15
Theory and Applications of OFDM and CDMA Wideband Wireless Communications Henrik Schulze and Christian L ¨ uders Both of Fachhochschule S¨ udwestfalen Meschede, Germany
Theory and Applications ofOFDM and CDMA
Wideband Wireless Communications
Henrik SchulzeandChristian Luders
Both ofFachhochschule SudwestfalenMeschede, Germany
Innodata0470017392.jpg
Theory and Applications ofOFDM and CDMA
Theory and Applications ofOFDM and CDMA
Wideband Wireless Communications
Henrik SchulzeandChristian Luders
Both ofFachhochschule SudwestfalenMeschede, Germany
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Contents
Preface ix
1 Basics of Digital Communications 11.1 Orthogonal Signals and Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 The Fourier base signals . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 The signal space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Transmitters and detectors . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 Walsh functions and orthonormal transmit bases . . . . . . . . . . . 121.1.5 Nonorthogonal bases . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Baseband and Passband Transmission . . . . . . . . . . . . . . . . . . . . . 181.2.1 Quadrature modulator . . . . . . . . . . . . . . . . . . . . . . . . . 201.2.2 Quadrature demodulator . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3 The AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.3.1 Mathematical wideband AWGN . . . . . . . . . . . . . . . . . . . . 251.3.2 Complex baseband AWGN . . . . . . . . . . . . . . . . . . . . . . 251.3.3 The discrete AWGN channel . . . . . . . . . . . . . . . . . . . . . 29
1.4 Detection of Signals in Noise . . . . . . . . . . . . . . . . . . . . . . . . . 301.4.1 Sufficient statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.4.2 Maximum likelihood sequence estimation . . . . . . . . . . . . . . 321.4.3 Pairwise error probabilities . . . . . . . . . . . . . . . . . . . . . . 34
1.5 Linear Modulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 381.5.1 Signal-to-noise ratio and power efficiency . . . . . . . . . . . . . . 381.5.2 ASK and QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401.5.3 PSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431.5.4 DPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2 Mobile Radio Channels 512.1 Multipath Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.2 Characterization of Fading Channels . . . . . . . . . . . . . . . . . . . . . . 54
2.2.1 Time variance and Doppler spread . . . . . . . . . . . . . . . . . . 542.2.2 Frequency selectivity and delay spread . . . . . . . . . . . . . . . . 602.2.3 Time- and frequency-variant channels . . . . . . . . . . . . . . . . . 622.2.4 Time-variant random systems: the WSSUS model . . . . . . . . . . 63
vi CONTENTS
2.2.5 Rayleigh and Ricean channels . . . . . . . . . . . . . . . . . . . . . 662.3 Channel Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.4 Digital Transmission over Fading Channels . . . . . . . . . . . . . . . . . 72
2.4.1 The MLSE receiver for frequency nonselective and slowly fadingchannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.4.2 Real-valued discrete-time fading channels . . . . . . . . . . . . . . 742.4.3 Pairwise error probabilities for fading channels . . . . . . . . . . . 762.4.4 Diversity for fading channels . . . . . . . . . . . . . . . . . . . . . 782.4.5 The MRC receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.4.6 Error probabilities for fading channels with diversity . . . . . . . . 822.4.7 Transmit antenna diversity . . . . . . . . . . . . . . . . . . . . . . . 86
2.5 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 902.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3 Channel Coding 933.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.1.1 The concept of channel coding . . . . . . . . . . . . . . . . . . . . 933.1.2 Error probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 973.1.3 Some simple linear binary block codes . . . . . . . . . . . . . . . . 1003.1.4 Concatenated coding . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.1.5 Log-likelihood ratios and the MAP receiver . . . . . . . . . . . . . 105
3.2 Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1143.2.1 General structure and encoder . . . . . . . . . . . . . . . . . . . . . 1143.2.2 MLSE for convolutional codes: the Viterbi algorithm . . . . . . . . 1213.2.3 The soft-output Viterbi algorithm (SOVA) . . . . . . . . . . . . . . 1243.2.4 MAP decoding for convolutional codes: the BCJR algorithm . . . . 1253.2.5 Parallel concatenated convolutional codes and turbo decoding . . . 128
3.3 ReedSolomon Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313.3.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313.3.2 Galois field arithmetics . . . . . . . . . . . . . . . . . . . . . . . . 1333.3.3 Construction of ReedSolomon codes . . . . . . . . . . . . . . . . 1353.3.4 Decoding of ReedSolomon codes . . . . . . . . . . . . . . . . . . 140
3.4 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1423.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4 OFDM 1454.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.1.1 The concept of multicarrier transmission . . . . . . . . . . . . . . . 1454.1.2 OFDM as multicarrier transmission . . . . . . . . . . . . . . . . . 1494.1.3 Implementation by FFT . . . . . . . . . . . . . . . . . . . . . . . . 1534.1.4 OFDM with guard interval . . . . . . . . . . . . . . . . . . . . . . . 154
4.2 Implementation and Signal Processing Aspects for OFDM . . . . . . . . . . 1604.2.1 Spectral shaping for OFDM systems . . . . . . . . . . . . . . . . . 1604.2.2 Sensitivity of OFDM signals against nonlinearities . . . . . . . . . . 166
4.3 Synchronization and Channel Estimation Aspects for OFDM Systems . . . 1754.3.1 Time and frequency synchronization for OFDM systems . . . . . . 1754.3.2 OFDM with pilot symbols for channel estimation . . . . . . . . . . 181
CONTENTS vii
4.3.3 The Wiener estimator . . . . . . . . . . . . . . . . . . . . . . . . . 1834.3.4 Wiener filtering for OFDM . . . . . . . . . . . . . . . . . . . . . . 186
4.4 Interleaving and Channel Diversity for OFDM Systems . . . . . . . . . . . 1924.4.1 Requirements of the mobile radio channel . . . . . . . . . . . . . . 1924.4.2 Time and frequency interleavers . . . . . . . . . . . . . . . . . . . 1944.4.3 The diversity spectrum of a wideband multicarrier channel . . . . . 199
4.5 Modulation and Channel Coding for OFDM Systems . . . . . . . . . . . . 2084.5.1 OFDM systems with convolutional coding and QPSK . . . . . . . 2084.5.2 OFDM systems with convolutional coding and M2-QAM . . . . . 2134.5.3 Convolutionally coded QAM with real channel estimation and
imperfect interleaving . . . . . . . . . . . . . . . . . . . . . . . . . 2274.5.4 Antenna diversity for convolutionally coded QAM multicarrier
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2354.6 OFDM System Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
4.6.1 The DAB system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2424.6.2 The DVB-T system . . . . . . . . . . . . . . . . . . . . . . . . . . 2514.6.3 WLAN systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
4.7 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2614.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
5 CDMA 2655.1 General Principles of CDMA . . . . . . . . . . . . . . . . . . . . . . . . . 265
5.1.1 The concept of spreading . . . . . . . . . . . . . . . . . . . . . . . 2655.1.2 Cellular mobile radio networks . . . . . . . . . . . . . . . . . . . . 2695.1.3 Spreading codes and their properties . . . . . . . . . . . . . . . . . 2775.1.4 Methods for handling interference in CDMA mobile radio networks 284
5.2 CDMA Transmission Channel Models . . . . . . . . . . . . . . . . . . . . . 3045.2.1 Representation of CDMA signals . . . . . . . . . . . . . . . . . . . 3045.2.2 The discrete channel model for synchronous transmission in a
frequency-flat channel . . . . . . . . . . . . . . . . . . . . . . . . . 3075.2.3 The discrete channel model for synchronous wideband MC-CDMA
transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3105.2.4 The discrete channel model for asynchronous wideband CDMA
transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3125.3 Receiver Structures for Synchronous Transmission . . . . . . . . . . . . . . 315
5.3.1 The single-user matched filter receiver . . . . . . . . . . . . . . . . 3165.3.2 Optimal receiver structures . . . . . . . . . . . . . . . . . . . . . . 3215.3.3 Suboptimal linear receiver structures . . . . . . . . . . . . . . . . . 3285.3.4 Suboptimal nonlinear receiver structures . . . . . . . . . . . . . . . 339
5.4 Receiver Structures for MC-CDMA and Asynchronous Wideband CDMATransmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3425.4.1 The RAKE receiver . . . . . . . . . . . . . . . . . . . . . . . . . . 3425.4.2 Optimal receiver structures . . . . . . . . . . . . . . . . . . . . . . 347
5.5 Examples for CDMA Systems . . . . . . . . . . . . . . . . . . . . . . . . . 3525.5.1 Wireless LANs according to IEEE 802.11 . . . . . . . . . . . . . . 3525.5.2 Global Positioning System . . . . . . . . . . . . . . . . . . . . . . . 355
viii CONTENTS
5.5.3 Overview of mobile communication systems . . . . . . . . . . . . . 3575.5.4 Wideband CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . 3625.5.5 Time Division CDMA . . . . . . . . . . . . . . . . . . . . . . . . . 3755.5.6 cdmaOne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3805.5.7 cdma2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
5.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3925.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
Bibliography 397
Index 403
Preface
Wireless communication has become increasingly important not only for professional appli-cations but also for many fields in our daily routine and in consumer electronics. In 1990,a mobile telephone was still quite expensive, whereas today most teenagers have one, andthey use it not only for calls but also for data transmission. More and more computers usewireless local area networks (WLANs), and audio and television broadcasting has becomedigital.
Many of the above-mentioned communication systems make use of one of two sophis-ticated techniques that are known as orthogonal frequency division multiplexing (OFDM)and code division multiple access (CDMA).
The first, OFDM, is a digital multicarrier transmission technique that distributes thedigitally encoded symbols over several subcarrier frequencies in order to reduce the symbolclock rate to achieve robustness against long echoes in a multipath radio channel. Eventhough the spectra of the individual subcarriers overlap, the information can be completelyrecovered without any interference from other subcarriers. This may be surprising, butfrom a mathematical point of view, this is a consequence of the orthogonality of the basefunctions of the Fourier series.
The second, CDMA, is a multiple access scheme where several users share the samephysical medium, that is, the same frequency band at the same time. In an ideal case,the signals of the individual users are orthogonal and the information can be recoveredwithout interference from other users. Even though this is only approximately the case, theconcept of orthogonality is quite important to understand why CDMA works. It is due tothe fact that pseudorandom sequences are approximately orthogonal to each other or, inother words, they show good correlation properties. CDMA is based on spread spectrum,that is, the spectral band is spread by multiplying the signal with such a pseudorandomsequence. One advantage of the enhancement of the bandwidth is that the receiver can takebenefit from the multipath properties of the mobile radio channel.
OFDM transmission is used in several digital audio and video broadcasting systems.The pioneer was the European DAB (Digital Audio Broadcasting) system. At the time whenthe project started in 1987, hardly any communication engineers had heard about OFDM.One author (Henrik Schulze) remembers well that many practical engineers were very sus-picious of these rather abstract and theoretical underlying ideas of OFDM. However, onlya few years later, the DAB system became the leading example for the development of thedigital terrestrial video broadcasting system, DVB-T. Here, in contrast to DAB, coherenthigher-level modulation schemes together with a sophisticated and powerful channel esti-mation technique are utilized in a multipath-fading channel. High-speed WLAN systemslike IEEE 802.11a and IEEE 802.11g use OFDM together with very similar channel coding
x PREFACE
and modulation. The European standard HIPERLAN/2 (High Performance Local Area Net-work, Type 2) has the same OFDM parameters as these IEEE systems and differs only ina few options concerning channel coding and modulation. Recently, a broadcasting systemcalled DRM (Digital Radio Mondiale) has been developed to replace the antiquated analogAM radio transmission in the frequency bands below 30 MHz. DRM uses OFDM togetherwith a sophisticated multilevel coding technique.
The idea of spread spectrum systems goes back to military applications, which aroseduring World War II, and were the main field for spread spectrum techniques in the follow-ing decades. Within these applications, the main benefits of spreading are to hide a signal,to protect it against eavesdropping and to achieve a high robustness against intended in-terference, that is, to be able to separate the useful signal from the strong interfering one.Furthermore, correlating to a spreading sequence may be used within radar systems to obtainreliable and precise values of propagation delay for deriving the position of an object.
A system where different (nearly orthogonal) spreading sequences are used to sepa-rate the signals transmitted from different sources is the Global Positioning System (GPS)developed in about 1970. Hence, GPS is the first important system where code divisionmultiple access (CDMA) is applied. Within the last 10 years, CDMA has emerged as themost important multiple access technique for mobile communications. The first conceptfor a CDMA mobile communication system was developed by Qualcomm Incorporatedin approx 1988. This system proposal was subsequently refined and released as the so-called IS-95 standard in North America. In the meantime, the system has been rebrandedas cdmaOne, and there are more than 100 millions of cdmaOne subscribers in more than40 countries. Furthermore, cdmaOne has been the starting point for cdma2000, a third-generation mobile communication system offering data rates of up to some Mbit/s. Anothervery important third-generation system using CDMA is the Universal Mobile Telecommu-nications System (UMTS); UMTS is based on system proposals developed within a numberof European research projects. Hence, CDMA is the dominating multiple access techniquefor third generation mobile communication systems.
This book has both theoretical and practical aspects. It is intended to provide the readerwith a deeper understanding of the concepts of OFDM and CDMA. Thus, the theoreticalbasics are analyzed and presented in some detail. Both of the concepts are widely appliedin practice. Therefore, a considerable part of the book is devoted to system design andimplementation aspects and to the presentation of existing communication systems.
The book is organized as follows. In Chapter 1, we give a brief overview of the basicprinciples of digital communications and introduce our notation. We represent signals asvectors, which often leads to a straightforward geometrical visualization of many seeminglyabstract mathematical facts. The concept of orthogonality between signal vectors is a keyto the understanding of OFDM and CDMA, and the Euclidean distance between signalvectors is an important concept to analyze the performance of a digital transmission system.Wireless communication systems often have to cope with severe multipath fading in amobile radio channel. Chapter 2 treats these aspects. First, the physical situation of multipathpropagation is analyzed and statistical models of the mobile radio channel are presented.Then, the problems of digital transmission over these channels are discussed and the basicprinciples of Chapter 1 are extended for those channels. Digital wireless communicationover fading channels is hardly possible without using some kind of error protection orchannel coding. Chapter 3 gives a brief overview of the most important channel coding
PREFACE xi
techniques that are used in the above-mentioned communication systems. Convolutionalcodes are typically used in these systems, and many of the systems have very closelyrelated (or even identical) channel coding options. Thus, the major part of Chapter 3 isdedicated to convolutional codes as they are applied in these systems. A short presentationof ReedSolomon Codes is also included because they are used as outer codes in the DVB-T system, together with inner convolutional codes. Chapter 4 is devoted to OFDM. First,the underlying ideas and the basic principles are explained by using the basic principlespresented in Chapter 1. Then implementation aspects are discussed as well as channelestimation and synchronization aspects that are relevant for the above-mentioned systems.All these systems are designed for mobile radio channels and use channel coding. Therefore,we give a comprehensive discussion of system design aspects and how to fit all thesethings together in an optimal way for a given channel. Last but not least, the transmissionschemes for DAB, DVB-T and WLAN systems are presented and discussed. Chapter 5is devoted to CDMA, focusing on its main application area mobile communications.This application area requires not only sophisticated digital transmission techniques andreceiver structures but also some additional methods as, for example, a soft handover, afast and exact power control mechanism as well as some special planning techniques toachieve an acceptable radio network performance. Therefore, the first section of Chapter 5discusses these methods and some general principles of CDMA and mobile radio networks.CDMA receivers may be simple or quite sophisticated, thereby making use of knowledgeabout other users. These theoretically involved topics are treated in the following threesubsections. As examples of CDMA applications we discuss the most important systemsalready mentioned, namely, GPS, cdmaOne (IS-95), cdma2000 and UMTS with its twotransmission modes called Wideband CDMA and Time Division CDMA. Furthermore,Wireless LAN systems conforming to the standard IEEE 802.11 are also included in thissection as some transmission modes of these systems are based on spreading.
This book is supported by a companion website on which lecturers and instructorscan find electronic versions of the figures contained within the book, a solutions manualto the problems at the end of each chapter and also chapter summaries. Please go toftp://ftp.wiley.co.uk/pub/books/schulze
1
Basics of Digital Communications
1.1 Orthogonal Signals and Vectors
The concept of orthogonal signals is essential for the understanding of OFDM (orthogonalfrequency division multiplexing) and CDMA (code division multiple access) systems. Inthe normal sense, it may look like a miracle that one can separately demodulate overlappingcarriers (for OFDM) or detect a signal among other signals that share the same frequencyband (for CDMA). The concept of orthogonality unveils this miracle. To understand theseconcepts, it is very helpful to interpret signals as vectors. Like vectors, signals can beadded, multiplied by a scalar, and they can be expanded into a base. In fact, signals fit intothe mathematical structure of a vector space. This concept may look a little bit abstract.However, vectors can be visualized by geometrical objects, and many conclusions canbe drawn by simple geometrical arguments without lengthy formal derivations. So it isworthwhile to become familiar with this point of view.
1.1.1 The Fourier base signals
To visualize signals as vectors, we start with the familiar example of a Fourier series. Forreasons that will become obvious later, we do not deal with a periodic signal, but cutoff outside the time interval of one period of length T . This means that we consider awell-behaved (e.g. integrable) real signal x(t) inside the time interval 0 t T and setx(t) = 0 outside. Inside the interval, the signal can be written as a Fourier series
x(t) = a02+
k=1
ak cos
(2
k
Tt
)
k=1
bk sin
(2
k
Tt
). (1.1)
The Fourier coefficients ak and bk are given by
ak = 2T
T0
cos
(2
k
Tt
)x(t) dt (1.2)
Theory and Applications of OFDM and CDMA Henrik Schulze and Christian Luders 2005 John Wiley & Sons, Ltd
