Table of contents for Antennas and propagation for wireless communication systems / Simon R. Saunders, Alejandro Aragon-Zavala.

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Contents
Preface to the Second Edition xix
Preface to the First Edition
1. Introduction: The Wireless Communication Channel 1
1.1 INTRODUCTION 1
1.2 CONCEPT OF A WIRELESS CHANNEL 2
1.3 THE ELECTROMAGNETIC SPECTRUM 4
1.4 HISTORY 5
1.5 SYSTEM TYPES 7
1.6 AIMS OF CELLULAR SYSTEMS 8
1.7 CELLULAR NETWORKS 9
1.8 THE CELLULAR CONCEPT 9
1.9 TRAFFIC 13
1.10 MULTIPLE ACCESS SCHEMES AND DUPLEXING 17
1.10.1 Frequency Division Multiple Access 17
1.10.2 Time Division Multiple Access 18
1.10.3 Code Division Multiple Access 18
1.11 AVAILABLE DATA RATES 19
1.12 STRUCTURE OF THIS BOOK 20
1.13 CONCLUSION 22
REFERENCES 22
PROBLEMS 23
2. Properties of Electromagnetic Waves 25
2.1 INTRODUCTION 25
2.2 MAXWELL?S EQUATIONS 25
2.3 PLANE WAVE PROPERTIES 26
2.3.1 FIELD RELATIONSHIPS 27
2.3.2 WAVE IMPEDANCE 27
Q1
2.3.3 Poynting Vector 28
2.3.4 Phase Velocity 28
2.3.5 Lossy Media 28
2.4 POLARISATION 32
2.4.1 Polarisation States 32
2.4.2 Mathematical Representation of Polarisation 32
2.4.3 Random Polarisation 33
2.5 CONCLUSION 34
REFERENCES 34
PROBLEMS 34
3. Propagation Mechanisms 37
3.1 INTRODUCTION 37
3.2 REFLECTION, REFRACTION AND TRANSMISSION 37
3.2.1 Lossless Media 37
3.2.2 Lossy Media 41
3.2.3 Typical Reflection and Transmission Coefficients 42
3.3 ROUGH SURFACE SCATTERING 45
3.4 GEOMETRICAL OPTICS 47
3.4.1 Principles 47
3.4.2 Formulation 49
3.5 DIFFRACTION 50
3.5.1 Principle 50
3.5.2 Single Knife-Edge Diffraction 51
3.5.3 Other Diffracting Obstacles: Geometrical Theory of Diffraction 54
3.6 CONCLUSION 59
REFERENCES 59
PROBLEMS 59
4. Antenna Fundamentals 61
4.1 INTRODUCTION 61
4.2 PRINCIPLES 61
4.2.1 What is an Antenna? 61
4.2.2 Necessary Conditions for Radiation 62
4.2.3 Near-Field and Far-Field Regions 62
4.2.4 Far-Field Radiation from Wires 63
4.3 ANTENNA PARAMETERS 65
4.3.1 Radiation Pattern 65
4.3.2 Directivity 67
4.3.3 Radiation Resistance and Efficiency 67
4.3.4 Power Gain 68
4.3.5 Bandwidth 70
4.3.6 Reciprocity 70
4.3.7 Receiving Antenna Aperture 71
4.3.8 Beamwidth and Directivity 71
4.3.9 The Friis Formula: Antennas in Free Space 71
4.3.10 Polarisation Matching 72
viii Contents
4.4 PRACTICAL DIPOLES 73
4.4.1 Dipole Structure 73
4.4.2 Current Distribution 74
4.4.3 Radiation Pattern 74
4.4.4 Input Impedance 77
4.5 ANTENNA ARRAYS 77
4.5.1 Introduction 77
4.5.2 Linear and Planar Arrays 77
4.5.3 The Uniform Linear Array 77
4.5.4 Parasitic Elements: Uda?Yagi Antennas 78
4.5.5 Reflector Antennas 79
4.5.6 Monopole Antennas 80
4.5.7 Corner Reflectors 80
4.5.8 Parabolic Reflector Antennas 81
4.6 HORN ANTENNAS 82
4.7 LOOP ANTENNAS 83
4.8 HELICAL ANTENNAS 83
4.9 PATCH ANTENNAS 84
4.10 CONCLUSION 85
REFERENCES 85
PROBLEMS 86
5. Basic Propagation Models 89
5.1 INTRODUCTION 89
5.2 DEFINITION OF PATH LOSS 89
5.3 A BRIEF NOTE ON DECIBELS 92
5.4 NOISE MODELLING 93
5.5 FREE SPACE LOSS 97
5.6 PLANE EARTH LOSS 98
5.7 LINK BUDGETS 101
5.8 CONCLUSION 103
REFERENCE 103
PROBLEMS 103
6. Terrestrial Fixed Links 105
6.1 INTRODUCTION 105
6.2 PATH PROFILES 105
6.3 TROPOSPHERIC REFRACTION 108
6.3.1 Fundamentals 108
6.3.2 Time Variability 111
6.3.3 Ducting and Multipath 111
6.4 OBSTRUCTION LOSS 113
6.5 APPROXIMATE MULTIPLE KNIFE-EDGE
DIFFRACTION 115
6.5.1 The Deygout Method 115
6.5.2 The Causebrook Correction 116
6.5.3 The Giovanelli Method 117
Contents ix
6.5.4 Test Cases 117
6.6 THE MULTIPLE-EDGE DIFFRACTION INTEGRAL 121
6.6.1 Slope-UTD Multiple-Edge Diffraction Model 122
6.6.2 Test Case: Comparison of Multiple Models 126
6.7 DIFFRACTION OVER OBJECTS OF FINITE SIZE 127
6.8 OTHER METHODS FOR PREDICTING TERRAIN DIFFRACTION 129
6.8.1 The Integral Equation Model 129
6.8.2 The Parabolic Equation Method 131
6.9 INFLUENCE OF CLUTTER 134
6.10 CONCLUSION 135
REFERENCES 135
PROBLEMS 137
7. Satellite Fixed Links 139
7.1 INTRODUCTION 139
7.2 TROPOSPHERIC EFFECTS 140
7.2.1 Attenuation 140
7.2.2 Rain Attenuation 141
7.2.3 Gaseous Absorption 146
7.2.4 Tropospheric Refraction 148
7.2.5 Tropospheric Scintillation 148
7.2.6 Depolarisation 151
7.2.7 Sky Noise 153
7.3 IONOSPHERIC EFFECTS 155
7.3.1 Faraday Rotation 158
7.3.2 Group Delay 159
7.3.3 Dispersion 159
7.3.4 Ionospheric Scintillation 160
7.3.5 Summary of Ionospheric Effects 160
7.4 SATELLITE EARTH STATION ANTENNAS 160
7.5 CONCLUSION 161
REFERENCES 161
PROBLEMS 162
8. Macrocells 163
8.1 INTRODUCTION 163
8.2 DEFINITION OF PARAMETERS 163
8.3 EMPIRICAL PATH LOSS MODELS 164
8.3.1 Clutter Factor Models 165
8.3.2 The Okumura?Hata Model 167
8.3.3 The Cost 231?Hata Model 169
8.3.4 The Lee Model 169
8.3.5 The Ibrahim and Parsons Model 170
8.3.6 Environment Categories 171
8.4 PHYSICAL MODELS 172
8.4.1 The Allsebrook and Parsons Model 172
x Contents
8.4.2 The Ikegami Model 173
8.4.3 Rooftop Diffraction 174
8.4.4 The Flat Edge Model 175
8.4.5 The Walfisch?Bertoni Model 178
8.4.6 Cost 231/Walfisch?Ikegami Model 180
8.5 ITU-R MODELS 181
8.5.1 ITU-R Recommendation P.1411 181
8.5.2 ITU-R Recommendation P.1546 182
8.6 COMPARISON OF MODELS 182
8.7 COMPUTERISED PLANNING TOOLS 183
8.8 CONCLUSION 183
REFERENCES 183
PROBLEMS 185
9. Shadowing 187
9.1 INTRODUCTION 187
9.2 STATISTICAL CHARACTERISATION 187
9.3 PHYSICAL BASIS FOR SHADOWING 189
9.4 IMPACT ON COVERAGE 189
9.4.1 Edge of Cell 189
9.4.2 Whole Cell 192
9.5 LOCATION VARIABILITY 195
9.6 CORRELATED SHADOWING 196
9.6.1 Serial Correlation 197
9.6.2 Site-to-Site Correlation 199
9.7 CONCLUSION 205
REFERENCES 205
PROBLEMS 206
10. Narrowband Fast Fading 209
10.1 INTRODUCTION 209
10.2 BASEBAND CHANNEL REPRESENTATION 209
10.3 THE AWGN CHANNEL 210
10.4 THE NARROWBAND FADING CHANNEL 213
10.5 WHEN DOES FADING OCCUR IN PRACTICE? 214
10.6 THE RAYLEIGH DISTRIBUTION 215
10.7 DISTRIBUTION OF THE SNR FOR A RAYLEIGH CHANNEL 218
10.8 THE RICE DISTRIBUTION 221
10.9 THE NAKAGAMI- m DISTRIBUTION 226
10.10 OTHER FADING DISTRIBUTIONS 227
10.11 SECOND-ORDER FAST-FADING STATISTICS 227
10.11.1 The Doppler Effect 228
10.11.2 The Classical Doppler Spectrum 230
10.12 AUTOCORRELATION FUNCTION 236
10.13 NARROWBAND MOBILE RADIO CHANNEL SIMULATIONS 238
10.14 CONCLUSION 239
Contents xi
REFERENCES 239
PROBLEMS 240
11. Wideband Fast Fading 241
11.1 INTRODUCTION 241
11.2 EFFECT OF WIDEBAND FADING 242
11.3 WIDEBAND CHANNEL MODEL 245
11.4 WIDEBAND CHANNEL PARAMETERS 246
11.5 FREQUENCY DOMAIN EFFECTS 251
11.6 THE BELLO FUNCTIONS 252
11.7 WIDEBAND FADING IN FIXED LINKS 253
11.8 OVERCOMING WIDEBAND CHANNEL IMPAIRMENTS 254
11.9 CONCLUSION 254
REFERENCES 255
PROBLEMS 255
12. Microcells 257
12.1 INTRODUCTION 257
12.2 EMPIRICAL MODELS 257
12.2.1 Dual-Slope Model 257
12.2.2 The Lee Microcell Model 259
12.2.3 The Har?Xia-Bertoni Model 260
12.3 PHYSICAL MODELS 262
12.4 LINE-OF-SIGHT MODELS 264
12.4.1 Two-Ray Model 264
12.4.2 Street Canyon Models 265
12.4.3 ITU-R P.1411 Street Canyon Model 267
12.4.4 Random Waveguide Model 268
12.5 NON-LINE-OF-SIGHT MODELS 270
12.5.1 Propagation Mechanisms and Cell Planning Considerations 270
12.5.2 Recursive Model 273
12.5.3 ITU-R P.1411 Non-Line-of-Sight Model 274
12.5.4 Site-Specific Ray Models 275
12.6 DISCUSSION 276
12.7 MICROCELL SHADOWING 277
12.8 NARROWBAND FADING 277
12.9 WIDEBAND EFFECTS 277
12.10 CONCLUSION 278
REFERENCES 279
PROBLEMS 280
13. Picocells 283
13.1 INTRODUCTION 283
13.2 EMPIRICAL MODELS OF PROPAGATION WITHIN BUILDINGS 283
13.2.1 Wall and Floor Factor Models 283
xii Contents
13.2.2 COST231 Multi-Wall Model 285
13.2.3 Ericsson Model 286
13.2.4 Empirical Models for Wireless Lan 286
13.2.5 Measurement-Based Prediction 288
13.3 PHYSICAL MODELS OF INDOOR PROPAGATION WITHIN
BUILDINGS 288
13.3.1 Ray-Tracing Models for Picocells 289
13.3.2 Reduced-Complexity UTD Indoor Model 289
13.3.3 Propagation Between Floors 291
13.3.4 Propagation on Single Floors 292
13.4 MODELS OF PROPAGATION INTO BUILDINGS 293
13.4.1 Introduction 293
13.4.2 Measured Behaviour 294
13.4.3 COST231 Line-of-Sight Model 294
13.4.4 Floor Gain Models 295
13.4.5 COST231 Non-line-of-Sight Model 296
13.4.6 Propagation Mechanisms 297
13.5 CONSTITUTIVE PARAMETERS OF BUILDING MATERIALS
FOR PHYSICAL MODELS 299
13.6 SHADOWING 300
13.7 MULTIPATH EFFECTS 300
13.8 ULTRA-WIDEBAND INDOOR PROPAGATION 302
13.9 PROPAGATION IN TUNNELS AND OTHER ENCLOSED
SPACES 303
13.9.1 Measured Behaviour 303
13.9.2 Models of Tunnel Propagation 305
13.10 DISCUSSION 309
13.11 DISTRIBUTION SYSTEMS FOR INDOOR AND ENCLOSED
SPACE APPLICATIONS 309
13.11.1 Distributed Antenna Systems ? General Considerations 310
13.11.2 Passive Distributed Antenna Systems 310
13.11.3 Active Distributed Antenna Systems 311
13.11.4 Hybrid Systems 314
13.11.5 Radiating Cables 314
13.11.6 Repeaters 319
13.11.7 Digital Distribution 320
13.11.8 Selecting The Most Appropriate Distribution System 321
13.12 INDOOR LINK BUDGETS 321
13.13 CONCLUSION 326
REFERENCES 326
PROBLEMS 328
14. Megacells 331
14.1 INTRODUCTION 331
14.2 SHADOWING AND FAST FADING 332
14.2.1 Introduction 332
Contents xiii
14.2.2 Local Shadowing Effects 333
14.2.3 Local Multipath Effects 334
14.3 EMPIRICAL NARROWBAND MODELS 336
14.4 STATISTICAL MODELS 337
14.4.1 Loo Model 339
14.4.2 Corazza Model 341
14.4.3 Lutz Model 341
14.5 SHADOWING STATISTICS 345
14.6 PHYSICAL-STATISTICAL MODELS FOR BUILT-UP AREAS 345
14.6.1 Building Height Distribution 348
14.6.2 Time-Share of Shadowing 349
14.6.3 Time Series Model 350
14.7 WIDEBAND MODELS 353
14.8 MULTI-SATELLITE CORRELATIONS 354
14.9 OVERALL MOBILE SATELLITE CHANNEL MODEL 356
14.10 CONCLUSION 357
REFERENCES 357
PROBLEMS 359
15. Antennas for Mobile Systems 361
15.1 INTRODUCTION 361
15.2 MOBILE TERMINAL ANTENNAS 361
15.2.1 Performance Requirements 361
15.2.2 Small Antenna Fundamentals 362
15.2.3 Dipoles 364
15.2.4 Helical Antennas 366
15.2.5 Inverted-F Antennas 366
15.2.6 Patches 368
15.2.7 Mean Effective Gain (MEG) 368
15.2.8 Human Body Interactions and Specific Absorption Rate
(SAR) 370
15.2.9 Mobile Satellite Antennas 374
15.3 BASE STATION ANTENNAS 376
15.3.1 Performance Requirements in Macrocells 376
15.3.2 Macrocell Antenna Design 377
15.3.3 Macrocell Antenna Diversity 380
15.3.4 Microcell Antennas 381
15.3.5 Picocell Antennas 382
15.3.6 Antennas for Wireless Lan 385
15.4 CONCLUSION 386
REFERENCES 386
PROBLEMS 388
16. Overcoming Narrowband Fading via Diversity 391
16.1 INTRODUCTION 391
16.2 CRITERIA FOR USEFUL BRANCHES 392
xiv Contents
16.3 SPACE DIVERSITY 393
16.3.1 General Model 393
16.3.2 Mobile Station Space Diversity 395
16.3.3 Handset Diversity Antennas 397
16.3.4 Base Station Space Diversity 397
16.4 POLARISATION DIVERSITY 399
16.4.1 Base Station Polarisation Diversity 399
16.4.2 Mobile Station Polarisation Diversity 400
16.5 TIME DIVERSITY 402
16.6 FREQUENCY DIVERSITY 403
16.7 COMBINING METHODS 403
16.7.1 Selection Combining 403
16.7.2 Switched Combining 405
16.7.3 Equal-Gain Combining 406
16.7.4 Maximum Ratio Combining 407
16.7.5 Comparison of Combining Methods 408
16.8 DIVERSITY FOR MICROWAVE LINKS 409
16.9 MACRODIVERSITY 410
16.10 TRANSMIT DIVERSITY 410
16.11 CONCLUSION 411
REFERENCES 411
PROBLEMS 412
17. Overcoming Wideband Fading 413
17.1 INTRODUCTION 413
17.2 SYSTEM MODELLING 413
17.2.1 Continuous-Time System Model 413
17.2.2 Discrete-Time System Model 414
17.2.3 First Nyquist Criterion 415
17.3 LINEAR EQUALISERS 416
17.3.1 Linear Equaliser Structure 416
17.3.2 Zero-Forcing Equaliser 417
17.3.3 Least Mean Square Equaliser 418
17.4 ADAPTIVE EQUALISERS 419
17.4.1 Direct Matrix Inversion 420
17.4.2 LMS Algorithm 421
17.4.3 Other Convergence Algorithms 421
17.5 NON-LINEAR EQUALISERS 422
17.5.1 Decision Feedback 423
17.5.2 Maximum Likelihood Sequence Estimator 423
17.5.3 Viterbi Equalisation 424
17.6 RAKE RECEIVERS 427
17.7 OFDM RECEIVERS 430
17.8 CONCLUSION 435
REFERENCES 435
PROBLEMS 436
Contents xv
18. Adaptive Antennas 437
18.1 INTRODUCTION 437
18.2 BASIC CONCEPTS 437
18.3 ADAPTIVE ANTENNA APPLICATIONS 438
18.3.1 Example of Adaptive Antenna Processing 438
18.3.2 Spatial Filtering for Interference Reduction 440
18.3.3 Space Division Multiple Access 441
18.3.4 Multiple-Input Multiple-Output Systems 441
18.4 OPTIMUM COMBINING 443
18.4.1 Formulation 443
18.4.2 Steering Vector for Uniform Linear Array 445
18.4.3 Steering Vector for Arbitrary Element Positions 446
18.4.4 Optimum Combiner in a Free Space Environment 447
18.4.5 Optimum Combiner in a Fading Environment 449
18.4.6 Implementation of Adaptive Antennas 450
18.4.7 Adaptive Antenna Channel Parameters 450
18.5 MULTIPLE-INPUT MULTIPLE-OUTPUT SYSTEMS 453
18.5.1 MIMO Signal Model 453
18.5.2 MIMO Channel Capacity 455
18.5.3 Trade-Off Between Diversity and Capacity for MIMO 458
18.5.4 Particular STC Schemes 459
18.5.5 MIMO Channel Modelling 460
18.5.6 MIMO Channel Models for Specific Systems 462
18.5.7 Impact of Antennas on MIMO Performance 464
18.6 ADAPTIVE ANTENNAS IN A PRACTICAL SYSTEM 465
18.7 CONCLUSION 466
REFERENCES 466
PROBLEMS 468
19. Channel Measurements for Mobile Systems 469
19.1 INTRODUCTION 469
19.2 APPLICATIONS FOR CHANNEL MEASUREMENTS 469
19.2.1 Tuning Empirical Path Loss Models 469
19.2.2 Creating Synthetic Channel Models 470
19.2.3 Existing Coverage 471
19.2.4 Design Survey 471
19.3 IMPACT OF MEASUREMENT INACCURACIES 471
19.4 SIGNAL SAMPLING ISSUES 473
19.4.1 Estimators of the Local Mean 473
19.4.2 Sampling Rate 476
19.5 MEASUREMENT SYSTEMS 479
19.5.1 Narrowband Channel Sounding 479
19.5.2 Wideband Channel Measurement Techniques 480
19.5.3 Other Measurements 481
19.6 EQUIPMENT CALIBRATION AND VALIDATION 481
19.6.1 General 481
19.6.2 Transmitters 482
xvi Contents
19.6.3 Receivers 482
19.6.4 Passive Elements 483
19.7 OUTDOOR MEASUREMENTS 484
19.7.1 General 484
19.7.2 Measurement Campaign Plan 484
19.7.3 Navigation 484
19.7.4 Size and Shape of Area for Averaging 486
19.7.5 Outdoor Testing Guidelines 488
19.8 INDOOR MEASUREMENTS 488
19.8.1 General 488
19.8.2 Navigation 489
19.8.3 Selection of Walk Routes 490
19.8.4 Equipment 491
19.8.5 Documentation 493
19.9 CONCLUSION 493
REFERENCES 493
PROBLEMS 494
20. Future Developments in the Wireless Communication Channel 497
20.1 INTRODUCTION 497
20.2 HIGH-RESOLUTION DATA 497
20.3 ANALYTICAL FORMULATIONS 498
20.4 PHYSICAL-STATISTICAL CHANNEL MODELLING 498
20.5 MULTIDIMENSIONAL CHANNEL MODELS 498
20.6 REAL-TIME CHANNEL PREDICTIONS 498
20.7 INTELLIGENT ANTENNAS 499
20.8 DISTRIBUTED AND AD-HOC CELL ARCHITECTURES 499
20.9 CONCLUSION 500
REFERENCES 500
Appendix A Statistics, Probability and Stochastic Processes 501
A.1 INTRODUCTION 501
A.2 SINGLE RANDOM VARIABLES 501
A.3 MULTIPLE RANDOM VARIABLES 502
A.4 GAUSSIAN DISTRIBUTION AND CENTRAL LIMIT THEOREM 503
A.5 RANDOM PROCESSES 504
REFERENCES 504
Appendix B Tables and Data 505
B.1 NORMAL (GAUSSIAN) DISTRIBUTION 505
B.2 ERROR FUNCTION 507
B.3 FRESNEL INTEGRALS 508
B.4 GAMMA FUNCTION 508
B.5 BESSEL FUNCTION 511
REFERENCE 511
Abbreviations 513
Index 517
Contents xvii
Preface to the Second Edition
Since the publication of the first edition of this book in 1999, much has changed in the
wireless world. Third-generation cellular systems based on wideband CDMA have been
widely deployed and are allowing high-rate applications such as video calling and music
streaming to be accessed over wide areas. Wireless LAN systems, based mainly on Wi?Fi
protocols and increasingly using MIMO antenna systems, have allowed access to very high
data rates, particularly in indoor environments, and also increasingly in urban areas. Fixed
wireless access to provide broadband services over the wide area is enjoying a resurgence of
interest following the creation of the WiMax family of standards. Broadcasting is delivering
increased numbers of channels, richness of content and interactivity via digitisation of both
video and audio. The pace of change has increased as a result of factors such as increasing
deregulation of the radio spectrum, new technologies such as software radio and greater
convergence of fixed and mobile services via multimode devices for concurrent computing
and communications.
Despite these changes, the fundamental importance of antennas and propagation has
continued. All wireless systems are subject to the variations imposed by the wireless channel,
and a good understanding of these variations is needed to answer basic questions such as
??How far does it go??? ??How fast can I transmit data??? and ??How many users can I support???
This book aims to equip the reader with the knowledge and understanding to answer these
questions for a very wide range of wireless systems.
The first edition of the book reached a larger audience than originally expected, including
adoptions by many course tutors and by many seeking a primer in the field without being
expert practitioners. At the same time many helpful comments were received, leading to the
changes which have been incorporated in this revised edition. Most significantly, many people
commented that the title of the book suggested that more weight should be given to antenna
topics; this has been addressed via Chapters 4 and 14 devoted to the fundamentals of antennas
and to their applications in mobile systems. Chapter 19 has also been added, giving practical
details of channel measurement techniques for mobile systems. Throughout the book,
enhancements and corrections have been made to reflect the current practice and to address
specific comments from readers.
In addition to the acknowledgements of the first addition, I am particularly grateful to my
co-author, Dr. Alejandro Arago?n -Zavala of ITESM in Mexico, who did most of the hard work
on the updates to allow this second edition to be produced in a reasonably timely fashion
despite my efforts to the contrary. Thanks are also due to many friends, colleagues, customers
and suppliers for continued insights into the real world of wireless systems. Particular thanks
for contributions and comments in this edition to Tim Brown, Abdus Owadally, Dave Draffin,
Steve Leach, Stavros Stavrou, Rodney Vaughan, J?rgen Bach Andersen and Constantine
Balanis. Lastly to Sarah Hinton at Wiley for patience above and beyond the call of duty.
Updates and further information regarding this book, including presentation slides, are
available from the following web site:
http://www.simonsaunders.com/apbook
In addition, a solutions manual is available to lecturers at http://www.wiley.com/go/
saunders.
Comments and suggestions are gratefully received via email to: apbook
@simonsaunders.com
Simon R. Saunders
xx Preface to the Second Edition
Q1: Please provide Preface to the First Edition

Library of Congress Subject Headings for this publication:

Antennas (Electronics).
Wireless communication systems.