Modern Quadrature Amplitude Modulation
Principles and Applications for Fixed and Wireless Channels

W.T. Webb, L.Hanzo

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Contents

PART I: Background to QAM

1      Introduction and Background 1
1.1      Modulation methods 2
1.2      History of QAM 6
1.2.1      Determining the optimum constellation 6
1.2.1.1      Coherent and non-coherent reception 7
1.2.1.2      Clock recovery 8
1.2.1.3      The Type I, II and III constellations 9
1.2.2      Satellite links 13
1.2.2.1      Odd-bit constellations 14
1.2.3      QAM modem implementation 14
1.2.3.1      Non-linear amplification 16
1.2.3.2      Frequency selective fading and channel equalisers 17
1.2.3.3      Filtering 17
1.2.4      Advanced prototypes 18
1.2.5      QAM for mobile radio 19
1.3      Summary 23
1.4      Outline of Topics 23
2      Communications Channels 34
2.1      Fixed Communication Channels 34
2.1.1      Introduction 34
2.1.2      Fixed Channel Types 35
2.1.3      Characterisation of Noise 36
2.2      Telephone Channels 40
2.3      Mobile Radio Channels 42
2.3.1      Introduction 42
2.3.2      Equivalent Baseband and Passband Systems 44
2.3.3      Gaussian Mobile Radio Channel 51
2.3.4      Narrow-band fading Channels 52
2.3.4.1      Propagation Pathloss Law 54
2.3.4.2      Slow Fading Statistics 57
2.3.4.3      Fast Fading Statistics 58
2.3.4.4      Doppler Spectrum 64
2.3.4.5      Simulation of Narrowband Channels 66
2.3.4.5.1      Frequency-domain fading simulation 67
2.3.4.5.2      Time-domain fading simulation 68
2.3.4.5.3      Füller Algorithm of AWGN generation 68
2.3.5      Wideband Channels 69
2.3.5.1      Modelling of Wideband Channels 69
2.4      Mobile Satellite Propagation 73
2.4.1      Fixed-link satellite channels 73
2.4.2      Satellite-to-mobile channels 75
2.5      Summary 76
3      Introduction to modems 80
3.1      Analogue to digital conversion 82
3.2      Mapping 83
3.3      Filtering 85
3.4      Modulation and demodulation 89
3.5      Data recovery 91
3.6      Summary 92

PART II: QAM for Gaussian Channels

4      Basic QAM Techniques 94
4.1      Constellations for Gaussian channels 94
4.2      General Pulse-Shaping Techniques 98
4.2.1      Baseband Equivalent System 98
4.2.2      Nyquist Filtering 101
4.2.3      Raised-Cosine Nyquist Filtering 105
4.2.4      The Choice of Roll-off Factor 105
4.2.5      Optimum Transmit and Receive Filtering 107
4.2.6      Characterisation of ISI by Eye-Diagrams 109
4.2.7      Non-Linear Filtering 112
4.3      Methods of Generating QAM 115
4.3.1      Generating Conventional QAM 115
4.3.2      Superposed QAM 116
4.3.3      Offset QAM 117
4.3.4      Non-Linear Amplification 121
4.4      Methods of Detecting QAM Signals 122
4.4.1      Threshold Detection of QAM 122
4.4.2      Matched Filtered Detection 123
4.4.3      Correlation receiver 127
4.5      Linearisation of Power Amplifiers 128
4.5.1      The Linearisation Problem 128
4.5.2      Linearisation by Predistortion 129
4.5.2.1      The Predistortion Concept 129
4.5.2.2      Predistorter Description 130
4.5.2.3      Predistorter Coefficient Adjustment 135
4.5.2.4      Predistorter Performance 136
4.5.3      Postdistortion of NLA-QAM 139
4.5.3.1      The Postdistortion Concept 139
4.5.3.2      Postdistorter Description 142
4.5.3.3      Postdistorter Coefficient Adaptation 145
4.5.3.4      Postdistorter Performance 145
4.6      Non-differential coding for square QAM 146
4.7      Differential coding for square QAM 147
4.8      Summary 152
5      Square QAM 156
5.1      Decision Theory 156
5.2      QAM modulation and transmission 159
5.3      16-QAM Demodulation in AWGN 160
5.4      64-QAM Demodulation in AWGN 161
5.5      Summary 167
6      Clock and Carrier Recovery 170
6.1      Introduction 170
6.2      Clock Recovery 171
6.2.1      Times-two clock recovery 171
6.2.2      Early-late clock recovery 172
6.2.3      Zero crossing clock recovery 173
6.2.4      Synchroniser 175
6.3      Carrier Recovery 175
6.3.1      Times-n carrier recovery 179
6.3.2      Decision directed carrier recovery 182
6.3.2.1      Frequency and phase detection systems 185
6.4      Summary 192
7      Basic Equaliser Techniques 197
7.1      Introduction 197
7.2      Linear Equalisers 199
7.2.1      Zero-Forcing Equalisers 199
7.2.2      Least Mean-Squared Equalisers 204
7.2.3      Decision-Directed Adaptive Equalisers 208
7.3      Decision Feedback Equalisers 211
7.4      Fast Converging Equalisers 214
7.4.1      Least Squares Method 214
7.4.2      Recursive Least Squares Method 218
7.4.2.1      Cost-Function Weighting 218
7.4.2.2      Recursive Correlation Update 219
7.4.2.3      The Ricatti Equation of RLS Estimation 220
7.4.2.4      Recursive Equaliser Coefficient Update 221
7.5      Adaptive Equalisers for QAM 224
7.6      Viterbi Equalisers 227
7.6.1      Partial Response Modulation 227
7.6.2      Viterbi Equalisation 229
7.7      Summary 233
8      Trellis Coded Modulation 236
8.1      Introduction 236
8.2      TCM Fundamentals 238
8.3      8-PSK TCM 240
8.4      16-QAM TCM 247
8.5      TCM Under Phase Rotation 253
8.6      Summary 253
9      QAM Modems 257
9.1      Introduction 257
9.2      Transmission Bitrate Limits 259
9.3      V.29 Modem 260
9.3.1      Signal Constellation 261
9.3.2      Training Signals 263
9.3.3      Scrambling and Descrambling 266
9.3.4      Channel Equalisation and Synchronisation 268
9.4      V.32 Modem 268
9.4.1      General Features 268
9.4.2      Signal Constellation and Bit Mapping 269
9.4.2.1      Non-Redundant 16-QAM 269
9.4.2.2      Trellis-Coded 32-QAM 270
9.4.3      Scrambler and Descrambler 273
9.5      V.33 Modem 274
9.5.1      General Features 274
9.5.2      Signal Constellations and Bit Mapping 275
9.5.3      Synchronising Signals 277
9.6      Summary 278

PART III: QAM for Mobile Radio

10      Square QAM for fading channels 280
10.1      16-QAM Performance 280
10.2      64-QAM Performance 288
10.3      Reference Assisted Coherent QAM 292
10.3.1      Transparent Tone In
10.3.1.1      Introduction 293
10.3.1.2      Principles of TTIB 294
10.3.1.3      TTIB Subcarrier Recovery 297
10.3.1.4      TTIB Schemes Using Quadrature Mirror Filters 300
10.3.1.5      Residual Frequency
10.3.1.6      TTIB System
10.3.2      Pilot Symbol Assisted
10.3.2.1      Introduction 309
10.3.2.2      PSAM System Description 310
10.3.2.3      Channel Gain Estimation 313
10.3.2.4      PSAM Parameters 315
10.3.2.5      PSAM Performance 316
10.4      Summary 318
11      Star QAM 324
11.1      Introduction 324
11.2      Star QAM Transmissions 325
11.2.1      Differential coding 325
11.2.2      Differential decoding 326
11.2.3      Effect of oversampling 327
11.2.4      Star 16-QAM Performance 329
11.3      Trellis coded modulation for QAM 331
11.4      Block Coding 333
11.5      64-level TCM 335
11.6      Bandwidth efficient coding results 338
11.7      Overall coding strategy 339
11.7.1      Square 16-QAM/PSAM/TCM Scheme 340
11.8      Distorted Constellation Star QAM 342
11.8.1      Introduction 342
11.8.2      Distortion of the Star 343
11.8.2.1      Amplitude Distortion 343
11.8.2.2      Phase Variations 345
11.9      Practical Considerations 348
11.9.1      Introduction 348
11.9.2      Hardware imperfections 349
11.9.2.1      Quantisation Levels 349
11.9.2.2      I-Q Crosstalk 352
11.9.2.3      Oversampling Ratio 353
11.9.2.4      AM-AM and AM-PM distortion 354
11.10      Summary 357
12      Timing Recovery for Mobile Radio 362
12.1      Introduction 362
12.2      Times-two clock recovery for QAM 362
12.3      Early-Late Clock Recovery 363
12.4      Modified Early-Late Clock Recovery 367
12.5      Clock Recovery in the Presence of ISI 370
12.5.1      Wideband Channel Models 370
12.5.2      Clock Recovery in Two-Path Channels 372
12.5.2.1      Case of $\tau \not =nT$ 372
12.5.2.2      Case of $\tau =nT$ 373
12.5.3      Clock Recovery Performance in Smeared ISI 375
12.6      Implementation Details 376
12.7      Carrier recovery 377
12.8      Summary 382
13      Variable Rate QAM 384
13.1      Introduction 384
13.2      Variable QAM Constellations 387
13.3      The RSSI Switching System 388
13.3.1      Results 393
13.4      The Error Detector Switching System 394
13.4.1      Results 396
13.5      Co-Channel Interference 399
13.6      Application to a DECT-Type System 402
13.7      Summary 404
14      Wideband QAM Transmissions 407
14.1      Introduction 407
14.2      The RAKE Combiner 408
14.3      The Proposed Equaliser 411
14.3.1      Linear Equaliser 411
14.3.2      Iterative Equaliser System 412
14.3.2.1      The One Symbol Window Equaliser 413
14.3.2.2      The Limited Correction DFE 417
14.3.3      Use of Error Correction Coding 418
14.4      Diversity in the wideband system 422
14.5      Summary 424

PART IV: Advanced QAM Techniques

15      Orthogonal Multiplex Systems 428
15.1      Introduction 428
15.2      Principles of QAM-FDM 432
15.3      Modulation by DFT 434
15.4      Transmission via Bandlimited Channels 440
15.5      Generalised Nyquist Criterion 443
15.6      OMPX Modem Implementations 449
15.7      Reducing MDI by Block Extension 453
15.8      Reducing MDI by Compensation 454
15.8.1      Transient System Analysis 454
15.8.2      Recursive MDI Compensation 457
15.9      Adaptive Channel Equalisation 459
15.10      Wide-Sense Orthogonality 461
15.11      OMPX Bandwidth Efficiency 466
15.12      Performance of an OMPX Scheme 467
15.13      Summary 470
16      Quadrature-Quadrature AM 476
16.1      Introduction 476
16.2      Q$^2$PSK 477
16.3      Q$^2$AM 482
16.3.1      Square 16-QAM 482
16.3.2      Star 16-QAM 484
16.4      Spectral efficiency 486
16.5      Bandlimiting 16-Q$^2$AM 487
16.6      Results 488
16.7      Summary 492
17      Spectral Efficiency of QAM 496
17.1      Introduction 496
17.2      Efficiency in Large Cells 499
17.3      Spectrum Efficiency in Microcells 503
17.3.1      Microcellular Clusters 504
17.3.2      System Design for Microcells 506
17.3.3      Microcellular Radio Capacity 507
17.3.4      Modulation Schemes for Microcells 507
17.4      Summary 509
18      QAM Speech Systems 512
18.1      Introduction 512
18.2      Modem Schemes 513
18.2.1      GMSK Modulation 513
18.2.2      PI/4--DQPSK Modulation 515
18.3      Speech Codecs 516
18.3.1      Adaptive Differential Pulse Code Modulation 516
18.3.2      Analysis-by-synthesis speech coding 518
18.3.2.1      The RPE-LTP Speech Encoder 518
18.3.2.2      The RPE-LTP Speech Decoder 522
18.4      Speech Quality Measures 525
18.5      Discontinuous Transmission 527
18.6      Channel Coding and Bit-mapping 527
18.7      Speech Transmission Systems 530
18.8      Packet Reservation Multiple Access 533
18.8.1      PRMA performance 536
18.9      Summary 538
19      Glossary 543
20      Index 549