Digital Communications 2 – Digital Modulations

Preface xi
<p>List of Acronyms xiii</p>
<p>Notations. xvii</p>
<p>Introduction xix</p>
<p>Chapter 1. Background 1</p>
<p>1.1. Introduction 1</p>
<p>1.2. Common operations and functions 1</p>
<p>1.2.1. Convolution 1</p>
<p>1.2.2. Scalar product 2</p>
<p>1.2.3. Dirac function, Dirac impulse and Kronecker s symbol 2</p>
<p>1.2.4. Step function 3</p>
<p>1.2.5. Rectangular function 3</p>
<p>1.3. Common transforms 3</p>
<p>1.3.1. Fourier transform 3</p>
<p>1.3.2. The z transform 6</p>
<p>1.4. Probability background 6</p>
<p>1.4.1. Discrete random variables 7</p>
<p>1.4.2. Continuous random variables 9</p>
<p>1.4.3. Jensen s inequality 9</p>
<p>1.4.4. Random signals 10</p>
<p>1.5. Background on digital signal processing 13</p>
<p>1.5.1. Sampling 13</p>
<p>1.5.2. Discrete, linear and time–invariant systems 14</p>
<p>1.5.3. Finite impulse response filters 17</p>
<p>1.5.4. Infinite impulse response filters 17</p>
<p>Chapter 2. Baseband Transmissions 19</p>
<p>2.1. Introduction 19</p>
<p>2.2. Line codes 20</p>
<p>2.2.1. Non–return to zero (NRZ) code 20</p>
<p>2.2.2. Unipolar return–to–zero (RZ) code 23</p>
<p>2.2.3. Bipolar return–to–zero (RZ) code 25</p>
<p>2.2.4. Manchester code 25</p>
<p>2.2.5. Alternate mark inversion code 26</p>
<p>2.2.6. Miller code 28</p>
<p>2.2.7. Non–return to zero inverted (NRZI) 31</p>
<p>2.2.8. Multi level transmit 3 (MLT–3) code 32</p>
<p>2.2.9. RLL(d,k) codes 33</p>
<p>2.2.10. M–ary NRZ code 35</p>
<p>2.3. Additive white Gaussian noise channel 36</p>
<p>2.4. Optimum reception on the additive white Gaussian noise channel 38</p>
<p>2.4.1. Introduction 38</p>
<p>2.4.2. Modulator s block diagram 39</p>
<p>2.4.3. Optimum receiver for the additive white Gaussian noise channel 44</p>
<p>2.4.4. Evaluation of the bit error rate for the binary NRZ signal on the additive white Gaussian noise channel 52</p>
<p>2.5. Nyquist criterion 60</p>
<p>2.5.1. Introduction 60</p>
<p>2.5.2. Transmission channel 61</p>
<p>2.5.3. Eye diagram 62</p>
<p>2.5.4. Nyquist criterion 63</p>
<p>2.5.5. Transmit and receive filters with matched filter 66</p>
<p>2.6. Conclusion 68</p>
<p>2.7. Exercises 69</p>
<p>2.7.1. Exercise 1: power spectrum density of several line codes 69</p>
<p>2.7.2. Exercise 2: Manchester code 70</p>
<p>2.7.3. Exercise 3: study of a magnetic recording system 70</p>
<p>2.7.4. Exercise 4: line code and erasure 72</p>
<p>2.7.5. Exercise 5: 4 levels NRZ modulation 73</p>
<p>2.7.6. Exercise 6: Gaussian transmit filter 74</p>
<p>2.7.7. Exercise 7: Nyquist criterion 75</p>
<p>2.7.8. Exercise 8: raised cosine filter 76</p>
<p>Chapter 3. Digital Modulations on Sine Waveforms 77</p>
<p>3.1. Introduction 77</p>
<p>3.2. Passband transmission and equivalent baseband chain 78</p>
<p>3.2.1. Narrowband signal 78</p>
<p>3.2.2. Filtering of a narrowband signal in a passband channel 82</p>
<p>3.2.3. Complex order of a second–order stationary random process 84</p>
<p>3.2.4. Synchronous detection 90</p>
<p>3.3. Linear digital modulations on sine waveforms 92</p>
<p>3.3.1. Main characteristics of linear digital modulations 92</p>
<p>3.3.2. Parameters of an M–symbols modulation 96</p>
<p>3.3.3. Amplitude shift keying 98</p>
<p>3.3.4. Phase shift keying 106</p>
<p>3.3.5. Quadrature amplitude modulations 113</p>
<p>3.3.6. Link between Eb N0 and signal–to–noise ratio depending on the power values 119</p>
<p>3.3.7. Power spectrum density of regular modulations 120</p>
<p>3.3.8. Conclusion 121</p>
<p>3.4. Frequency shift keying 122</p>
<p>3.4.1. Definitions 122</p>
<p>3.4.2. Discontinuous–phase FSK 124</p>
<p>3.4.3. Continuous–phase FSK 126</p>
<p>3.4.4. Demodulation 126</p>
<p>3.4.5. GMSK modulation 130</p>
<p>3.4.6. Performances 132</p>
<p>3.5. Conclusion 135</p>
<p>3.6. Exercises 135</p>
<p>3.6.1. Exercise 1: constellations of 8–QAM 135</p>
<p>3.6.2. Exercise 2: irregular ASK modulation 136</p>
<p>3.6.3. Exercise 3: comparison of two PSK 137</p>
<p>3.6.4. Exercise 4: comparison of QAM and PSK modulations 137</p>
<p>3.6.5. Exercise 5: comparison of 8–PSK and 8–QAM modulations 138</p>
<p>3.6.6. Exercise 6: comparison of 2–FSK and 2–ASK modulations 139</p>
<p>3.6.7. Exercise 7: comparison of 16–QAM and 16–FSK 140</p>
<p>Chapter 4. Synchronization and Equalization 141</p>
<p>4.1. Introduction 141</p>
<p>4.2. Synchronization 142</p>
<p>4.2.1. Frequency shift correction 144</p>
<p>4.2.2. Time synchronization 150</p>
<p>4.2.3. Channel estimate with training sequence 153</p>
<p>4.2.4. Cramer Rao s bound 154</p>
<p>4.3. Equalization 157</p>
<p>4.3.1. Channel generating distortions 158</p>
<p>4.3.2. Discrete representation of a channel with inter–symbol interference and preprocessing 159</p>
<p>4.3.3. Linear equalization 162</p>
<p>4.3.4. Decision–feedback equalization 177</p>
<p>4.3.5. Maximum likelihood sequence estimator 180</p>
<p>4.4. Conclusion 186</p>
<p>4.5. Exercises 187</p>
<p>4.5.1. Exercise 1: estimation of a constant signal from noisy observations 187</p>
<p>4.5.2. Exercise 2: frequency shift correction 188</p>
<p>4.5.3. Exercise 3: zero–forcing equalization 188</p>
<p>4.5.4. Exercise 4: MMSE equalization 189</p>
<p>4.5.5. Exercise 5: MMSE–DFE equalization 190</p>
<p>4.5.6. Exercise 6: MLSE equalization with one shift register 190</p>
<p>4.5.7. Exercise 7: MLSE equalization with two shift registers 190</p>
<p>Chapter 5. Multi–carrier Modulations 193</p>
<p>5.1. Introduction 193</p>
<p>5.2. General principles of multi–carrier modulation 196</p>
<p>5.2.1. Parallel transmission on subcarriers 196</p>
<p>5.2.2. Non–overlapping multi–carrier modulations: FMT 197</p>
<p>5.2.3. Overlapping multi–carrier modulations 198</p>
<p>5.2.4. Chapter s structure 199</p>
<p>5.3. OFDM 199</p>
<p>5.3.1. Transmission and reception in OFDM 201</p>
<p>5.3.2. Cyclic prefix principle 202</p>
<p>5.3.3. Optimum power allocation in OFDM 209</p>
<p>5.3.4. PAPR 215</p>
<p>5.3.5. Sensitivity to asynchronicity 218</p>
<p>5.3.6. OFDM synchronization techniques 219</p>
<p>5.4. FBMC/OQAM 225</p>
<p>5.4.1. Principles of continuous–time FBMC/OQAM 225</p>
<p>5.4.2. Discrete–time notations for FBMC/OQAM 231</p>
<p>5.4.3. Prototype filter 233</p>
<p>5.5. Conclusion 236</p>
<p>5.6. Exercises 236</p>
<p>5.6.1. Exercise 1 236</p>
<p>5.6.2. Exercise 2 237</p>
<p>Chapter 6. Coded Modulations 239</p>
<p>6.1. Lattices 240</p>
<p>6.1.1. Definitions 240</p>
<p>6.1.2. Group properties of a lattice 245</p>
<p>6.1.3. Lattice classification 248</p>
<p>6.1.4. Lattice performances on the additive white Gaussian noise channel 251</p>
<p>6.2. Block–coded modulations 255</p>
<p>6.2.1. Main algebraic constructions of lattices 256</p>
<p>6.2.2. Construction of block–coded modulations 259</p>
<p>6.3. Trellis–coded modulations 270</p>
<p>6.3.1. Construction of trellis–coded modulations 271</p>
<p>6.3.2. Decoding of trellis–coded modulations 275</p>
<p>6.4. Conclusion 276</p>
<p>Appendices 277</p>
<p>Appendix A 279</p>
<p>Appendix B 285</p>
<p>Bibliography 291</p>
<p>Index 297</p>
<p>Summary of Volume 1 299</p>