand, displays no PAPR value above 4.4 and stays close to its mean PAPR level of 2.5.

Figure 6.12 demonstrates the standard deviation of the PAPR as a function of increasing number of carriers. As the number of carriers increases, the standard deviation of OFDM’s PAPR also increases, but the opposite is true in PO-CI/OFDM: in PO-CI/OFDM, the standard deviation of the PAPR decreases with increasing number of carriers. For the 32-bit, 32carrier OFDM and 64-bit, 32-carrier PO-CI/OFDM systems shown in Figure 6.11, OFDM’s PAPR demonstrates a standard deviation of 1.23 (a variance of 1.5), while PO-CI/OFDM’s standard deviation is only 0.355 (a variance of 0.125).

When compared to an OFDM system that has had the clipping algorithm of [28] applied, similar results are none-the-less observed. Figure 6.13 displays the PAPR levels across 10,000 transmit symbols for a 32-bit, 32-carrier OFDM system with clipping (in black), and the 64-bit, 32-carrier

145 PO-CI/OFDM system (in gray). Here, a Clipping Ratio (CR), (defined in [27]), of 1.4 was implemented.

Referring to Figure 6.13, the clipping algorithm greatly reduces the number of times the PAPR exceeds a level of 5, but spurious levels are still

146 prevalent. The mean and standard deviation of OFDM’s PAPR, with clipping, are reduced to 2.412 and 1.053 respectively. However, these are still far worse than of PO-CI/OFDM’s PAPR values, where the mean is effectively the same but the standard deviation is only 0.355.

Figure 6.14 plots the pdf (probability density function) of the PAPR for OFDM, OFDM with clipping, and PO-CI/OFDM.

147 Referring to Figure 6.14, we see how clipping effectively concentrates the PAPR levels about the mean, but does little to contain the spurious peaks. This can be directly attributed to the in-band distortion caused by clipping.

Figure 6.15 plots the cumulative distribution function (CDF) of the PAPR. Clipping improves the PAPR statistics (relative to OFDM), but it is not until y = 22.5 that Pr(PAPR = y) = 100%, which is a result similar to that of unclipped OFDM. PO-CI/OFDM, on the other hand, demonstrates Pr(PAPR < y) = 100% when y = 4.4.

6.7 Conclusions In this chapter, Carrier Interferometry and Pseudo-Orthogonal Carrier Interferometry are introduced to current OFDM architectures. The resulting CI/OFDM system outperforms OFDM by 10 dB at a BER of without any loss in throughput, and PO-CI/OFDM outperforms OFDM by 8 dB at a BER of and provides a doubling in throughput. This dramatic gain is a result of CI/OFDM and PO-CI/OFDM’s inherent ability to exploit the full frequency diversity benefit. We have also demonstrated that while traditional

148 COFDM also produces a dramatic gain in performance, CI/OFDM offers almost the same performance gain at a BER of while avoiding the cost in decreased throughput (by a factor of 2) and the cost of increased receiver complexity (to implement a VA).

Furthermore, we introduced a coded version of CI/OFDM and POCI/OFDM, namely CI/COFDM and PO-CI/COFDM. The following result is one of great significance: the PO-CI/COFDM system equals the performance of COFDM while achieving the throughput of OFDM. This is made possible by PO-CI/COFDM’s ability to exploit frequency diversity, time diversity, and channel coding. Systems employing OFDM technologies will greatly benefit by implementing the Carrier Interferometry alternatives, namely CI/OFDM, CI/COFDM, PO-CI/OFDM, and PO-CI/COFDM. Moreover, while the performance and throughput benefits are particularly significant, it has also been shown that when using CI/OFDM and

PO-CI/OFDM, no PAPR problems arrise. The cost of added transmitter and receiver complexity in CI/OFDM and PO-CI/OFDM, relative to current OFDM, is minimal when compared to the substantial throughput, performance, and PAPR benefits.

References [1] R. R. Mosier, and R.G. Clabaugh, “Kineplex, a bandwidth efficient binary transmission system,” AIEE Trans., Vol. 76, pp. 723 - 728, Jan. 1958. [2] B. R. Saltzberg, “Performance of an efficient parallel data transmission system,” IEEE Trans. Comm., Vol. COM-15, pp. 805 – 813, Dec. 1967. [3]Weinstein, S. B., and P. M. Ebert, “Data transmission by frequency division multiplexing using the discrete fourier transform,” IEEE Trans. Comm., Vol. COM-19, pp. 628-634, Oct. 1971. [4] W. E. Keasler, and D. L. Bitzer, “High speed modem suitable for operating with a switched network,” U.S. Patent No. 4,206,320, June 1980. [5] P. S. Chow, J. C. Tu and J. M. Cioffi, “Performance evaluation of a multichannel transceiver system for ADSL and VHDSL services,” IEEE J. Selected Area, Vol., SAC-9, No. 6, pp. 909 – 919, Aug. 1991. [6] P. S. Chow, J. C. Tu and J. M. Cioffi, “A discrete miltitone transceiver system for HDSL applications,” IEEE J. Selected Areas in Comm., Vol. SAC-9, No. 6, pp. 909 – 919, Aug. 1991. [7] R. V. Paiement, “Evaluation of single carrier and multicarrier modulation techniques for

digital ATV terrestrial broadcasting,” CRC Report, No. CRC-RP-004, Ottawa, Canada, Dec. 1994. [8] R. B. Marks, “The IEEE 802.16 working group on broadband wireless,” IEEE Network,

Vol. 13, Issue 2, pp. 4-5, March-April 1999. [9] Anna Hac, Multimedia applications support for wireless ATM networks. Prentice Hall PTR, Upper Saddle River, NJ, 2000. [10] R. V. Paiement, “Evaluation of single carrier and multicarrier modulation techniques for

digital ATV terrestrial broadcasting,” CRC Report, No. CRC-RP-004, Ottawa.Canada, Dec. 1994.

149 [11] T. de Couasnon and et al, “OFDM for digital TV broadcasting,” Signal Processing, vol. 39, pp. 1-32, 1994.

[12] IEEE 802.11, “Draft supplement to standard for telecommunications and information exchange between systems – LAN/MSN specific requirements – Part 11: wireless MAC and PHY specifications: High speed physical layer in the 5 GHz band,” P802.1la/D6.0, May 1999. [13] TR 101 031, “Broadband radio access networks (BRAN); high performance radio local area network (HIPERLAN) Type 2; requirements and architectures for wireless broadband access,” January 1999. [14] P. Ramjee and R. van Nee, OFDM for Wireless Multimedia Communications. Artech House Publishers, Boston, 2000. [15] B. Le Flock, M. Alard, and C. Berrou, “Coded orthogonal frequency division multiplex,” Proceedings of the IEEE, Vol. 83, no. 6, June l995. [16] Q. Wang and L. Y. Onotera, “Coded QAM using a binary convolutional code,” IEEE Transactions on Communications, vol. 43, No. 6, June 1995.

[17] L. H. Charles Lee, Convolutional coding: Fundamentals and Applications, London: Artech House, 1997. [18] G. Uhgerboeck, “Channel coding with multilevel/phase signals,” IEEE Transactions on Information Theory, vol. IT-28, No.l, pp.55-67, Jan. 1982. [19] N. Yee, J.P. Linnartz, and G. Fettweis, “Multi-Carrier CDMA in indoor wireless radio,” in Proc. PIMRC ’93, Yokohama, Japan, Dec. 1993, pp.109-113. [20] S. Kara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Communications Magazine. Vol. 35, no. 12, pp. 126 – 133, Dec.1997. [21] H. Hashemi, “The indoor propagation channel,” Proc. IEEE, vol.81, no. 7, July 1993, pp. 943-68. [22]

TR 101 112, “Universal mobile telecommunications system (UMTS); Selection

procedures for the choice of radio transmission technologies of the UMTS (UMTS 30.03 version 3.1.0),” November 1997. [23] W. C. Jakes, Ed., Microwave Mobile Communications, New York: IEEE Press, 1974. [24] T. A. Wilkinson and A. E. Jones, “Minimization of the peak to mean envelope power ratio in multicarrier transmission schemes by block coding,” in Proc. VTC’95, July 1995, pp. 825-831. [25] S. H. Muller and J. B. Huber, “OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences,” elec. Letts., Vol. 33, No. 5, Feb 1997, pp. 368-369. [26] E. Lawrey and C. J. Kikkert, “Peak to average power ratio reduction of OFDM signals

using peak reduction carriers,” Signal Processing and Its Applications, 1999, ISSPA ’99,

Proceedings of the Fifth International Symposium on, Vol. 2, Aug. 1999, pp. 737740. [27] X. Li and L. J. Cimini, Jr., “Effects of clipping and filtering on the performance of OFDM,” in Proc. VTC’97, May 1997, pp. 1634-1638.

[28] T. May and H. Rohling, “Reducing the peak-to-average power ratio in OFDM radio transmission systems,” in Proc. VTC ’98, (Ottawa, Canada), 18-21.5. 1998. [29] D. A. Wiegandt and C. R. Nassar, “High performance OFDM via carrier interferometry,” accepted for presentation at 3Gwireless’01 IEEE International Conference on Third Generation Wireless and Beyond. [30] D. A. Wiegandt and C. R. Nassar, “High-throughput, High-performance OFDM via pseudo-orthogonal carrier interferometry coding,” accepted for presentation at PIMRC 2001 IEEE International Symposium on Personal, Indoor and Mobile Radio Communication. [31] D. A. Wiegandt, C. R. Nassar, and Z. Wu, “Overcoming peak-to-average power ratio issues in OFDM via carrier interferometry codes,” accepted for presentation at VTC 2001 (Atlantic City, NJ).

150 [32] D. A. Wiegandt, and C. R. Nassar, “Peak-to-average power reduction in highperformance, high-throughput OFDM via pseudo-orthogonal carrier interferometry coding,” accepted for presentation at PACRIM 2001 (Victoria, Brinish Columbia). [33] D. A. Wiegandt, and C. R. Nassar, “High-Performance 802.1la wireless LAN via carrier interferometry orthogonal frequency division multiplexing at 5 GHz,” accepted for presentation at Globecom 2001 (San Antonio, TX). [34] D. A. Wiegandt, and C. R. Nassar, “High-performance wireless ATM via application of carrier interferometry to OFDM,” accepted for presentation at WOC ‘01 (Banff, Alberta,

Canada).

Chapter 7 THE MARRIAGE OF SMART ANTENNA ARRAYS AND MULTI-CARRIER SYSTEMS SPATIAL SWEEPING, TRANSMIT DIVERSITY AND DIRECTIONALITY

Smart antennas located at the base station (BS) represent an important technological innovation. These antennas are capable of increasing the network capacity and probability-of-error performance. Network capacity is enhanced by use of space division multiple access (SDMA) [1] and probability-of-error performance (at the mobile) is enhanced by transmit diversity techniques [2-8]. An introduction to these diversity techniques follows. In general, diversity techniques refer to the transmission of a signal over L independent fading channels, ensuring a low probability that all signal components fade simultaneously [9]. Diversity techniques such as frequency, time and space diversity traditionally come at a considerable cost in system bandwidth (frequency diversity), bit rate (time diversity) and/or expense (spatial diversity) as well as costs in complexity of the receiver structure. The amount of diversity is traditionally chosen based on compromise between performance gain and system cost.

Novel diversity techniques minimizing mobile receiver cost have been among recent antenna array applications. Of particular interest have been transmit diversity methods which achieve diversity benefits at the receiving mobile when the antenna array is located at the transmitting base station. For

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example, in delay diversity [2][3], the transmitter sends N data bearing signals, one per array element, where each element has a unique delay chosen to create an artificially resolvable multipath at the receiver. In [2] and [3], however, the diversity gain comes at a considerable cost to receiver complexity, and, moreover, antenna directionality is no longer available. In antenna hopping [4], another novel transmit diversity scheme, consecutive bursts of information are transmitted on different antennas. When antenna branches are exposed to different multipath fading, a diversity gain is achieved. Antenna hopping combined with frequency hopping, i.e., applying different frequencies to different antennas, is shown to further enhance performance [5]. In these antenna-hopping schemes, each signal is sent on each antenna in separate portions of time, eliminating the benefit of using the

whole antenna array as a smart antenna. Moreover, in order to achieve path diversity on transmissions from each element, antenna element separation is very high, resulting in large antenna dimensions. In addition, antenna switching produces abrupt periodic phase changes in the received signal, thereby causing periodic errors [6]. Phase sweeping [6] is another form of transmit diversity where a twobranch phase sweeping array at the transmitter induces more rapid fades at the receiver. This improves the channel coding gain in a very slow multipath fading environment. Phase sweeping transmit diversity is introduced as an alternative to antenna hopping as it avoids the periodic phase changes and corresponding error. However, by using two antennas spatially separated by a large distance it fails to offer the benefits associated with smart antenna

schemes. In space-time trellis coding [7], another transmit diversity technique, data is encoded by a channel coder and the encoded data is split into N unique streams, simultaneously transmitted on N transmit antennas. At the receiver, the symbols are decoded using a maximum likelihood decoder. This scheme combines the benefit of forward error correction, coding and diversity transmission to provide considerable performance gains. However, this technique involves additional receiver processing, which increases exponentially as a function of bandwidth efficiency (bits/sec/Hz) and the required diversity order; hence, it is not cost-effective for some applications [8]. Moreover, when antenna arrays are used in this fashion, directionality

benefits are no longer available. In this chapter, we introduce a novel antenna array system capable of providing both transmit diversity and directionality. As a direct result, this antenna array supports: (1) Excellent probability of error performance (via transmit diversity) and (2) large network capacity (via a directionality which

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in turn enables SDMA). Specifically, we demonstrate a BS antenna array that sweeps the beam pattern directed to the mobile such that: 1) At all times, the intended mobile lies within the 3dB beamwidth of the antenna pattern; 2) the beam pattern moves to create L independent fades within each symbol duration ; this leads to large performance benefits due to L-fold diversity gains; 3) after each , the antenna beam returns to its initial position, and sweeps the same area of space over (leading to an oscillating antenna pattern and easing parameter estimation); 4) the movement of the beam pattern, as a percentage of half power beam width (HPBW), is small, thereby allowing the beam pattern to maintain directionality. Specifically, we apply a carefully chosen set of time-varying phases to array elements, generating the mainlobe at the position of the intended user and small oscillations in the beam pattern. This beam pattern oscillation can be understood as a significant enhancement to jitter diversity [10,11], where an antenna array beam pattern is jittered for the sole purpose of avoiding deep fades. Unlike traditional transmit diversity methods presented in [2-8], this scheme allows wireless systems to benefit from: 1) directionality (SDMA), 2) L fold diversity, and 3) low receiver cost. We merge the novel antenna array system with CDMA systems. Specifically, remaining true to the context of this book, we examine the merger of the innovative antenna array system with CI/MC-CDMA (Chapter 3) and CI/DS-CDMA (Chapter 5). Through this marriage, we achieve (1) excellent performance at the mobile via joint frequency-time diversity (the frequency diversity is inherent in CI/MC-CDMA and CI/DS-CDMA, and the time diversity arises via beam pattern movement); and (2) very high network capacity via joint space-code division multiple access [12].

7.1 Smart Antennas With Spatial Sweeping: Achieving Directionality And Transmit Diversity In this section, we introduce the reader to the novel antenna array system capable of both transmit diversity and directionality.

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7.1.1 Proposed Antenna Array Structure For ease in presentation, we will assume an M-element antenna array mounted horizontally at the BS (Fig. 7.1). In order to oscillate the antenna pattern, a time varying delay function is applied to the antenna array element (Fig. 7.1). The normalized array factor characterizing the resulting antenna pattern corresponds to

Here,

where elements,

is the wavelength d is the distance between antenna where is the frequency of the transmitted signal, and

time t=0 refers to the first instant when the antenna array attempts to contact a mobile user. For simplicity in presentation, it is assumed throughout that the mobile is located at angle

Through appropriate selection of , an oscillating antenna beam pattern is created at the BS. The beam pattern is controlled to ensure the following two criteria are satisfied: 1) large scale fading, i.e., the mean and variance of the Rayleigh fade, is constant over symbol time ; and 2) the BS beam pattern oscillates just enough to allow the signals received in L different

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partitions of symbol duration to demonstrate independent fades. This creates an L-fold diversity gain at the mobile receiver. In other words, the BS antenna array sweeps the beam pattern directed at the mobile just enough to create constant large scale fading for the symbol duration while ensuring L independent fades within each (see Fig. 7.2). A. Criterion 1: Constant Large Scale Fading

Our first criterion ensures constant large-scale fading within the symbol time duration . This condition corresponds to:

where d /dt is the rate of antenna pattern movement and is the amount of antenna pattern movement in symbol duration Additionally, is the array half power beamwidth (HPBW), and is a parameter satisfying This parameter ensures us that the received signal is within the 3dB-beamwidth of the antenna pattern for the entire symbol duration (this assures the mobile of a strong line of sight component). Equation (7.3) can be solved to create an equation for (the antenna element delay in Fig. (7.1)) as follows: from (7.2) (with

and, hence,

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By substituting (7.5) in (7.3)

which, solving for

, reduces to:

where is introduced, when solving for , to maintain a symmetric movement of the beam pattern around its peak (over ). This suggests the selection of delay function which is a linear function of t with slope In practice, we employ a periodic over symbol time (Fig. 7.3). With this selection of , the antenna pattern returns to its initial position and sweeps the same area of space each . That is, the antenna array delay (Fig. 7.1) corresponds to the time function shown in Fig. 7.3, and leads to beam pattern movement shown in Fig. 7.4. Here, the fades are identical in neigboring symbols (i.e., symbols, k, k+1, k+2, ...). This enables fading parameters, e.g., phases, in each segment of to be tracked.

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B. Criterion 2: Independent fades

Next, we want a controlled beam pattern movement ensuring L independent fades over each symbol duration , i.e., assuring an independent fade at the receiver over each duration Our criteria corresponds to

That is, we want the spatial movement due to time varying array elements to induce a coherence time, , which allows for a constant fade over but independent fades between neighboring time intervals of duration (Fig. 7.2). With beam pattern movement based on (7.8) (Fig. 7.3), which contains a control parameter we set to various values (in ) and determine via channel simulation (see section 7.2). Ratios of combined with equation (7.9), provided us with achievable values for L, the diversity gain, as a function of the antenna array control parameter. Assuming a medium-sized city center to emulate the channel, we found whenever (see Section 7.2). Using and (7.9), we determine , i.e., a maximum diversity of 7-fold is available. This corresponds to a very significant performance benefit at the receiver side.

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7.1.2 Receiver Design for Smart Antenna with Spatial Sweeping Assuming BPSK for ease in presentation, then at the transmitter side the information bearing signal entering the transmit antenna array corresponds to

where or and contains the information bit. The transmitted signal, output by the antenna array, corresponds to

where AF is the array factor introduced in (7.1). The received signal in our

proposed system, with the mobile at

(i.e.,

) corresponds to

where

refers to the received signal over interval is an additive white Gaussian noise; and is a Rayleigh random variable (perfect phase tracking is assumed). With selected according to (7.5), and assuming typical parameter values for mobile communication systems, it is easily shown that the frequency offset induced by is less than 0.5% of a 1MHz bandwidth. Hence, frequency expansion due to time varying can typically be neglected. Additionally, the proposed array structure ensures an independent for different values of i. Fig. 7.5 presents the receiver for the represents the local oscillator term:

Over each interval of the integrator in Fig. 4 corresponds to

in (7.12). In this figure,

the signal at the output

159

where also, the

is a zero mean Gaussian random variable with variance and Following the creation of values, the detector can be designed on the basis of equal gain

combining (EGC) or maximal ratio combining (MRC) combining. In EGC

detection, the decision variable after combining is

while in MRC detection, the decision variable after the combiner corresponds to

7.1.3 Theoretical Performance In this section we present the theoretical performance of the receiver for the two combining schemes of (7.15) and (7.16). 7.1.3.1 EGC probability of error In EGC, the combining of (7.15) is employed, which leads to (using (7.14)):

in

160

where:

Assuming

is a Rayleigh random variable with the probability density

function

then the mean of

(Equation (7.18)

corresponds to

and the variance of

is

Additionally for the noise term, n, in (7.19), the mean remains zero, and the variance corresponds to:

Now, assuming we design the proposed system with L sufficiently large, we can apply the central limit theorem: from (7.18), we can assume is a Gaussian random variable with the mean and variance characterized by (7.20) and (7.21) respectively. Probability of error then corresponds to

where:

and

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After substituting (7.24) and (7.25) into (7.23), and performing mathematical manipulation:

Here, is the noise power. Letting second term in (7.26) will tend to zero, i.e.,

which is close to the

then, as L increases, the

of BPSK. in an AWGN channel.

7.1.3.2 Probability of error for MRC combining

Using the method presented in [13] for the computation of the probability for error of a diversity receiver employing MRC combining, and realizing that in our case each branch has signal energy rather than and each noise component has variance

rather than

we determine:

where

As then tends toward that of an AWGN channel. The theoretical probability of error results for both EGC and MRC, with L = 7, are provided in Fig. 7.6(a). Probability of error of MRC combining is better than that of

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EGC, but MRC combining requires amplitude tracking which increases receiver complexity. 7.1.4 Simulated Performance

Simulation results are generated for the proposed antenna array with a spatial sweeping system, assuming L=7 and BPSK transmission. To generate these results, we employed Monte Carlo simulation using the of (7.14). Fig. 7.6(b) presents simulation performance results. These results confirm that the proposed system, with little change in receiver complexity, moves performance away from poor fading channel performance and toward more desired AWGN results, observed that the introduction of the beam sweeping antenna arrays at the BS creates an improvement of more than 14 dB at a probability of error of (at the mobile) compared to “without transmit

diversity” condition. The simulations results support the theoretical suppositions. It is important to note that these performance benefits are achieved while maintaining directionality, i.e., enabling network capacity gain via SDMA.

7.2 Channel Modeling for Spatial Sweeping Smart Antennas: Establishing the Available Transmit Diversity The modeling and characterization of mobile channels has been the subject of much research over the past three decades. This research has lead to detailed mobile channel models in the presence of vehicle movement; however to the best of our knowledge, there has been no work done on modeling channels in the presence of beam pattern movement. Beam pattern movement is quite different than movement of the mobile; for example, as the beam pattern moves some buildings fall out of the antenna pattern mainlobe, while others enter. This section is dedicated to the modeling of wireless channels in the presence of beam pattern movement. The net result is that a small beam pattern movement leads to 7-fold time diversity benefits. For those not interested in any other channel model details, please skip to Section 7.3. Otherwise, read on.

163

versus

in dB) for EGC and ML taking L=7.

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7.2.1 Channel Model Assumptions Assume an antenna array located at the base station (BS), and a single element omnidirectional antenna at the mobile. In addition, the following is assumed for the channel: 1) Scatterers contributing to multipath are located in one of two possible coverage areas: A. a circle with the mobile at its center (Fig. 7.7(a)) (which is a suitable model when we assume the BS antenna has enough height to illuminate only an area approximated by the circle) [14-17]); or B. the semi-elliptic area in Fig. 7.7(b) (accurate when we assume the height of the BS antenna array is close to the height of the surronding buildings, [18,19]).

2) The movement generated by the antenna array oscillation is dominant, and hence we ignore the movement of the mobile as well as any other relative speed due to the movement of other objects in the environment. 3) Scatterers are assumed to have dimensions in accordance with a known PDF. 4) Scatterers in the environment surrounding the BS are uniformly distributed [20-22]. 5) Scatterers are considered diffuse reflectors which reflect the incident radiation in all directions [22-24].

6) The signal received at the mobile is the sum of horizontally propagated plane waves interacting with just one scatterer [22-24].

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7.2.2 Linear Time-Varying Channel Impulse Response Modeling A linear time-varying system best represents radio channels [25]. That is, the channel impulse response corresponds to [26,27]:

Here, t is the observation time, is the response time of the impulse at each t, and N(t), (t), (t) and (t) are random, time-varying parameters corresponding to the number of multipath components, the multipath amplitude, the multipath phase and the multipath time of arrival, respectively. Additionally, represents the impulse function.

A. The Amplitude of the Multipaths,

(t)

Antenna pattern ocsillation (Fig. 7.4) causes some scatterers to leave the

coverage area (departing scatterers), while others arrive (arriving scatterers). Most remain in the coverage area. Thus, the term (t) corresponds to

The term is a Rayleigh, Rician or Nakagami random variable (RV) [27]. The term (t) represents a decaying amplitude whose value diminishes as the effective radiated cross section of the scatterer decreases. This time dependent amplitude decay is modeled as a linear function corresponding to

Here, is a RV with statistics identical to , representing the amplitude of the multipath when the scatterer is fully present in the antenna pattern

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coverage. represents the time instant when the scatterer starts leaving the antenna pattern coverage area. A Poisson or modified Poisson model is used to determine the time instant [28,29]. In

addition, The time constant represents the time it takes for the scatterer to completely depart from the HPBW, and is directly proportional to , the scatterer dimension (Fig. 7.7(a)) (see [15] for additional details). The term

where

(t) is linearly increasing function corresponding to

is a RV representing the amplitude of the multipath when the

scatterer is fully present in the HPBW.

is the arrival time of the

scatterer, and where is the time constant representing the time it takes the scatterer to completely enter into the antenna pattern coverage area. The statistics of and are the same as those of and

, respectively.

B. The Signal Phase,

The phase

(t} and the time of Arrival,

(t) is determined by: 1) the distance

leads to phase offset reflection coefficient phase), , independent of

(t)

(Fig. 7.7(a)), which

and 2) the phase due to other sources (e.g., [30]. Typically,

is a RV uniform over

. Hence,

is a uniform RV over

For the time of arrival (TOA) of multipaths, (t), we assume a probability density function (PDF) corresponding to a Poisson process or its modified version, as shown in [27,31].

C The Number ofmultipaths, N(t)

167

As the beam pattern moves, scatterers enter and depart the mainlobe. The total number of scatterers in the mainlobe, as a function of time, is denoted N(t). Assuming the interval is sampled at times where is sufficiently large, can be represented according to

Here, we assume the time difference is so small that the probability of more than one arrival or departure is negligible. To generate , an initial guess is selected according to:

where

•

is the scatterer density measured in terms of

•

is the antenna pattern coverage area

In the case of circular coverage (Fig. 7.7(a)):

where the circle radius, R, is

here, is the distance between the BS and the mobile and denotes the BS antenna HPBW (half power beam width). For small values of can be approximated by Alternatively, in the case of a semi-elliptic coverage:

168

The probability of one arrival or one departure, p, in (7.34) is directly proportional to the change in coverage area of the antenna pattern (due to its movement in ). Specifically

where , for the case of circular coverage, approximated using geometric calculations shown in Fig. 7.8, is:

Here, is the azimuth angle variation within time (using (7.3))

, and corresponds to

Substituting (7.41) in (7.40) and (7.40) in (7.39) , and approximating by p corresponds to (for the circular coverage scenario)

Meanwhile, for semi-elliptic coverage, we again have:

169

where, now, 7.7(b)), is:

approximated using the geometry of the coverage area (Fig.

Substituting (7.44) into (7.43), p corresponds to

where

and is presented in (7.35) and

and is

well approximated by

7.2.2.1 The Flat Fading Channel Approximation without antenna array factor and its phase

If we assume the channel is flat, then the channel model of (7.30) simplifies to

For both the circular and semi-elliptic coverage areas (Fig. 7.7), a mobile to BS distance and HPBW=0.3 rad, the channel is well modeled as flat whenever

7.2.3 Evaluation of Coherence Time

A medium-size city center is assumed [32,33]. That is, simulation parameters are selected as follows: 1. HPBW is in the range of 0.1 to 0.3 rad. 2. Simulations are performed for and 1000m.

3.

is a value in the range of 0.001 to 0.005

170 4. The channel is assumed to be well modeled as flat (Equation (7.47)). 5. The control parameter (Equation (7.8)) is a value between 0.0005 to 0.05. 6. The scatterers dimension is a normal RV with mean 20m and variance

For simulation purposes, the interval sample times,

is discretized into

and the amplitude of the received signal,

(see

(7.47)), is calculated. The sample autocorrelation function (ACF) for then computed over

The coherence time

is

is determined by defining

as the time over which the ACF is above 0.5 [30]. The mean that results from simulation using a circlular coverage scenario (Fig. 7.7(a)) is

presented in Fig.7.9(a-f). Simulation results show coherence time decreases as: 1) the distance between BS and mobile, , increases; 2) the scattere’s density increases; 3) HPBW increases; and 4) the parameter inversely proportional to

, HPBW and

increases, i.e.,

is

In addition, refering to Fig.

7.9, appears to level off at 0.16, thus suggesting that up to L = 7 fold diversity can be exploited by beam pattern oscillation. While the curves of Fig. 7.9 were generated assuming a circular coverage, a similar result is deduced using of a semi-ellipitc coverage scenario. 7.2.4 Updates to the Channel Impulse Response: Antenna Array Factor and Phase A linear time-varying impulse response model is a widely accepted representation of the fading channel. However, in the model of (7.30), we have assumed that the array factor is 1 for all scatterers of interest, and we have ignored the phase effects introduced by the antenna array. Including these effects in the impulse response channel model leads to a more accurate impulse response model. Here, the impulse response of the channel corresponds to:

171

172

Here,

represents the angular position of the

area (Fig. 7.7);

scatterer in the coverage

represents the gain due to the

position in the antenna array mainlobe, and phase offset. We simplify our notation by defining

The statistics of N(t),

(t) and

scatterer’s

is the corresponding

are the same as those introduced in Section

7.2.2. Here, we introduce the statistics of and (7.49)).

and

(equations (7.48)

A. Angular position of the scatterers

Case 1: The Circular Coverage Scenario

The angular position of the with PDF

Fig.

, is modeled as a random variable

To determine this PDF we turn our attention to Fig. 7.7(a).

Here, it is apparent that via

where

scatterer, is related to

(angle of arrival (AOA) at the BS)

, shown in Fig. 7.7(a), is uniform over 7.7(a), is uniform over [0,R]; and

corresponds to distance.

, shown in

also shown in , where

Fig.

7.7(a),

is the MS-BS

Case 2: The Semi-Elliptic Scenario To determine the PDF of

assuming a uniform distribution of scatterers,

we begin with the cumulative density function (CDF) of to (Fig. 7.10)

This corresponds

173

where

is a portion of the coverage area contained within the angular

spread of

and

and corresponds to

is the total antenna pattern coverage area, i.e.,

Substituting (7.53) and (7.54) in (7.52) and differentiating, the PDF of

This PDF is shown in Fig. 7.11 for two different values of HPBW ( observed that as HPBW decreases, tends to a uniform PDF.

is

). It is

174

B. Phase offset,

We now turn our attention to phase offset Here, the phase is considered uniform over the previous subsection). Hence,

. (as shown in

where

Here,

is introduced in (7.2). If we discretize the interval

into

sample times, the phase offset can be determined using the value . This is achieved by calculating and and noting that

To determine which leads to

, we apply (7.57) and (7.8)

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Here, M represents the number of antenna array elements, d is the distance between array elements and Finally, the initial value corresponds to

C. Coherence time and available diversity benefit Next, we update the computation of coherence time when the impulse response is changed from its representation in (7.30) to that of (7.48). To compute this cohernce time, we maintain all of the assumptions made in subsection 7.2.3. Using simulation methods outlined in the previous subsection, the

mean that results, when assuming circular coverage, is presented in Fig. 7.12(a,b) and Fig. 7.13(a,b). Fig. 7.12(a,b) plots the coherence time as a function of the parameter controlling the rate of beam pattern oscillation (see (7.8) ) assuming HPBW = 0.5rad. In these figures, three curves are plotted, each for different scatterer density, , and Fig. 7.13(a,b) represents the dependence of coherence time on HPBW for three different scatterer densities. From Fig. 7.12 and 7.13 the coherence time decreases as control parameter increases (i.e., the sweeping rate increases), the scatterer’s density of increases, the HPBW increases and the BS to mobile station distance increases. Moreover, coherence time levels off at i.e., fold diversity over . This is consistent with an earlier result where antenna array gain and phase were neglected in the beam pattern’s mainlobe.

176

In the case of elliptical coverage, the mean that results from our simulations is presented in Fig. 7.14 and 7.15. Fig. 7.14(a,b) plots the coherence time as a function of the parameter controlling the rate of beam pattern oscillation (see (7.8)), assuming HPBW = 0.5rad. In this figure, three curves are plotted, each for different scatterer density, and Fig. 7.15 represents the dependence of coherence time on HPBW for three different scatterer densities.

From Fig. 7.14 coherence time decreases as: 1) control parameter increases (i.e., sweeping rate increases); 2) the scatterer’s density increases; and 3) BS-MS distance,

, increases. Here, coherence time levels

off at , i.e., fold diversity over coherence time decreases as HPBW increases.

. From Fig. 7.15,

177

Hence, we observe that, when an antenna array with an oscillating beam pattern is mounted on BS, up to 6 fold time diversity can be generated at the MS.

7.3 Innovative Combining of Multi-Carrier Systems and Smart Antennas with spatial sweeping In this section we introduce a novel merger of the proposed smart antenna array and code division multiple access (CDMA). Specifically, we merge the antenna array with: (1) first, CI/MC-CDMA as introduced in Chapter 3, and (2) second, CI/DS-CDMA, the topic of Chapter 5.

178

In MC-CDMA, each user’s data symbol is transmitted simultaneously over N carriers, with carriers coded using +1 or –1 (based on a pre-assigned spreading code). MC-CDMA receivers are capable of separating a large number of users occupying identical carriers while achieving high performance via frequency diversity. As demonstrated in Chapter 3, when the +1 or –1 spreading code values in MC-CDMA are replaced by phase offsets corresponding to interferometery patterns (creating CI/MC-CDMA), network capacity and performance are both enhanced. Unlike MC-CDMA, in DS-CDMA, each user’s bit is multiplied by a sequence of N chips (short pulses of duration ), where each chip has

amplitude +1 or –1. By careful selection of +1 and –1 values (spreading sequences), the receiver can separate users from one another. To enhance

performance via path diversity, most DS-CDMA systems employ RAKE

receivers, which attempt to separate and linearly recombine the multiple paths. Recently, a novel chip shape referred to as the CI (Carrier Interferometery) chip shape was introduced to DS-CDMA (Chapter 5). Here, each chip is decomposable into N orthogonal carrier components. As a result, when applying these chip shapes, the DS-CDMA receiver: 1) achieves a frequency diversity benefit (rather than a path diversity benefit) by decomposing chips into carrier components and frequency recombining; and 2) the use of frequency combining in place of path combining (as done in the RAKE receiver) leads to significantly improved performance via the ability to avoid inter-path interference [34].

Employing CI/MC-CDMA or CI/DS-CDMA with the proposed antenna array at the BS, we achieve: 1) directionality which supports space division multiple access (SDMA); 2) a time diversity gain using only a single antenna at the receiver in the mobile unit; and 3) increased capacity and performance via CI-CDMA’s ability to support both code division multiple access and frequency diversity benefits. Hence, merging CI/MC-CDMA or CI/DSCDMA with BS single antenna arrays in an innovative fashion, we achieve high performance at the mobile via joint frequency-time diversity, and high network capacity via joint space-code division multiple access.

179

Receivers are constructed to exploit both the transmit diversity, which corresponds to an induced time diversity, as well as the frequency diversity of the CI system. Different receiver structures are examined, including EGC/MRC/MMSEC (Equal Gain Combining / Maximal Ratio Combining / Minimum Mean Square Error Combining) performed in the time and

frequency domains. In what follows, we focus on the performance benefits achievable with this novel merger. 7.3.1 The Transmit Side

7.3.1.1 Brief review of the CI/MC-CDMA system In MC-CDMA, each user’s bit is transmitted simultaneously over N . narrowband subcarriers. Subcarriers are equally spaced in frequency by To ensure separability of users at the receiver side, a unique spreading code is applied to each user’s carriers. Hence, the user’s data bit, , is sent as:

where is +1 or –1, is the center or carrier frequency, and the spreading code, corresponding to

Here,

is employed to maintain carrier orthogonality, and g(t) is a

rectangular waveform of unity height over 0 to

element of user (i.e.,

(t) is

Finally,

refers to the

spreading sequence, where traditionally ). However, when CI codes are employed,

for users 0, 1, ..., N-1, (i.e., ). In this way, N orthogonal users are supported (similar to the case of Hadamard-Walsh codes); moreover, if additional users are to be supported, an additional N users can be introduced pseudo-orthogonally by adding users with spreading codes characterized by:

180

for users N, N+1, ..., 2N-1 (i.e.,

). (See Chapter 3 for details)

7.3.1.2 Brief Review of CI/DS-CDMA System

In DS-CDMA, a unique time sequence (N chips each with amplitude +1 or –1) is assigned to each user. In CI/DS-CDMA, each of the N chips are a superpositioning of N narrowband subcarriers (equally spaced in frequency by . Hence, the user’s data bit, , is sent as:

where is the

is +1 or –1, is the center or carrier frequency, and user spreading code, corresponding to

(t)

Here, is the element of user spreading code, g(t) is a rectangular waveform limiting the chip shape to duration , and h(t) is the chip shape which corresponds to the superposition of N carriers, i.e.,

It is important to note that and , are orthogonal to one another. The CI chip shape of (7.67) corresponds to a frequency sampled version of the sinc(.) chip shape. 7.3.1.3 The Antenna Array Structure The following signal enters the antenna array:

181

where

(t) is the CI/MC-CDMA signal of (7.61) or the CI/DS-CDMA

signal of (7.65), and K is the number of users in the multi-access system. This signal enters the antenna array structure of Fig. 7.1 prior to transmission over the channel, enabling both transmit diversity (in the form of time diversity) and SDMA (via directionality) [35]. 7.3.2 The Receiver Side 7.3.2.1 Receiver Design for CI/MC-CDMA

The

user’s transmitted signal, without an antenna array (using (7.61)

and (7.62)), corresponds to

Now, considering the antenna array, the signal in (7.69) enters the smart antenna array. The output of the element, after application of offset (t), is simply:

where The total downlink transmitted signal, considering all antenna elements (all m) and all users (all k) is (from (7.70))

At the receiver side, considering the transmit diversity which leads to an L fold time diversity, the received signal in can be divided into time slots where and each time slot has independent fade. This signal corresponds to

182

Here,

is an additive white Gaussian noise, independent for differing

carriers (n) and different time slots (l);

is the fade on the

carrier in the

time slot (due to fading) and is the phase offset in the carrier and time slot (due to fading) (hereafter, phase is assumed to be tracked and removed). From [36], the fades over the N subcarriers, are correlated Rayleigh random variables with correlation coefficient between the subcarrier fade and the subcarrier fade characterized by:

where is the coherence bandwidth of the channel. Applying the summation over m (the set of antenna array elements), (7.72) can be rewritten as:

Here, (introduced in (7.1)) is the normalized array factor of the smart antenna arrays. Assuming a narrow-beamwidth smart antenna (and assuming the MS is located at (7.74) can be approximated by and for all values of within the antenna array HPBW and all times. The CI/MC-CDMA receiver for user , is shown in Fig. 7.16. In this figure, a bank of band pass filters separates the MC-CDMA signal into its N multiple carriers. Next, each carrier is multiplied by a local oscillator generating

Once each of the N MC-CDMA carriers (located in parallel branches) has been returned to baseband, the baseband signal is integrated over each interval

183

over which the fade is constant, i.e., over . After applying the spreading code of user j to seperate users, the received signal for each subcarrier and time interval l, , corresponds to:

where and is a zero mean Gaussian random variable with variance The first term in (7.76) represents the component of the desired signal, the second term is multi-access interference and the third term is noise.

7.3.2.2 Combining Schemes With diversity components, N over frequency and L over time, the combiner can be designed using EGC, MRC or MMSEC, applied to the

frequency components then the time components (or vice versa). Examples of the combiner follow:

184

a. EGC-EGC scheme: EGC is applied in time then in frequency, or equivalently EGC applied to the frequency components, then in time. This results in

b. MRC-EGC scheme: MRC applied to the frequency components (or time components) followed by EGC in time (or frequency) leads to:

c. EGC-MRC scheme: Applying EGC to the time components, then MRC in frequency results in:

where

and

Applying EGC in frequency then MRC in time leads to:

where

185

and

d. MMSEC-EGC scheme: Applying the Wienner filter principle [37] to determine the MMSEC across CI/MC-CDMA carriers, the decision variable with K=N (i.e., K=N users on N carriers) is:

where

and

is the noise variance of

e. EGC-MMSEC scheme: Here, the decision variable corresponds to:

where

and P are as defined in (7.80), (7.81) and (7.89) respectively

and is the noise variance of Additionally,

in (7.82), i.e.,

186

where and

and

are defined in (7.84), (7.85) and (7.86) respectively

is the noise variance of

in (7.87), i.e.,

7.3.2.3 Receiver design for CI/DS-CDMA User k’s signal, transmitted into the base station antenna array, corresponds to (using (7.65) and (7.66))

which, using (7.67), leads to

where The output of the element of the antenna array, after application of phase offset in Fig. 7.1, is simply:

where

. The total downlink transmitted signal, considering all

antenna elements (all m) and all users (all k) in

is (from (7.95))

At the receiver side, the transmit diversity (due to antenna array movement generated by ) leads to an L fold time diversity. Hence, the received

187

signal in

can be divided into time slots where , and each time slot contains a signal with an independent fade. This signal corresponds to

Here,

is the white Gaussian noise on the

carrier and the

time slot,

is the fade on the carrier in the time slot (due to fading) and is the phase offset in the carrier and time slot (due to fading) (hereafter, phase is assumed to be tracked and removed). The fades over the

subcarriers, that make up each CI chip, i.e., , are correlated Rayleigh random variables with correlation coefficient given in (7.73). The CI/DS-CDMA receiver for user h is shown in Fig. 7.17(a,b), where Fig. 7.17(a) shows the overall receiver structure, and Fig. 7.17(b) details the block entitled ‘chip j receiver’ (in Fig. 7.17(a)). In other words, the receiver operates as follows: first, the received signal is processed through a total of N chip receivers, where chip j’s receiver (a) decomposes its chip into N carrier components, and (b) recombines across the carrier components to recreate the chip while achieving frequency diversity benefit. In addition, because a time diversity benefit is available (via transmit diversity), chip j’s receiver also (c) combines across time components to recreate the chip with a frequency-time diversity gain. Next, once each chip is recreated with an enhanced diversity

benefit, the receiver of Fig. 7.17(a) shows a combining across the chips in a usual DS-CDMA manner to eliminate other users’ signals. Mathematically, the receiver proceeds as follows: a bank of band pass filters separates the chip into its N frequency components. Each frequency component is returned to baseband by multiplication by a local oscillator, i.e., an oscillator generating

Once the frequency components that make up the CI chip are returned to baseband, each baseband signal is integrated over each interval over which the fade is constant, i.e., over . Next, we apply phase offsets to the N frequency components which corresponds to the delay (which seperates chips from other chips). The received signal

188

189

for each subcarrier n, corresponds to:

where

and time interval l,

,

In (7.99), the first term represents the desired term

(chip j for the desired user (user h)), the second term is the multi-access interference due to other chips of user h, the third term is the intereference due to the same chip of other users and the fourth term represents the effect of the other chips from the other users. Moreover, is a zero mean Gaussian random variable with variance , independent across differing carriers n and different time slots l, but correlated across chips (see Chapter 5).

In the case of (i.e., in the case of an AWGN channel), a linear equal gain combining across carriers eliminates the second and fourth terms in (7.99), since chip and are orthogonal. However, the frequency selective fade (i.e., constant) does not allow for such an elegant elimination of inter-chip interfernce. Using the linear combining scheme discussed next, we combine the over time and frequency components (with diversity components, L over time and N over frequency) to reduce the inter-chip interfernce and the noise, while achieving diversity gains. This leads to the output, shown in Fig. 7.17(b). This output is combined across the chips (across j) in the usual DSCDMA manner (Fig. 7.17(a)) to eliminate other users interference (term 2 in (7.99)), i.e.,

190

Detailing the time-frequency combiner in Fig. 7.17(b): it is designed using EGC applied across time components followed by MMSEC applied across N frequency components. The details follow. Applying the Wienner filter principle [11] to determine the MMSEC across CI/DS-CDMA carriers, the decision variable corresponds to:

where

and

is the noise variance of

in (7.104), i.e.,

and

7. 3. 3 Simulated Performance

We simulate the following CDMA systems with the smart antenna array: 1) A processing gain of N = 32 (i.e., 32 carriers per user in CI/MC-CDMA and 32 chips per symbol in CI/DS-CDMA); 2) K = 32 orthogonal users on the CDMA system; 3) Beam pattern movement results in L = 7 independent fades in the duration ; and 4) A frequency selective channel with 4-fold frequency diversity over the entire bandwidth is assumed.

191

7. 3. 3.1 CI/MC-CDMA results

CI/MC-CDMA simulation results are shown in Fig. 7.18 for EGC, MRC and MMSEC combining in the frequency domain followed by EGC in the time domain. It is noted that the performance results for all combining strategies are very close, with EGC-EGC slightly better than those of MMSEC-EGC and MRC-EGC for signal to noise ratios above 8dB. The same result can be observed in the performance curves of Fig. 7.19, where EGC, MRC or MMSEC combining schemes are applied in the time domain followed by EGC in the frequency domain. In Fig. 7.20 the simulation results are provided for EGC in the time domain followed by EGC, MRC or MMSEC in the frequency domain, where again the EGC-EGC curve demonstrates a slightly better performance than its competitors. Finally, in Fig. 7.21, EGC is applied in the frequency domain followed by an EGC, MRC or MMSEC combining in the time domain. In all cases, comparing the simulation results with CI/MC-CDMA without the smart antenna at the BS, an improvement of more than 7dB at a

probability of error of

is observed.

192

193

7.3.3.2 CI/DS-CDMA results

In Fig. 7.22 the simulated results are provided for CI/DS-CDMA schemes assuming a receiver with EGC in the time domain followed by MMSEC in the frequency domain. The simulation results in Fig. 7.22 are compared with CI/DS-CDMA without the oscillating-pattem smart antenna at the BS. Here, MMSEC is applied to the subcarriers of the received CI/DS-CDMA signal. It is noted that the introduction of the antenna array at the BS introduces an improvement of more than 11 dB at a probability of error of (at the mobile) compared to “non-antenna array” CI/DS-CDMA. When compared to traditional DS-CDMA with a RAKE receiver an even more significant performance improvement is achieved.

7.4 Conclusion In this chapter, we proposed a novel antenna array structure for use at the base station. Providing both transmit diversity and directionality (simultaneously), we determined the antenna array ability to improve both performance (via diversity) and network capacity (via SDMA). Focusing our attention on performance benefits, we demonstrated how the proposed antenna array achieves significant gains at the mobile in (1) a simple BPSK system, (2) the CI/MC-CDMA system, and (3) the CI/DS-CDMA system. These performance benefits are in addition to the network capacity improvement and are available with only minor increase in mobile receiver complexity.

194

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INDEX

Antenna Array Structure, 154 Channel Model Antenna Array Factor and Phase, 170 Channel Impulse Response, 165 CI/DS-CDMA, 114 CI/MC-CDMA, 49 CI/OFDM, 136 CI/TDMA, 81 Evaluation of Coherence Time, 169 Smart Antenna, 164 CI Chip Shaping, 97

CI Codes, 43, 127 CI/COFDM, 127 Cl/DS-CDMA, 27, 89 Receiver, Antenna Array, 181 Transmit, Antenna Array, 179 CI/MC-CDMA, 21,44 Receiver, Antenna Array, 181 Transmit, Antenna Array, 179 CI/OFDM, 31,125 CI Signal, 15 Orthogonal, 18 Pseudo-Orthogonal, 19 CI/TDMA, 22, 78 Bandwidth efficiency, 80 COFDM, 7,125 Correlated Rayleigh Envelopes, 66 Crest Factor (CF), 58 Downlink, 60 Reduction Technique, 62 Uplink, 60 DS-CDMA, 91 GSM, 75 High-Capacity CI/DS-CDMA, 106, 109 CI/OFDM, 131 MMSE Combiner, CI/DS-CDMA, 101

198

CI/MC-CDMA, 69 CI/OFDM, 134 CI/TDMA, 82 OFDM, 5,125 PAPR, CI/MC-CDMA, 58 CI/OFDM, 141 OFDM, 141 PO-CI/OFDM, 144 Performance CI/DS-CDMA, 116 CI/DS-CDMA, Antenna Array, 193 CI/MC-CDMA, 52 CI/MC-CDMA, Antenna Array, 193 CI/OFDM, 137 CI/TDMA, 83 Frequency Offset, 55 Phase Jitter, 53 Theoretical, Smart Antenna, BPSK, 159 Simulation, Smart Antenna, BPSK, 162 Receiver CI/DS-CDMA, 101 CI/MC-CDMA, 50 CI/OFDM, 134 CI/TDMA, 82 Smart Antenna, BPSK, 157 Smart Antenna, 151 Spatial Sweeping, 151, 153 TDMA, 75 Transmit Diversity, 151, 162 Transmitter CI/COFDM, 127 CI/DS-CDMA, 97 CI/OFDM, 127