mohatta2015.pdf

Recommendations

Info

136 MAXIMUM LIKELIHOOD SEQUENCE DETECTION POWER CONTROL It)" 1 Œ LU ω IQ" 2 10 3 -2 0 2 4 6 8 10 12 14 avg Eb/NO (dB) Figure 6.14 BER vs. E b /N 0 for QPSK. root-raised-cosine pulse .shaping (0.22 rolloff), fading, two-tap, symbol-spaced channel, with relative path strengths 0 and —1 dB, target-C power control. an option of transmitting a speech frame by dividing it up into multiple time slots and sending each slot on a different carrier frequency, which hopefully experiences different fading and interference. The speech frame is recovered by collecting bits from multiple slots and passing them through an FEC decoder. The coding is designed so that the FEC decoder performance depends on the average SINR of the different slots. Thus, speech quality is directly related to average BER, averaged over different fading realizations. However, there are other applications and systems for which average BER isn't the best way to measure performance. For example, consider an indoor, LTE system in which a short packet (1 ms) is sent over a nondispersive channel. Rate adaptation is used, depending on the performance of the receiver. A convenient measure of output performance is the notion of output SINR, (we will define this shortly). So for the example considered, it makes more sense to examine the distribution of output SINR, which is related to the distribution of data rates that can be supported. For example, the median output SINR will determine the median data rate supported. The data rate supported translates into how fast data is transported, which impacts the overall delay experienced by the user (latency). How do we measure the output SINR of an equalizer? One approach is to use analytical expressions that relate performance to the input SNR, the channel coefficients, and the equalization approach. While such analysis is highly useful in gaining insight into the performance of a particular equalization approach, there are some limitations to such analyses. Analysis can be difficult, cumbersome, and
THE MATH 137 sometimes inaccurate when approximations are made. Only in special cases is performance accurately predicted by a relatively simple analysis. An example is linear equalization of CDM signals with large spreading factors, in which SINR expressions are easy to compute, and performance is related directly to SINR because ISI can be accurately modeled as Gaussian, similar to the noise. A second approach is to measure performance at the output of the equalizer and map the result to an effective SINR. Here we will measure symbol error rate. Using the relations in (A.6) and (A.7), we can determine an effective E s /Nn, which we will define as output SINR. In practice, these equations are used to generate a table of SINR and SER values. Interpolation of table values is then used to determine an effective SINR from a measured SER. This second approach also has limitations. One limitation is that enough symbols must be simulated at each fading realization to obtain an accurate estimate of SER. This can be challenging when the instantaneous SINR is high, so that few, if any, symbols are in error. This also gives rise to a granularity issue, as we can only measure error rates of the form 0, 1/N S , 2/N s , etc., where N s is the number of symbols simulated. These limitations can be overcome by ensuring that N s is large so that the range of interesting SINR. values corresponds to many error events (recall the 100 error events rule). Effective SINR. results were obtained for the TwoTSfade channel by generating 1000 symbols (plus edge symbols not counted) for each of 2000 fading realizations. In Fig. 6.15, cumulative distribution functions (CDFs) are provided for various receivers for a 6 dB average received Eb/Na level (9 dB E s /No). Recall that the CDF value (y-axis) is the probability that the effective SINR is less than or equal to a particular SINR value (z-axis). Thus, smaller is better. For the MFB, output SINR was determined via measurement rather than semi-analytically. Observe that equalization provides a rightward shift in the CDF, making smaller SINR values less likely (larger SINR values more likely). As expected, the MMSE DFE provides higher SINR values than the MMSE LE. While difficult to see, the CDFs cross at low SINR, so that the MMSE DFE has more lower SINR values due to error propagation. The MFB acts as a lower bound CDF. Results with power control are given in Fig. 6.16. Relative to the previous results, there is less variation in effective SINR (quicker transition from 0 to 1) as expected. For the MFB, power control ensures that the effective SINR is the same for each fading realization (9 dB). However, because we used measured results, we see a slight variation. Similar to the previous results, the MMSE DFE provides more higher SINR values than MMSE LE. At low SINR, there is no crossover, as power control and the high target value ensure few decision errors. Sometimes certain receivers work well under certain fading conditions, whereas other receivers work well under other conditions. Such behavior can be identified using a scatter plot, plotting the effective SINR of one receiver against the effective SINR of the other receiver. Scatter plots can also be useful in determining behaviors under different fading scenarios. In Fig. 6.17, a scatter plot of MMSE DFE effective SINR vs. MMSE LE effective SINR is given. While the simulation was run for 2000 fading realizations, only the first 1000 realizations are used to generate the scatter plot (making the individual
Page 2 and 3:
Channel Equalization for Wireless C
Page 4 and 5:
To my colleagues at Ericsson
Page 6 and 7:
CONTENTS List of Figures List of Ta
Page 8 and 9:
CONTENTS XI 4.2 4.3 4.4 4.5 4.6 4.1
Page 10 and 11:
CONTENTS XIII 8 Practical Considera
Page 12 and 13:
xvi LIST OF FIGURES 2.2 Matched fil
Page 14 and 15:
XviÜ LIST OF FIGURES 6.18 Scatter
Page 16 and 17:
XX Prologue Alice was nervous. Woul
Page 18 and 19:
XXÜ PREFACE is introduced as neede
Page 20 and 21:
ACRONYMS AC A/D ADC AMLD AMPS ASK A
Page 22 and 23:
ML MLD MLPD MLSD MLSE MRC MSE MSB O
Page 24 and 25:
2 INTRODUCTION Table 1.1 Possible m
Page 26 and 27:
4 INTRODUCTION s o S 1 8 2 S 3 S 0
Page 28 and 29:
6 INTRODUCTION A block diagram of t
Page 30 and 31:
8 INTRODUCTION Figure 1.7 QPSK. tra
Page 32 and 33:
10 INTRODUCTION phases (phase modul
Page 34 and 35:
12 INTRODUCTION rollo« 0.22 0.8 Ί
Page 36 and 37:
14 INTRODUCTION is the "channel" re
Page 38 and 39:
16 INTRODUCTION 1.4 MORE MATH In th
Page 40 and 41:
18 INTRODUCTION For K = 1 (order 0)
Page 42 and 43:
20 INTRODUCTION The K = 4 main bloc
Page 44 and 45:
22 INTRODUCTION A sample of the noi
Page 46 and 47:
24 INTRODUCTION The receiver may ha
Page 48 and 49:
26 INTRODUCTION 1.5.1 Reference sys
Page 50 and 51:
28 INTRODUCTION a) What most likely
Page 53 and 54:
CHAPTER 2 MATCHED FILTERING In this
Page 55 and 56:
MORE DETAILS 33 2.2 MORE DETAILS So
Page 57 and 58:
THE MATH 35 Now compare the output
Page 59 and 60:
THE MATH 37 The correlation in (2.2
Page 61 and 62:
THE MATH 39 correlation function f(
Page 63 and 64:
THE MATH 41 Thus, in the complex pl
Page 65 and 66:
THE MATH 43 to the medium response
Page 67 and 68:
THE MATH 45 We can interpret f(t) a
Page 69 and 70:
MORE MATH 47 10" 1 Odeg 90 deg X 18
Page 71 and 72:
MORE MATH 49 With despread-level Ra
Page 73 and 74:
MORE MATH 51 Figure 2.6 OFDM exampl
Page 75 and 76:
MORE MATH 53 2.4.3 MF in colored no
Page 77 and 78:
PROBLEMS 55 period) is examined in
Page 79 and 80:
CHAPTER 3 ZERO-FORCING DECISION FEE
Page 81 and 82:
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: THE MATH 135 IQ" 1 oc LU CD 10 2 10
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).
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 and 216:
APPENDIX B NOTATION Channel Equaliz
Page 217:
NOTATION 195 Variable Meaning p(t)
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.
show all

mohatta2015.pdf

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?