Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communication

Tapan K. Sarkar, PhD, is a professor in the Department of Electrical Engineering and Computer Science at Syracuse University, New York, USA. Magdalena Salazar Palma, PhD, is a professor in the Department of Signal Theory and Communications at Universidad Carlos III de Madrid, Spain. Mohammad Najib Abdallah, PhD, is a researcher at Syracuse University.

• Preface xiAcknowledgments xvii1 The Mystery of Wave Propagation and Radiation from an Antenna 1Summary 11.1 Historical Overview of Maxwell’s Equations 31.2 Review of Maxwell–Hertz–Heaviside Equations 51.2.1 Faraday’s Law 51.2.2 Generalized Ampere’s Law 81.2.3 Gauss’s Law of Electrostatics 91.2.4 Gauss’s Law of Magnetostatics 101.2.5 Equation of Continuity 111.3 Development of Wave Equations 121.4 Methodologies for the Solution of the Wave Equations 161.5 General Solution of Maxwell’s Equations 191.6 Power (Correlation) Versus Reciprocity (Convolution) 241.7 Radiation and Reception Properties of a Point Source Antenna in Frequency and in Time Domain 281.7.1 Radiation of Fields from Point Sources 281.7.1.1 Far Field in Frequency Domain of a Point Radiator 291.7.1.2 Far Field in Time Domain of a Point Radiator 301.7.2 Reception Properties of a Point Receiver 311.8 Radiation and Reception Properties of Finite‐Sized Dipole‐Like Structures in Frequency and in Time 331.8.1 Radiation Fields from Wire‐Like Structures in the Frequency Domain 331.8.2 Radiation Fields from Wire‐Like Structures in the Time Domain 341.8.3 Induced Voltage on a Finite‐Sized Receive Wire‐Like Structure Due to a Transient Incident Field 341.8.4 Radiation Fields from Electrically Small Wire‐Like Structures in the Time Domain 351.9 An Expose on Channel Capacity 441.9.1 Shannon Channel Capacity 471.9.2 Gabor Channel Capacity 511.9.3 Hartley‐Nyquist‐Tuller Channel Capacity 531.10 Conclusion 56References 572 Characterization of Radiating Elements Using Electromagnetic Principles in the Frequency Domain 61Summary 612.1 Field Produced by a Hertzian Dipole 622.2 Concept of Near and Far Fields 652.3 Field Radiated by a Small Circular Loop 682.4 Field Produced by a Finite‐Sized Dipole 702.5 Radiation Field from a Finite‐Sized Dipole Antenna 722.6 Maximum Power Transfer and Efficiency 742.6.1 Maximum Power Transfer 752.6.2 Analysis Using Simple Circuits 772.6.3 Computed Results Using Realistic Antennas 812.6.4 Use/Misuse of the S‐Parameters 842.7 Radiation Efficiency of Electrically Small Versus Electrically Large Antenna 852.7.1 What is an Electrically Small Antenna (ESA)? 862.7.2 Performance of Electrically Small Antenna Versus Large Resonant Antennas 862.8 Challenges in Designing a Matched ESA 902.9 Near‐ and Far‐Field Properties of Antennas Deployed Over Earth 942.10 Use of Spatial Antenna Diversity 1002.11 Performance of Antennas Operating Over Ground 1042.12 Fields Inside a Dielectric Room and a Conducting Box 1072.13 The Mathematics and Physics of an Antenna Array 1202.14 Does Use of Multiple Antennas Makes Sense? 1232.14.1 Is MIMO Really Better than SISO? 1322.15 Signal Enhancement Methodology Through Adaptivity on Transmit Instead of MIMO 1382.16 Conclusion 148Appendix 2A Where Does the Far Field of an Antenna Really Starts Under Different Environments? 149Summary 1492A.1 Introduction 1502A.2 Derivation of the Formula 2D2/λ 1532A.3 Dipole Antennas Operating in Free Space 1572A.4 Dipole Antennas Radiating Over an Imperfect Ground 1622A.5 Epilogue 164References 1673 Mechanism of Wireless Propagation: Physics, Mathematics, and Realization 171Summary 1713.1 Introduction 1723.2 Description and Analysis of Measured Data on Propagation Available in the Literature 1733.3 Electromagnetic Analysis of Propagation Path Loss Using a Macro Model 1843.4 Accurate Numerical Evaluation of the Fields Near an Earth–Air Interface 1903.5 Use of the Numerically Accurate Macro Model for Analysis of Okumura et al.’s Measurement Data 1923.6 Visualization of the Propagation Mechanism 1993.7 A Note on the Conventional Propagation Models 2033.8 Refinement of the Macro Model to Take Transmitting Antenna’s Electronic and Mechanical Tilt into Account 2073.9 Refinement of the Data Collection Mechanism and its Interpretation Through the Definition of the Proper Route 2103.10 Lessons Learnt: Possible Elimination of Slow Fading and a Better Way to Deploy Base Station Antennas 2173.10.1 Experimental Measurement Setup 2243.11 Cellular Wireless Propagation Occurs Through the Zenneck Wave and not Surface Waves 2273.12 Conclusion 233Appendix 3A Sommerfeld Formulation for a Vertical Electric Dipole Radiating Over an Imperfect Ground Plane 234Appendix 3B Asymptotic Evaluation of the Integrals by the Method of Steepest Descent 247Appendix 3C Asymptotic Evaluation of the Integrals When there Exists a Pole Near the Saddle Point 252Appendix 3D Evaluation of Fields Near the Interface 254Appendix 3E Properties of a Zenneck Wave 258Appendix 3F Properties of a Surface Wave 259References 2614 Methodologies for Ultrawideband Distortionless Transmission/ Reception of Power and Information 265Summary 2654.1 Introduction 2664.2 Transient Responses from Differently Sized Dipoles 2684.3 A Travelling Wave Antenna 2764.4 UWB Input Pulse Exciting a Dipole of Different Lengths 2794.5 Time Domain Responses of Some Special Antennas 2814.5.1 Dipole Antennas 2814.5.2 Biconical Antennas 2924.5.3 TEM Horn Antenna 2994.6 Two Ultrawideband Antennas of Century Bandwidth 3054.6.1 A Century Bandwidth Bi‐Blade Antenna 3064.6.2 Cone‐Blade Antenna 3104.6.3 Impulse Radiating Antenna (IRA) 3134.7 Experimental Verification of Distortionless Transmission of Ultrawideband Signals 3154.8 Distortionless Transmission and Reception of Ultrawideband Signals Fitting the FCC Mask 3274.8.1 Design of a T‐pulse 3294.8.2 Synthesis of a T‐pulse Fitting the FCC Mask 3314.8.3 Distortionless Transmission and Reception of a UWB Pulse Fitting the FCC Mask 3324.9 Simultaneous Transmission of Information and Power in Wireless Antennas 3384.9.1 Introduction 3384.9.2 Formulation and Optimization of the Various Channel Capacities 3424.9.2.1 Optimization for the Shannon Channel Capacity 3424.9.2.2 Optimization for the Gabor Channel Capacity 3444.9.2.3 Optimization for the Hartley‐Nyquist‐Tuller Channel Capacity 3454.9.3 Channel Capacity Simulation of a Frequency Selective Channel Using a Pair of Transmitting and Receiving Antennas 3474.9.4 Optimization of Each Channel Capacity Formulation 3534.10 Effect of Broadband Matching in Simultaneous Information and Power Transfer 3554.10.1 Problem Description 3574.10.1.1 Total Channel Capacity 3584.10.1.2 Power Delivery 3614.10.1.3 Limitation on VSWR 3614.10.2 Design of Matching Networks 3624.10.2.1 Simplified Real Frequency Technique (SRFT) 3624.10.2.2 Use of Non‐Foster Matching Networks 3664.10.3 Performance Gain When Using a Matching Network 3674.10.3.1 Constraints of VSWR < 2 3674.10.3.2 Constraints of VSWR < 3 3694.10.3.3 Without VSWR Constraint 3714.10.3.4 Discussions 3724.10.4 PCB (Printed Circuit Board) Implementation of a Broadband‐ Matched Dipole 3734.11 Conclusion 376References 377Index 383