TEAM LinG Theory and Applications of OFDM and CDMA Theory and Applications of OFDM and CDMA Wideband Wireless Communications Henrik Schulze and Christian L ¨ uders Both of Fachhochschule S¨udwestfalen Meschede, Germany Copyright  2005 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. 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Contents Preface ix 1 Basics of Digital Communications 1 1.1 Orthogonal Signals and Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 TheFourierbasesignals 1 1.1.2 Thesignalspace 5 1.1.3 Transmitters and detectors . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.4 Walsh functions and orthonormal transmit bases . . . . . . . . . . . 12 1.1.5 Nonorthogonal bases . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2 BasebandandPassbandTransmission 18 1.2.1 Quadrature modulator . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.2 Quadrature demodulator . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3 TheAWGNChannel 23 1.3.1 MathematicalwidebandAWGN 25 1.3.2 ComplexbasebandAWGN 25 1.3.3 ThediscreteAWGNchannel 29 1.4 DetectionofSignalsinNoise 30 1.4.1 Sufficientstatistics 30 1.4.2 Maximum likelihood sequence estimation . . . . . . . . . . . . . . 32 1.4.3 Pairwise error probabilities . . . . . . . . . . . . . . . . . . . . . . 34 1.5 Linear Modulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.5.1 Signal-to-noise ratio and power efficiency . . . . . . . . . . . . . . 38 1.5.2 ASKandQAM 40 1.5.3 PSK 43 1.5.4 DPSK 44 1.6 BibliographicalNotes 46 1.7 Problems 47 2 Mobile Radio Channels 51 2.1 Multipath Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2 CharacterizationofFadingChannels 54 2.2.1 Time variance and Doppler spread . . . . . . . . . . . . . . . . . . 54 2.2.2 Frequency selectivity and delay spread . . . . . . . . . . . . . . . . 60 2.2.3 Time- and frequency-variant channels . . . . . . . . . . . . . . . . . 62 2.2.4 Time-variant random systems: the WSSUS model . . . . . . . . . . 63 vi CONTENTS 2.2.5 Rayleigh and Ricean channels . . . . . . . . . . . . . . . . . . . . . 66 2.3 ChannelSimulation 67 2.4 DigitalTransmissionoverFadingChannels 72 2.4.1 The MLSE receiver for frequency nonselective and slowly fading channels 72 2.4.2 Real-valued discrete-time fading channels . . . . . . . . . . . . . . 74 2.4.3 Pairwise error probabilities for fading channels . . . . . . . . . . . 76 2.4.4 Diversityforfadingchannels 78 2.4.5 The MRC receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.4.6 Error probabilities for fading channels with diversity . . . . . . . . 82 2.4.7 Transmitantennadiversity 86 2.5 BibliographicalNotes 90 2.6 Problems 91 3 Channel Coding 93 3.1 GeneralPrinciples 93 3.1.1 Theconceptofchannelcoding 93 3.1.2 Error probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.1.3 Some simple linear binary block codes . . . . . . . . . . . . . . . . 100 3.1.4 Concatenatedcoding 103 3.1.5 Log-likelihood ratios and the MAP receiver . . . . . . . . . . . . . 105 3.2 Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.2.1 Generalstructureandencoder 114 3.2.2 MLSE for convolutional codes: the Viterbi algorithm . . . . . . . . 121 3.2.3 The soft-output Viterbi algorithm (SOVA) . . . . . . . . . . . . . . 124 3.2.4 MAP decoding for convolutional codes: the BCJR algorithm . . . . 125 3.2.5 Parallel concatenated convolutional codes and turbo decoding . . . 128 3.3 Reed–SolomonCodes 131 3.3.1 Basicproperties 131 3.3.2 Galoisfieldarithmetics 133 3.3.3 Construction of Reed–Solomon codes . . . . . . . . . . . . . . . . 135 3.3.4 Decoding of Reed–Solomon codes . . . . . . . . . . . . . . . . . . 140 3.4 BibliographicalNotes 142 3.5 Problems 143 4 OFDM 145 4.1 GeneralPrinciples 145 4.1.1 Theconceptofmulticarriertransmission 145 4.1.2 OFDMasmulticarriertransmission 149 4.1.3 ImplementationbyFFT 153 4.1.4 OFDMwithguardinterval 154 4.2 Implementation and Signal Processing Aspects for OFDM . . . . . . . . . . 160 4.2.1 SpectralshapingforOFDMsystems 160 4.2.2 Sensitivity of OFDM signals against nonlinearities . . . . . . . . . . 166 4.3 Synchronization and Channel Estimation Aspects for OFDM Systems . . . 175 4.3.1 Time and frequency synchronization for OFDM systems . . . . . . 175 4.3.2 OFDM with pilot symbols for channel estimation . . . . . . . . . . 181 CONTENTS vii 4.3.3 TheWienerestimator 183 4.3.4 WienerfilteringforOFDM 186 4.4 Interleaving and Channel Diversity for OFDM Systems . . . . . . . . . . . 192 4.4.1 Requirements of the mobile radio channel . . . . . . . . . . . . . . 192 4.4.2 Time and frequency interleavers . . . . . . . . . . . . . . . . . . . 194 4.4.3 The diversity spectrum of a wideband multicarrier channel . . . . . 199 4.5 Modulation and Channel Coding for OFDM Systems . . . . . . . . . . . . 208 4.5.1 OFDM systems with convolutional coding and QPSK . . . . . . . 208 4.5.2 OFDM systems with convolutional coding and M 2 -QAM 213 4.5.3 Convolutionally coded QAM with real channel estimation and imperfectinterleaving 227 4.5.4 Antenna diversity for convolutionally coded QAM multicarrier systems 235 4.6 OFDMSystemExamples 242 4.6.1 TheDABsystem 242 4.6.2 TheDVB-Tsystem 251 4.6.3 WLANsystems 258 4.7 BibliographicalNotes 261 4.8 Problems 263 5 CDMA 265 5.1 GeneralPrinciplesofCDMA 265 5.1.1 Theconceptofspreading 265 5.1.2 Cellularmobileradionetworks 269 5.1.3 Spreading codes and their properties . . . . . . . . . . . . . . . . . 277 5.1.4 Methods for handling interference in CDMA mobile radio networks 284 5.2 CDMATransmissionChannelModels 304 5.2.1 RepresentationofCDMAsignals 304 5.2.2 The discrete channel model for synchronous transmission in a frequency-flatchannel 307 5.2.3 The discrete channel model for synchronous wideband MC-CDMA transmission 310 5.2.4 The discrete channel model for asynchronous wideband CDMA transmission 312 5.3 Receiver Structures for Synchronous Transmission . . . . . . . . . . . . . . 315 5.3.1 The single-user matched filter receiver . . . . . . . . . . . . . . . . 316 5.3.2 Optimal receiver structures . . . . . . . . . . . . . . . . . . . . . . 321 5.3.3 Suboptimal linear receiver structures . . . . . . . . . . . . . . . . . 328 5.3.4 Suboptimal nonlinear receiver structures . . . . . . . . . . . . . . . 339 5.4 Receiver Structures for MC-CDMA and Asynchronous Wideband CDMA Transmission 342 5.4.1 The RAKE receiver . . . . . . . . . . . . . . . . . . . . . . . . . . 342 5.4.2 Optimal receiver structures . . . . . . . . . . . . . . . . . . . . . . 347 5.5 ExamplesforCDMASystems 352 5.5.1 Wireless LANs according to IEEE 802.11 . . . . . . . . . . . . . . 352 5.5.2 GlobalPositioningSystem 355 viii CONTENTS 5.5.3 Overview of mobile communication systems . . . . . . . . . . . . . 357 5.5.4 WidebandCDMA 362 5.5.5 TimeDivisionCDMA 375 5.5.6 cdmaOne 380 5.5.7 cdma2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 5.6 BibliographicalNotes 392 5.7 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, and they use it not only for calls but also for data transmission. More and more computers use wireless local area networks (WLANs), and audio and television broadcasting has become digital. 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 the digitally encoded symbols over several subcarrier frequencies in order to reduce the symbol clock rate to achieve robustness against long echoes in a multipath radio channel. Even though the spectra of the individual subcarriers overlap, the information can be completely recovered without any interference from other subcarriers. This may be surprising, but from a mathematical point of view, this is a consequence of the orthogonality of the base functions of the Fourier series. The second, CDMA, is a multiple access scheme where several users share the same physical 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 recovered without interference from other users. Even though this is only approximately the case, the concept of orthogonality is quite important to understand why CDMA works. It is due to the fact that pseudorandom sequences are approximately orthogonal to each other or, in other 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 pseudorandom sequence. One advantage of the enhancement of the bandwidth is that the receiver can take benefit 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 when the 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, only a few years later, the DAB system became the leading example for the development of the digital terrestrial video broadcasting system, DVB-T. Here, in contrast to DAB, coherent higher-level modulation schemes together with a sophisticated and powerful channel esti- mation technique are utilized in a multipath-fading channel. High-speed WLAN systems like IEEE 802.11a and IEEE 802.11g use OFDM together with very similar channel coding [...]... in CDMA signaling We regard them as an example to discuss an orthonormal base that can be interpreted as a base of signals or as a base in an Euclidean space The M × M Walsh–Hadamard (WH) matrices HM , where M is a power of two, are defined by H1 = 1 and the recursive relation HM = HM/2 HM/2 HM/2 −HM/2 For example, the matrix H4 is given by   1 1 1 1  1 1 1 1   H4 =   1 1 1 1  1 1 1 1 14 ... )2 (1. 27) have a very similar shape if we relate α and β in such a way that their flanks V (f ) have the same first derivative at f = 0 This is the case for β= 2α π 12 BASICS OF DIGITAL COMMUNICATIONS 1 0.9 0.8 0.7 H(f ) 0.6 0.5 0.4 0.3 0.2 0 .1 0 1 –0.8 –0.6 –0.4 –0.2 0 f TS 0.2 0.4 0.6 0.8 1 Figure 1. 4 RC and Gaussian Nyquist filter shape for α = 0.2 0 –2 –4 –6 10 log H(f ) –8 10 12 14 16 18 –20... in CDMA (code division multiple access) Each Walsh function corresponds to another code that may be allocated to 16 BASICS OF DIGITAL COMMUNICATIONS s1 g1 s g2 s2 Figure 1. 8 The orthonormal Walsh–Hadamard base s1 g1 s1 , s2 Dg1 s1 TX/ DEMUX MUX s2 g2 Dg2 s1 , s2 s2 Figure 1. 9 Orthogonal channels a certain user in a mobile radio scenario The downlink of the Qualcomm CDMA system IS-95 (now called cdmaOne,... strictly band-limited to B/2, then u, x = u, x , v, y = v, y ˜ ˜ ˜ ˜ (1. 40) holds As a special case, we observe that both I- and Q-modulator leave the signal energy ˜ ˜ unchanged, that is, x 2 = x 2 and y 2 = y 2 BASICS OF DIGITAL COMMUNICATIONS 21 x(t) ˜ ˜ D x(t) D ˜ ˜ D[x] = I-MOD D[x] Figure 1. 11 Equivalence of baseband and passband detection The proof of the theorem is left to Problem 3 Equation (1. 39)... 1 –0.8 –0.6 –0.4 –0.2 0 f TS 0.2 0.4 0.6 0.8 1 Figure 1. 5 RC and Gaussian Nyquist filter shape for α = 0.2 (decibel scale) BASICS OF DIGITAL COMMUNICATIONS 13 1 0.8 0.6 h(t ) 0.4 0.2 0 –0.2 –0.4 –5 –4 –3 –2 1 0 t/ TS 1 2 3 4 5 Figure 1. 6 RC and Gaussian Nyquist pulse shape for α = 0.2 For this case and α = 0.2, both filter shapes are depicted in Figure 1. 4, and with a logarithmic scale, in Figure 1. 5... ˜ (1. 35) s(t) = (t) ∗ We note that the upconversion from s(t) to s (t) as described by Equation (1. 34) doubles ˜ the bandwidth of the two components (real and imaginary part) of the baseband signal, 20 BASICS OF DIGITAL COMMUNICATIONS resulting in one signal of bandwidth B instead of two (real) signals of bandwidth B/2 We write s(t) = x(t) + jy(t) and call the real part, x(t), the I- (inphase) and. .. interval of one period of length T This means that we consider a well-behaved (e.g integrable) real signal x(t) inside the time interval 0 ≤ t ≤ T and set x(t) = 0 outside Inside the interval, the signal can be written as a Fourier series a0 x(t) = + 2 ∞ k =1 k ak cos 2π t − T ∞ bk sin 2π k =1 k t T (1. 1) The Fourier coefficients ak and bk are given by ak = Theory and Applications of OFDM and CDMA  2005... the book, a solutions manual to the problems at the end of each chapter and also chapter summaries Please go to ftp://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 (orthogonal frequency division multiplexing) and CDMA (code division multiple access) systems In the normal... organized as follows In Chapter 1, we give a brief overview of the basic principles of digital communications and introduce our notation We represent signals as vectors, which often leads to a straightforward geometrical visualization of many seemingly abstract mathematical facts The concept of orthogonality between signal vectors is a key to the understanding of OFDM and CDMA, and the Euclidean distance... as the amplitude of x in the direction of vi α2 x v2 v1 1 Figure 1. 1 A signal vector in two dimensions BASICS OF DIGITAL COMMUNICATIONS 3 The Fourier expansion (1. 1) is of the same type as the expansion (1. 4), except that the sum is infinite For a better comparison, we may write ∞ x(t) = αi vi (t) i=0 with the normalized base signal vectors vi (t) defined by v0 (t) = t 1 − T 2 1 T and k 2 cos 2π t . TEAM LinG Theory and Applications of OFDM and CDMA Theory and Applications of OFDM and CDMA Wideband Wireless Communications Henrik Schulze and Christian L ¨ uders Both of Fachhochschule. BibliographicalNotes 14 2 3.5 Problems 14 3 4 OFDM 14 5 4 .1 GeneralPrinciples 14 5 4 .1. 1 Theconceptofmulticarriertransmission 14 5 4 .1. 2 OFDMasmulticarriertransmission 14 9 4 .1. 3 ImplementationbyFFT 15 3 4 .1. 4 OFDMwithguardinterval. production. Contents Preface ix 1 Basics of Digital Communications 1 1 .1 Orthogonal Signals and Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1 1 .1. 1 TheFourierbasesignals 1 1 .1. 2 Thesignalspace 5 1. 1.3 Transmitters