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194 NOTATION Variable Meaning a lc m M Symbol waveform A Amplitude k ( m '°)' k( m ) B{m), B(r m ,i,j) Transmitted modem bits Viterbi algorithm branch metric ce Channel coefficient c¡¿ m(nX c ) Symbol chip sequence value C n (ti,Í2) Covariance function for n(i) dj Equalization processing delay Ei, Energy per bit E { c\ E { c\k) Energy per chip E s , E ( s i} , E¡ i] (k) Energy per symbol /c Carrier frequency fo f n (x) Frequency offset Probability density function for n F„(x) Cumulative distribution function for n ge, gi Medium response coefficient(s) h(t), h k m (t) Channel response including symbol waveform and medium response i Transmit antenna index j \/ — lj processing delay index; symbol value index J Number of processing delays k Parallel multiplexing channel index K Number of parallel multiplexing channels from common transmitter i Path delay index, s-parameter index L Number of path delays m Modem symbol period index M Number of possible symbol values (M-ary modulation) M q MLSD metric n Chip index n m Noise value (after filtering and sampling) n(i) Noise waveform N c Number of chips per symbol period (spreading factor in CDM) NCP Number of chips in the cyclic prefix (OFDM) NMB Number of chips in the main block (OFDM) N r Number of receive antennas N s Number of symbols Nt Number of transmit antennas No One-sided noise power spectral density
NOTATION 195 Variable Meaning p(t) Pulse shape Pb Probability of bit error Pm(i) P s Viterbi algorithm path metric Probability of symbol error Pr{·} Likelihood (probability or pdf function) q Receive sample index qm, q(m), qm(i), q Hypothesized symbol values Q Number of samples per chip period Qm(i) Viterbi algorithm path history r(t), r(i) Received signal waveform r m Received signal sample (after filtering and sampling) R P (T) Pulse autocorrelation function s m , s(m), s¿ (m) Modem symbol s(m), s Hard or soft decision detected symbol(s) S Set of possible symbol values S m The mth possible symbol value in set S S(() Viterbi algorithm s-parameter Sp Set of possible symbol sequences S(£) S-parameters t Time v(qT s ) Received signal after filtering and sampling w, Wj Equalization weight vector x'''(i) Transmit signal z m , z(m), z¿ (m) Decision variable re Path delay σ 2 Noise variance
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Channel Equalization for Wireless C
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To my colleagues at Ericsson
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CONTENTS List of Figures List of Ta
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CONTENTS XI 4.2 4.3 4.4 4.5 4.6 4.1
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CONTENTS XIII 8 Practical Considera
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xvi LIST OF FIGURES 2.2 Matched fil
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XviÜ LIST OF FIGURES 6.18 Scatter
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XX Prologue Alice was nervous. Woul
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XXÜ PREFACE is introduced as neede
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ACRONYMS AC A/D ADC AMLD AMPS ASK A
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ML MLD MLPD MLSD MLSE MRC MSE MSB O
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2 INTRODUCTION Table 1.1 Possible m
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4 INTRODUCTION s o S 1 8 2 S 3 S 0
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6 INTRODUCTION A block diagram of t
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8 INTRODUCTION Figure 1.7 QPSK. tra
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10 INTRODUCTION phases (phase modul
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12 INTRODUCTION rollo« 0.22 0.8 Ί
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14 INTRODUCTION is the "channel" re
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16 INTRODUCTION 1.4 MORE MATH In th
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18 INTRODUCTION For K = 1 (order 0)
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20 INTRODUCTION The K = 4 main bloc
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22 INTRODUCTION A sample of the noi
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24 INTRODUCTION The receiver may ha
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26 INTRODUCTION 1.5.1 Reference sys
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28 INTRODUCTION a) What most likely
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CHAPTER 2 MATCHED FILTERING In this
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MORE DETAILS 33 2.2 MORE DETAILS So
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THE MATH 35 Now compare the output
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THE MATH 37 The correlation in (2.2
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THE MATH 39 correlation function f(
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THE MATH 41 Thus, in the complex pl
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THE MATH 43 to the medium response
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THE MATH 45 We can interpret f(t) a
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MORE MATH 47 10" 1 Odeg 90 deg X 18
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MORE MATH 49 With despread-level Ra
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MORE MATH 51 Figure 2.6 OFDM exampl
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MORE MATH 53 2.4.3 MF in colored no
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PROBLEMS 55 period) is examined in
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CHAPTER 3 ZERO-FORCING DECISION FEE
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MORE DETAILS 59 1/c r m —► H i
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MORE DETAILS 61 where «i = m - (d/
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MORE MATH 63 Because there is no IS
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MORE MATH 65 In the later chapter o
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PROBLEMS 67 b) What is the detected
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CHAPTER 4 LINEAR EQUALIZATION With
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THE IDEA 71 estimate of symbol s 2
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THE IDEA 73 Notice that £2 (MSE) d
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MORE DETAILS 75 The first term is t
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MORE DETAILS 77 To obtain the unity
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THE MATH 79 and SINR becomes w T h
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THE MATH 81 To obtain the MMSE solu
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THE MATH 83 where *m n = ν ^ ^ ^ '
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THE MATH 85 power is much larger th
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MORE MATH 87 IQ' 1 OC 111 ω 10 2 1
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MORE MATH 89 values of h k m (f) fr
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MORE MATH 91 where C(d(),d 0 ) . C(
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AN EXAMPLE 93 between z and s. This
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PROBLEMS 95 Another aspect of cocha
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PROBLEMS 97 The math 4.11 Consider
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100 MMSE AND ML DECISION FEEDBACK E
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CHAPTER 6 MAXIMUM LIKELIHOOD SEQUEN
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MORE DETAILS 117 r 2 Ht, r, fcl + f
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MORE DETAILS 119 Figure 6.3 MLSD tr
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THE MATH 121 legs of the journey is
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THE MATH 123 Figure 6.8 MLSD trelli
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THE MATH 125 We would then identify
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THE MATH 127 Expanding the square,
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THE MATH 129 Consider the matched f
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THE MATH 131 6.3.5.1 M-algorithm Wi
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THE MATH 133 results, DFE and MLSD
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THE MATH 135 IQ" 1 oc LU CD 10 2 10
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THE MATH 137 sometimes inaccurate w
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MORE MATH 139 POWER CONTROL effecti
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MORE MATH 141 15 POWER CONTROL 10
Page 165 and 166: MORE MATH 143 6.4.3 More approximat
Page 167 and 168: THE LITERATURE 145 EDGE is an evolu
Page 169 and 170: PROBLEMS 147 the channel to minimum
Page 171: PROBLEMS 149 c) Suppose we know «o
Page 174 and 175: 152 ADVANCED TOPICS detecting the w
Page 176 and 177: 154 ADVANCED TOPICS Table 7.2 Examp
Page 178 and 179: 156 ADVANCED TOPICS Let's look at t
Page 180 and 181: 158 ADVANCED TOPICS Thus, for MAPSD
Page 182 and 183: 160 ADVANCED TOPICS Table 7.6 Examp
Page 184 and 185: 162 ADVANCED TOPICS If we assume no
Page 186 and 187: 164 ADVANCED TOPICS Now we can focu
Page 188 and 189: 166 ADVANCED TOPICS Notice we used
Page 190 and 191: 168 ADVANCED TOPICS to achieve spat
Page 192 and 193: 170 ADVANCED TOPICS c) What are the
Page 195 and 196: CHAPTER 8 PRACTICAL CONSIDERATIONS
Page 197 and 198: MORE DETAILS 175 8.2 MORE DETAILS I
Page 199 and 200: MORE DETAILS 177 One extreme is to
Page 201 and 202: THE MATH 179 8.3.1 Time-invariant c
Page 203 and 204: THE MATH 181 With recursive channel
Page 205 and 206: MORE PRACTICAL ASPECTS 183 timing).
Page 207 and 208: THE LITERATURE 185 8.6 THE LITERATU
Page 209 and 210: PROBLEMS 187 a) Draw the new receiv
Page 211 and 212: APPENDIX A SIMULATION NOTES Perform
Page 213 and 214: FADING CHANNELS 191 where JA = A 2
Page 215: APPENDIX B NOTATION Channel Equaliz
Page 220 and 221: 198 REFERENCES [Ari98] [Ari99] [Ari
Page 222 and 223: 200 REFERENCES [Bra91] W. R. Braun
Page 224 and 225: 202 REFERENCES [Div98] [Dou95] [Due
Page 226 and 227: 204 REFERENCES [Gon68] R. A. Gonsal
Page 228 and 229: 206 REFERENCES [Kaa94] [Kai60] V.-P
Page 230 and 231: 208 REFERENCES [ManOl] [Mar73] [Mar
Page 232 and 233: 210 REFERENCES [Pic95] [P0088] [Pri
Page 234 and 235: 212 REFERENCES [Sto93] [Sto96] [Sui
Page 236 and 237: 214 REFERENCES [Wan06a] T. Wang, J.
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