Filter Bank Transceivers for OFDM and DMT Systems

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1 Introduction......Page 15
Outline......Page 20
1.1 Notations......Page 21
2.1 Discrete-time channel models......Page 23
2.2 Equalization......Page 30
2.3 Digital modulation......Page 31
2.3.1 Pulse amplitude modulation (PAM)......Page 32
2.3.2 Quadrature amplitude modulation (QAM)......Page 36
2.4 Parallel subchannels......Page 42
2.6 Problems......Page 45
3 FIR equalizers......Page 47
3.1 Zero-forcing equalizers......Page 48
3.2 Orthogonality principle and linear estimation......Page 53
3.2.1 Biased and unbiased linear estimates......Page 55
3.2.2 Estimation of multiple random variables......Page 58
3.3.1 FIR channels......Page 59
Matrix formulation......Page 60
Zero-mean iid inputs......Page 61
3.3.2 MIMO frequency-nonselective channels......Page 62
Zero-mean iid inputs......Page 63
3.3.3 Examples......Page 64
3.4 Symbol detection for MMSE receivers......Page 70
3.5 Channel-shortening equalizers......Page 73
3.7 Problems......Page 79
4.1 Multirate building blocks......Page 85
4.1.1 Transform domain formulas......Page 87
4.1.2 Multirate identities......Page 89
4.1.3 Blocking and unblocking......Page 90
4.2 Decimation filters......Page 93
4.3 Interpolation filters......Page 94
4.3.2 The Nyquist(M) property......Page 96
4.4 Polyphase decomposition......Page 98
4.4.1 Decimation and interpolation filters......Page 101
4.4.2 Synthesis filter banks......Page 103
4.4.3 Analysis filter banks......Page 104
4.6 Problems......Page 105
5.1 Filter bank transceivers......Page 109
5.1.2 Redundancy in filter bank transceivers......Page 111
5.1.3 Types of distortion in transceivers......Page 114
5.2.1 ISI-free filter bank transceivers......Page 115
5.2.2 Polyphase approach......Page 117
5.2.3 Channel-independent ISI-free filter bank transceivers......Page 119
5.3.1 Pseudocirculants and blocked versions of scalar systems......Page 120
5.3.2 Circulants and circular convolutions......Page 122
5.4 Redundancy for IBI elimination......Page 125
Matrix formulation of the zero-padded systems......Page 126
5.4.2 Cyclic-prefixed systems......Page 129
Matrix formulation of the cyclic-prefixed systems......Page 131
5.4.3 Summary and comparison......Page 133
5.4.4 IBI-free systems with reduced redundancy......Page 135
5.5 Fractionally spaced equalizer systems......Page 136
5.5.1 Zero-forcing FSE systems......Page 138
5.5.2 Polyphase approach......Page 139
5.7 Problems......Page 143
6 DFT-based transceivers......Page 149
6.1 OFDM systems......Page 150
6.1.1 Noise analysis......Page 154
6.1.2 Bit error rate......Page 156
6.2.1 Zero-forcing receivers......Page 161
6.2.2 The MMSE receiver......Page 164
Remarks......Page 165
6.3 Single-carrier systems with cyclic prefix (SC-CP)......Page 166
6.3.1 Noise analysis: zero-forcing case......Page 169
6.3.2 The MMSE receiver......Page 170
6.3.3 Error analysis: MMSE case......Page 171
6.4 Single-carrier system with zero-padding (SC-ZP)......Page 174
6.5 Filter bank representation of OFDM systems......Page 177
6.5.1 Transmitted power spectrum......Page 180
6.6 DMT systems......Page 182
Remarks......Page 185
6.7.1 Pilot symbol aided modulation......Page 192
6.7.2 Synchronization of carrier frequency......Page 193
6.8 A historical note and further reading......Page 194
6.9 Problems......Page 195
7 Precoded OFDM systems......Page 207
7.1 Zero-forcing precoded OFDM systems......Page 208
Noise analysis......Page 209
7.2 Optimal precoders for QPSK modulation......Page 212
Error-equalizing precoders......Page 215
7.3 Optimal precoders: other modulations......Page 216
7.4 MMSE precoded OFDM systems......Page 217
7.4.1 MMSE receivers......Page 218
7.4.2 Optimal precoders for QPSK modulation......Page 221
7.4.3 Other modulation schemes......Page 223
7.5 Simulation examples......Page 225
7.6 Further reading......Page 233
7.7 Problems......Page 234
8.1 Zero-forcing block transceivers......Page 237
8.1.1 Zero-forcing ZP systems......Page 239
8.1.2 Zero-forcing ZJ systems......Page 240
8.2 Problem formulation......Page 242
8.3 Optimal bit allocation......Page 243
8.4.1 Optimal Gzp......Page 254
8.4.2 Optimal Azp......Page 255
8.4.3 Summary and discussions......Page 257
8.5.1 Optimal Szj......Page 261
8.5.3 Summary and discussions......Page 263
8.6 Further reading......Page 267
8.7 Problems......Page 268
9 DMT systems with improved frequency characteristics......Page 273
9.1 Sidelobes matter!......Page 274
9.2 Overall transfer matrix......Page 277
9.3 Transmitters with subfilters......Page 279
9.3.2 DFT bank implementation......Page 280
9.4 Design of transmit subfilters......Page 286
9.5 Receivers with subfilters......Page 290
9.5.2 DFT bank implementation......Page 291
9.6 Design of receiver subfilters......Page 294
9.8 Further reading......Page 299
9.9 Problems......Page 300
10 Minimum redundancy FIR transceivers......Page 305
10.1 Polyphase representation......Page 306
10.2 Properties of pseudocirculants......Page 307
10.2.1 Smith form decomposition......Page 308
10.2.2 DFT decomposition......Page 309
10.2.3 Properties derived from the two decompositions......Page 310
10.2.4 Congruous zeros......Page 311
10.3.2 IIR minimal transceivers......Page 315
10.4 Minimum redundancy......Page 317
10.5 Smith form of FIR pseudocirculants......Page 322
10.6 Proof of Theorem 10.2......Page 325
10.6.1 Identical Smith forms......Page 326
10.6.3 An example of deriving the Smith form of Sigma(z)......Page 327
10.6.4 Smith form of Sigma(z)......Page 330
10.8 Problems......Page 333
Matrix inversion lemma......Page 337
Fischer inequality......Page 338
Convex and concave functions......Page 339
B.1 Random variables......Page 341
Wide sense stationary processes......Page 343
Cyclo wide sense stationary processes......Page 345
Passage through LTI systems......Page 346
Passage through multirate blocks......Page 347
Blocking......Page 348
Unblocking......Page 349
B.4 Continuous-time random processes......Page 350
Passage through C/D and D/C converters......Page 351
References......Page 355
Index......Page 369