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112 MMSE AND ML DECISION FEEDBACK EQUALIZATION solved iteratively using Gauss/Seidel (SIC) [Jam96, Eld98] or Gauss/Jordan (PIC) [Eld98]. Forms of multistage PIC have been developed for TDM systems [ChaOl]. SIC can be combined with LE for suppressing other signals [Koh90, Yoo93]. Block DFE for CDMA can be found in [Kle93, Jun95b, Kle96]. In CDMA, code averaging in designing a time-invariant FF can be found in [Cho04]. Use of a periodically time-varying FF based on code averaging can be found in [BotlOa]. Group DFE has been examined primarily for CDMA systems [Var95, FaiOO]. Code averaging can be used to simplify group detection for CDM DFE [BotlOa]. When there are multiple receive antennas, signals can be grouped based on their spatial isolation [Pel07]. PROBLEMS The idea 5.1 Consider the Alice and Bob example. Suppose instead that r\ = —1 and r 2 — 4. Assume so = +1. a) What is the value of z\ and è\ with MMSE DFE? 5.2 Consider the Alice and Bob example, MMSE DFE, and the case when SQ is the incorrect value (—1). a) What is the resulting decision variable for si (21)? b) What is the resulting decision variable for s 2 (z 2 )? 5.3 Consider an example similar to Alice and Bob, in which r m = s m + 0.5s m _i. When detecting si using z\ — w\r\ + tt> 2 r 2 , what is the MSE as a function of wi and u> 2 ? More details 5.4 Consider the MIMO scenario in which c — 10, d = 7, e = 9, and / — 6. a) What are the MMSE weights for detecting s\l b) What is the output SINR for sj? c) What is X2 in terms of r\ and r 2 ? 5.5 Consider the general dispersive scenario with σ 2 = 10. a) With c = I, d = 0.2, use the MMSE DFE expressions in the text to determine the two forward weights and output S/(I + N). b) With c = 0.2, d = 1, use the MMSE DFE expressions in the text to determine the two forward weights and output S/(I + N). c) With c = 0.2, d = 1, what would the output S/(I + N) be if we ran an MMSE DFE backwards in time? 5.6 For the general dispersive scenario, determine the SINR when a decision error is made in MMSE DFE. 5.7 Consider the general MIMO case and (5.28).
PROBLEMS 113 a) Determine the model equations for y3 and 2/4. b) Determine expressions for the MMSE weights w^ and »4. The math 5.8 Derive the FF weight expression for ML DFE. 5.9 Derive the expression for output SINR for MMSE DFE, assuming perfect decisions. 5.10 For the general dispersive scenario (r m = cs m + ds m -\ + n m ), determine the input SNR such that MF and MMSE DFE have the same performance (same output SINR), a) assuming the MMSE DFE makes no decision errors. b) assuming the MMSE DFE makes a decision error half of the time, at random.
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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
Page 83 and 84: MORE DETAILS 61 where «i = m - (d/
Page 85 and 86: MORE MATH 63 Because there is no IS
Page 87 and 88: MORE MATH 65 In the later chapter o
Page 89 and 90: PROBLEMS 67 b) What is the detected
Page 91 and 92: CHAPTER 4 LINEAR EQUALIZATION With
Page 93 and 94: THE IDEA 71 estimate of symbol s 2
Page 95 and 96: THE IDEA 73 Notice that £2 (MSE) d
Page 97 and 98: MORE DETAILS 75 The first term is t
Page 99 and 100: MORE DETAILS 77 To obtain the unity
Page 101 and 102: THE MATH 79 and SINR becomes w T h
Page 103 and 104: 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 and 156: THE MATH 133 results, DFE and MLSD
Page 157 and 158: THE MATH 135 IQ" 1 oc LU CD 10 2 10
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
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162 ADVANCED TOPICS If we assume no
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164 ADVANCED TOPICS Now we can focu
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166 ADVANCED TOPICS Notice we used
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168 ADVANCED TOPICS to achieve spat
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170 ADVANCED TOPICS c) What are the
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CHAPTER 8 PRACTICAL CONSIDERATIONS
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MORE DETAILS 175 8.2 MORE DETAILS I
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MORE DETAILS 177 One extreme is to
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THE MATH 179 8.3.1 Time-invariant c
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THE MATH 181 With recursive channel
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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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