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134 MAXIMUM LIKELIHOOD SEQUENCE DETECTION 16-QAM 0 5 10 15 20 Eb/NO (dB) Figure 6.12 BER vs. E b /N 0 for 1G-QAM, root-raised-eosine pulso shaping (0.22 rolloff), static, two-tap. symbol-spaced channel, with relative path strengths 0 and —1 dB, and path angles 0 and !)() degrees, single feedback tap. determined by summing the squares of the path coefficients. While the gain is 1.0 on average, it will take on random values. For each value, the channel gain is used to scale the Eb/N» prior to evaluating the analytical expression. As the analytical expression assumes no ISI, this gives the matched filter bound. Each fading realization gives a different error rate. These error rates can then be averaged in the simulator to determine an average error rate. Another way that matched filter bound results were generated was by performing perfect ISI subtraction prior to matched filtering (results labeled MFB). Results for the TwoTSfade channel are given in Fig. 6.13. Note that the z-axis is labeled average Eb/NO to emphasize that it is averaged over the fading. Compared to the TwoTS results, the performance is worse for all receivers. While the fading sometimes gives a higher SINR and sometimes a lower SINR, it is the lower SINR error rates that dominate performance. Compared to the static results, the gains of DFE over LE are smaller. This is because performance is dominated by the cases when both paths fade, so that the instantaneous SNR is lower and the performance differences between the two approaches are less. Also notice that MF has a lower floor with fading. With a fading channel, there are two reasons why certain fading realizations give larger BER. One reason is that there is significant ISI (the two paths have similar strengths). The other reason is that the total signal power is low (both paths fade down at the same time). One way to isolate these two effects is to consider a system with power control.
THE MATH 135 IQ" 1 oc LU CD 10 2 10" 3 -2 O 2 4 6 8 10 12 14 avg Eb/NO (dB) Figure 6.13 BER vs. E b /N 0 for QPSK, root-raised-eosine pulse shaping (0.22 rolloff), fading, two-tap, symbol-spaced channel, with relative path strengths 0 and —1 dB. Power control is sometimes used to mitigate variation due to fading. Here we will focus on signal power variation and the technique of target-C power control. When the signal fades down in power, the receiver tells the transmitter to use more power. The transmitter ensures that the signal power (summed over all signal paths) is kept constant at the receiver. Such a form of power control makes sense, for example, for a CDMA uplink, in which users share how much power they are allowed to create at the intended receiver. Here we assume an ideal form, which is simulated by normalizing the fading coefficients of each fading realization so that their powers instantaneously sum to one. Note that we have ignored the fact that the transmitter has a maximum transmit power, so that it may not always be able to maintain a certain power at the receiver. Results for the TwoTSfade channel with power control are given in Fig. 6.14. Compared to the results without power control, overall performance is better, as the signal power is not allowed to vary either up or down due to fading. However, performance is more improved for LE and DFE than for MF. This is because with power control, performance is ISI limited at high SNR, and LE and DFE mitigate the effects of ISI. Thus, with power control, the gains of equalization are larger. So far we have examined bit error rate, averaged over different fading realizations. Is this what we should look at? The answer depends on how the communication system is being used (the application) and how the system is designed. For example, consider speech and the GSM system. Speech is divided into short speech frames, which are encoded with a forward error correction (FEC) code. The system has
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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
Page 105 and 106: THE MATH 83 where *m n = ν ^ ^ ^ '
Page 107 and 108: THE MATH 85 power is much larger th
Page 109 and 110: MORE MATH 87 IQ' 1 OC 111 ω 10 2 1
Page 111 and 112: MORE MATH 89 values of h k m (f) fr
Page 113 and 114: MORE MATH 91 where C(d(),d 0 ) . C(
Page 115 and 116: AN EXAMPLE 93 between z and s. This
Page 117 and 118: PROBLEMS 95 Another aspect of cocha
Page 119: PROBLEMS 97 The math 4.11 Consider
Page 122 and 123: 100 MMSE AND ML DECISION FEEDBACK E
Page 137 and 138: CHAPTER 6 MAXIMUM LIKELIHOOD SEQUEN
Page 139 and 140: MORE DETAILS 117 r 2 Ht, r, fcl + f
Page 141 and 142: MORE DETAILS 119 Figure 6.3 MLSD tr
Page 143 and 144: THE MATH 121 legs of the journey is
Page 145 and 146: THE MATH 123 Figure 6.8 MLSD trelli
Page 147 and 148: THE MATH 125 We would then identify
Page 149 and 150: THE MATH 127 Expanding the square,
Page 151 and 152: THE MATH 129 Consider the matched f
Page 153 and 154: THE MATH 131 6.3.5.1 M-algorithm Wi
Page 155: THE MATH 133 results, DFE and MLSD
Page 159 and 160: THE MATH 137 sometimes inaccurate w
Page 161 and 162: MORE MATH 139 POWER CONTROL effecti
Page 163 and 164: 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).
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THE LITERATURE 185 8.6 THE LITERATU
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PROBLEMS 187 a) Draw the new receiv
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APPENDIX A SIMULATION NOTES Perform
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FADING CHANNELS 191 where JA = A 2
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APPENDIX B NOTATION Channel Equaliz
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NOTATION 195 Variable Meaning p(t)
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198 REFERENCES [Ari98] [Ari99] [Ari
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200 REFERENCES [Bra91] W. R. Braun
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202 REFERENCES [Div98] [Dou95] [Due
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204 REFERENCES [Gon68] R. A. Gonsal
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206 REFERENCES [Kaa94] [Kai60] V.-P
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208 REFERENCES [ManOl] [Mar73] [Mar
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210 REFERENCES [Pic95] [P0088] [Pri
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212 REFERENCES [Sto93] [Sto96] [Sui
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214 REFERENCES [Wan06a] T. Wang, J.
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