The Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communication The Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communication Tapan K Sarkar Magdalena Salazar Palma Mohammad Najib Abdallah With Contributions from: Arijit De Walid Mohamed Galal Diab Miguel Angel Lagunas Eric L Mokole Hongsik Moon Ana I Perez‐Neira This edition first published 2018 © 2018 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions The right of Tapan K Sarkar, Magdalena Salazar Palma and Mohammad Najib Abdallah to be identified as the authors of this work has been asserted in accordance with law Registered Offices John Wiley 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any damages arising here from Library of Congress Cataloging‐in‐Publication Data Names: Sarkar, Tapan (Tapan K.), author | Salazar Palma, Magdalena, author | Abdallah, Mohammad Najib, 1983– author Title: The physics and mathematics of electromagnetic wave propagation in cellular wireless communication / Tapan K Sarkar, Magdalena Salazar Palma, Mohammad Najib Abdallah ; with contributions from Arijit De, Walid Mohamed Galal Diab, Miguel Angel Lagunas, Eric L Mokole, Hongsik Moon, Ana I Perez-Neira Description: Hoboken, NJ, USA : Wiley, 2018 | Includes bibliographical references and index | Identifiers: LCCN 2017054091 (print) | LCCN 2018000589 (ebook) | ISBN 9781119393139 (pdf ) | ISBN 9781119393122 (epub) | ISBN 9781119393115 (cloth) Subjects: LCSH: Cell phone systems–Antennas–Mathematical models | Radio wave propagation–Mathematical models Classification: LCC TK6565.A6 (ebook) | LCC TK6565.A6 S25 2018 (print) | DDC 621.3845/6–dc23 LC record available at https://lccn.loc.gov/2017054091 Cover design by Wiley Cover image: © derrrek/Gettyimages Set in 10/12pt Warnock by SPi Global, Pondicherry, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 v Contents Preface xi Acknowledgments xvii The Mystery of Wave Propagation and Radiation from an Antenna Summary 1.1 Historical Overview of Maxwell’s Equations 1.2 Review of Maxwell–Hertz–Heaviside Equations 1.2.1 Faraday’s Law 1.2.2 Generalized Ampère’s Law 1.2.3 Gauss’s Law of Electrostatics 1.2.4 Gauss’s Law of Magnetostatics 10 1.2.5 Equation of Continuity 11 1.3 Development of Wave Equations 12 1.4 Methodologies for the Solution of the Wave Equations 16 1.5 General Solution of Maxwell’s Equations 19 1.6 Power (Correlation) Versus Reciprocity (Convolution) 24 1.7 Radiation and Reception Properties of a Point Source Antenna in Frequency and in Time Domain 28 1.7.1 Radiation of Fields from Point Sources 28 1.7.1.1 Far Field in Frequency Domain of a Point Radiator 29 1.7.1.2 Far Field in Time Domain of a Point Radiator 30 1.7.2 Reception Properties of a Point Receiver 31 1.8 Radiation and Reception Properties of Finite‐Sized Dipole‐Like Structuresin Frequency and in Time 33 1.8.1 Radiation Fields from Wire‐Like Structures in the Frequency Domain 33 1.8.2 Radiation Fields from Wire‐Like Structures in the Time Domain 34 1.8.3 Induced Voltage on a Finite‐Sized Receive Wire‐Like Structure Due to a Transient Incident Field 34 1.8.4 Radiation Fields from Electrically Small Wire‐Like Structures in the Time Domain 35 vi Contents 1.9 An Expose on Channel Capacity 44 1.9.1 Shannon Channel Capacity 47 1.9.2 Gabor Channel Capacity 51 1.9.3 Hartley‐Nyquist‐Tuller Channel Capacity 53 1.10 Conclusion 56 References 57 Characterization of Radiating Elements Using Electromagnetic Principles in the Frequency Domain 61 Summary 61 2.1 Field Produced by a Hertzian Dipole 62 2.2 Concept of Near and Far Fields 65 2.3 Field Radiated by a Small Circular Loop 68 2.4 Field Produced by a Finite‐Sized Dipole 70 2.5 Radiation Field from a Finite‐Sized Dipole Antenna 72 2.6 Maximum Power Transfer and Efficiency 74 2.6.1 Maximum Power Transfer 75 2.6.2 Analysis Using Simple Circuits 77 2.6.3 Computed Results Using Realistic Antennas 81 2.6.4 Use/Misuse of the S‐Parameters 84 2.7 Radiation Efficiency of Electrically Small Versus Electrically Large Antenna 85 2.7.1 What is an Electrically Small Antenna (ESA)? 86 2.7.2 Performance of Electrically Small Antenna Versus Large Resonant Antennas 86 2.8 Challenges in Designing a Matched ESA 90 2.9 Near‐ and Far‐Field Properties of Antennas Deployed Over Earth 94 2.10 Use of Spatial Antenna Diversity 100 2.11 Performance of Antennas Operating Over Ground 104 2.12 Fields Inside a Dielectric Room and a Conducting Box 107 2.13 The Mathematics and Physics of an Antenna Array 120 2.14 Does Use of Multiple Antennas Makes Sense? 123 2.14.1 Is MIMO Really Better than SISO? 132 2.15 Signal Enhancement Methodology Through Adaptivity on Transmit Instead of MIMO 138 2.16 Conclusion 148 Appendix 2A Where Does the Far Field of an Antenna Really Starts Under Different Environments? 149 Summary 149 2A.1 Introduction 150 2A.2 Derivation of the Formula 2D2/λ 153 2A.3 Dipole Antennas Operating in Free Space 157 Contents 2A.4 Dipole Antennas Radiating Over an Imperfect Ground 162 2A.5 Epilogue 164 References 167 Mechanism of Wireless Propagation: Physics, Mathematics, and Realization 171 Summary 171 3.1 Introduction 172 3.2 Description and Analysis of Measured Data on Propagation Available in the Literature 173 3.3 Electromagnetic Analysis of Propagation Path Loss Using a Macro Model 184 3.4 Accurate Numerical Evaluation of the Fields Near an Earth–Air Interface 190 3.5 Use of the Numerically Accurate Macro Modelfor Analysis of Okumura et al.’s Measurement Data 192 3.6 Visualization of the Propagation Mechanism 199 3.7 A Note on the Conventional Propagation Models 203 3.8 Refinement of the Macro Model to Take TransmittingAntenna’s Electronic and Mechanical Tilt into Account 207 3.9 Refinement of the Data Collection Mechanismand its Interpretation Through the Definition of the Proper Route 210 3.10 Lessons Learnt: Possible Elimination of Slow Fadingand a Better Way to Deploy Base Station Antennas 217 3.10.1 Experimental Measurement Setup 224 3.11 Cellular Wireless Propagation Occurs Through the Zenneck Wave and not Surface Waves 227 3.12 Conclusion 233 Appendix 3A Sommerfeld Formulation for a Vertical Electric Dipole Radiating Over an Imperfect Ground Plane 234 Appendix 3B Asymptotic Evaluation of the Integrals by the Method of Steepest Descent 247 Appendix 3C Asymptotic Evaluation of the IntegralsWhen there Exists a Pole Near the Saddle Point 252 Appendix 3D Evaluation of Fields Near the Interface 254 Appendix 3E Properties of a Zenneck Wave 258 Appendix 3F Properties of a Surface Wave 259 References 261 Methodologies for Ultrawideband Distortionless Transmission/ Reception of Power and Information 265 Summary 265 4.1 Introduction 266 vii viii Contents 4.2 4.3 4.4 4.5 4.5.1 4.5.2 4.5.3 4.6 4.6.1 4.6.2 4.6.3 4.7 Transient Responses from Differently Sized Dipoles 268 A Travelling Wave Antenna 276 UWB Input Pulse Exciting a Dipole of Different Lengths 279 Time Domain Responses of Some Special Antennas 281 Dipole Antennas 281 Biconical Antennas 292 TEM Horn Antenna 299 Two Ultrawideband Antennas of Century Bandwidth 305 A Century Bandwidth Bi‐Blade Antenna 306 Cone‐Blade Antenna 310 Impulse Radiating Antenna (IRA) 313 Experimental Verification of Distortionless Transmission of Ultrawideband Signals 315 4.8 Distortionless Transmission and Reception of Ultrawideband Signals Fitting the FCC Mask 327 4.8.1 Design of a T‐pulse 329 4.8.2 Synthesis of a T‐pulse Fitting the FCC Mask 331 4.8.3 Distortionless Transmission and Reception of a UWB Pulse Fitting the FCC Mask 332 4.9 Simultaneous Transmission of Information and Power in Wireless Antennas 338 4.9.1 Introduction 338 4.9.2 Formulation and Optimization of the Various Channel Capacities 342 4.9.2.1 Optimization for the Shannon Channel Capacity 342 4.9.2.2 Optimization for the Gabor Channel Capacity 344 4.9.2.3 Optimization for the Hartley‐Nyquist‐Tuller Channel Capacity 345 4.9.3 Channel Capacity Simulation of a Frequency Selective Channel Using a Pair of Transmitting and Receiving Antennas 347 4.9.4 Optimization of Each Channel Capacity Formulation 353 4.10 Effect of Broadband Matching in Simultaneous Information and Power Transfer 355 4.10.1 Problem Description 357 4.10.1.1 Total Channel Capacity 358 4.10.1.2 Power Delivery 361 4.10.1.3 Limitation on VSWR 361 4.10.2 Design of Matching Networks 362 4.10.2.1 Simplified Real Frequency Technique (SRFT) 362 4.10.2.2 Use of Non‐Foster Matching Networks 366 4.10.3 Performance Gain When Using a Matching Network 367 4.10.3.1 Constraints of VSWR < 2 367 Contents 4.10.3.2 Constraints of VSWR < 3 369 4.10.3.3 Without VSWR Constraint 371 4.10.3.4 Discussions 372 4.10.4 PCB (Printed Circuit Board) Implementation of a Broadband‐ Matched Dipole 373 4.11 Conclusion 376 References 377 Index 383 ix xi Preface Wireless communication is an important area of research these days However, the promise of wireless communication has not matured as expected This is because some of the important principles of electromagnetics were not adhered to during system design over the years Therefore, one of the objectives of this book is to describe and document some of the subtle electromagnetic principles that are often overlooked in designing a cellular wireless system These involve both physics and mathematics of the concepts used in deploying antennas for transmission and reception of electromagnetic signals and selecting the proper methodology out of a plethora of scenarios The various scenarios are but not limited to: is it better to use an electrically small antenna, a resonant antenna or multiple antennas in a wireless system? However, the fact of the matter as demonstrated in the book is that a single antenna is sufficient if it is properly designed and integrated into the system as was done in the old days of the transistor radios where one could hear broadcasts from the other side of the world using a single small antenna operating at 1 MHz, where an array gain is difficult to achieve! The second objective of this book is to illustrate that the main function of an antenna is to capture the electromagnetic waves that are propagating through space and prepare them as a signal fed to the input of the first stage of the radio frequency (RF) amplifier The reality is that if the signal of interest is not captured and available for processing at the input of the first stage of the RF amplifier, then application of various signal processing techniques cannot recreate that signal Hence the modern introduction of various statistical concepts into this deterministic problem of electromagnetic wave transmission/reception is examined from a real system deployment point of view In this respect the responses of various sensors in the frequency and the time domain are observed It is important to note that the impulse response of an antenna is different in the transmit mode than in the receive mode Understanding of this fundamental principle can lead one to transmit ultrawideband signals through space using a pair of antennas without any distortion Experimental results are xii Preface provided to demonstrate how a distortion free tens of gigahertz bandwidth signal can be transmitted and received to justify this claim This technique can be achieved by recasting the Friis’s transmission formula (after Danish‐ American radio engineer Harald Trap Friis) to an alternate form which clearly illustrates that if the physics of the transmit and receive antennas are factored in the channel modelling then the path loss can be made independent of frequency The other important point to note is that in deploying an antenna in a real system one should focus on the radiation efficiency of the antenna and not on the maximum power transfer theorem which has resulted in the misuse of the S‐parameters Also two antennas which possess a century bandwidth (i.e., a 100:1 bandwidth) are also discussed The next topic that is addressed in the book is the illustration of the shortcomings of a MIMO system from both theoretical and practical aspects in the sense that it is difficult if not impossible to achieve simultaneously several orthogonal modes of transmission with good radiation efficiency In this context, a new deterministic methodology based on the principle of reciprocity is presented to illustrate how a signal can be directed to a desired user and simultaneously be made to have nulls along the directions of the undesired ones without an explicit characterization of the operational environment This is accomplished using an embarrassingly simple matrix inversion technique Since this principle also holds over a band of frequencies, then the characterization of the system at the uplink frequency can be used to implement this methodology in the downlink or vice versa Another objective of the book is to point out that all measurements related to propagation path loss in electromagnetic wave transmission over ground illustrate that the path loss from the base station in a cellular environment is approximately 30 dB per decade of distance within the cell of a few Km in radius and the loss is 40 dB per decade outside this cell This is true independent of the nature of the ground whether it be urban, suburban, rural or over water Also the path loss in the cellular band appears to be independent of frequency Therefore in order to propagate a signal from 1 m to 1 kilometer the total path loss, based on the 30 dB per decade of distance, is 90 dB And compared to this free space path loss over Earth, the attenuation introduced by buildings, trees and so on has a second order effect as it is shown to be of the order of 30–40 dB Even though this loss due to buildings, trees and the like is quite large, when compared to the free space path loss of approximately 90 dB over a 1 km, it is negligible! Also, the concept of slow fading appears to be due to interference of the direct wave from the transmitting antenna along with the ground wave propagation over earth and also emanating from it and generally occurs when majority of the cell area is located in a near field environment of the base station antenna These concepts have been illustrated from a physics based view point developed over a hundred years ago by German theoretical physicist Arnold Johannes Wilhelm Sommerfeld and have been validated using References operating in the receive mode, irrespective of the antenna type Moreover, observations of the output wave shapes (radiated field and received current) from the antennas provide important information about their transmitting and receiving properties, and certain relationships are obtained between the input and output wave shapes Consequently, one can conclude, for example, that if a bicone transmits to a receiving TEM horn, then the induced current in the horn will be exactly identical to the driving point voltage of the bicone Such observations can have very important ramifications in broadband high‐speed information transmission Finally, a procedure is presented to design a time limited ultrawideband pulse fitting the FCC mask which has a good linear phase response Also this pulse is practically bandlimited in addition to having a finite time domain support Examples are given on how to transmit and receive such ultrawideband pulses without distortion using a special type transmit and receive antennas The implementation and the results of broadband matching in simultaneous information and power transfer have been described Electromagnetic simulation has been performed to calculate the power efficiency and voltage efficiency for power allocation over a number of disjoint frequency channels It has been demonstrated that the narrow bandwidth of the antenna would limit the performance of simultaneous information and power transfer Two methods for broadband matching have been proposed and presented: SRFT and non‐Foster matching From the analysis, it is demonstrated that the non‐Foster matching performs better, which can improve the design of a system in terms of channel capacity and power delivery However, the drawbacks of non‐Foster matching are the inclusion of NICS or NIIS, which would increase the complexity of the circuit and power consumption The broadband matching is a relatively simple approach that only includes some lumped components that can also be implemented by using a microstrip line A PCB implementation of a broadband‐matched dipole using parallel‐strip line has also been presented References B H Jung, T K Sarkar, S W Ting, Y Zhang, Z Mei, Z Ji, M Yuan, A De, M Salazar‐Palma, and S M Rao, Time and Frequency Domain Solutions of EM Problems Using Integral Equations and a Hybrid Methodology, IEEE Press/John Wiley & Sons, Inc., Hoboken, NJ, 2010 Y Zhang, T K Sarkar, X Zhao, D Garcia‐Donoro, W Zhao, M Salazar‐Palma, 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Sarkar, Magdalena Salazar Palma, and Mohammad Najib Abdallah © 2018 John Wiley & Sons, Inc Published 2018 by John Wiley & Sons, Inc 384 Index biconical antennas (cont’d ) radiated field from 294, 295, 297, 298 radiation pattern 292 resistive loading profile 297 structure 293 Brewster’s angle 228–230 Brewster’s phenomenon 240 Brewster–Zenneck wave 228 broadband matching effect, in dipole antennas 355 antenna configuration 357, 358 Gabor capacity 359–360 HNT capacity 360 PCB technology 373–376 performance gain using matching network 367–373 power delivery 361 power efficiency 358, 359 Shannon capacity 358–360 total channel capacity 358–360 voltage efficiency 358, 360 voltage standing wave ratios (VSWR) 359 constraints 367–370 electromagnetic simulation 358 limitation on 361–362 non‐foster matching networks 366–367 vs reflected power 356, 357 simplified real frequency technique 362–366 without VSWR constraint 371–372 C Cauchy principal integral method 231–232 century bandwidth bi‐blade antenna 306–310 channel capacity 339 broadband matching effect, in dipole antennas 358–360 formulation 353–355 frequency selective channel simulation 347–353 optimization for Gabor channel capacity 344–345 Hartley–Nyquist–Tuller channel capacity 345–347 Shannon channel capacity 342–344 Chu limit 93 cone‐blade antenna 313 for generating circular polarization 310, 311 monocycle pulse reception 311, 312 radiation from 311 structure 310, 311 transient input resistance 312 correlation and convolution Lorentz reciprocity theorem 25 Poynting’s theorem 27–28 principle of superposition 26–28 Rayleigh‐Carson reciprocity theorem 26 surface integrals 25–26 D D*dot antenna conical antenna 323 transmit and receive signal 325 ultra wideband signal transmission 323–325 dipole antennas 61 broadband matching see broadband matching effect, in dipole antennas effective illumination 281 free space 159–161 frequency spectrum 282 imperfect ground 162–164 impulse response 292 Index monocycle pulse reception 283, 285 radiation from 283–286 resistive loaded 283, 285, 287, 288 monocycle pulse reception 288–290 radiation efficiency 288, 291 radiation from 288–290 transient responses from dipoles separation 271–276 frequency domain code 268–269 Gaussian pulse 269–275 general‐purpose code 268 induced current 276, 277 radiated electric fields 272–275 E electrically small antennas (ESAs) 62, 149 definition 86 vs large resonant antennas performance 86–90 matching network Chu limit 93 Fano‐Bode limit 91 impedance of 90 non‐Foster elements 92 passive matching network 91 Q‐factor 92 electric field integral equation (EFIE) 280 electromagnetic macro model 171, 184–190 electromagnetic wave propagation and radiation channel capacity, concept of entropy and probability 45 Gabor channel capacity 51–53 Hartley–Nyquist–Tuller channel capacity 53–56 second law of thermodynamics 45 Shannon channel capacity 47–51 statistical mechanics 44 statistical thermodynamics 45–46 deleterious effects far field in frequency domain 29–30 of point radiator 30–31 impulse response, of antenna Maxwell–Hertz–Heaviside Equations equation of continuity 11 Faraday’s law 5–7 Gauss’s law of electrostatics 9–10 Gauss’s law of magnetostatics 10–11 generalized Ampere’s Law 8–9 Maxwell’s equations 3–5 receive antenna pattern reception properties finite‐sized dipole‐like structures, in frequency and time 33–44 of point receiver 31–33 reciprocity theorem spatial directivity wave equation AC voltages 15 Doppler frequency 18 energy transmission 16 Euler’s identity 16 fading characteristics 17 free space 12 frequency domain and time domain 17 magnitude and phase characteristics 17 oscillating electric and magnetic fields 13 power frequencies 17 scalar quantity 16 temporal and spatial variation 14 385 386 Index Ericsson in‐building path loss model 174 external resonance phenomenon F Fano‐Bode limit 91 far field see also radiated far field derivation of the formula electric and magnetic fields 150 magnitude of total electric field 151–155 planar and antenna radiation pattern 149 radiated far field see radiated far field Fast‐Fourier‐Transform (FFT) technique 281 finite‐sized dipole current and field distribution 70 electric fields 71, 72 magnetic fields 71 near field 72 sinusoidal approximation 70 vector potential 70 free space antenna array, half wave dipole in 95 dipole antennas 159–161 electromagnetic wave propagation and radiation 12 half wave dipole in 95 G Gabor channel capacity 51–53 optimization for 344–345 vs power delivery with VSWR constraints 368, 370 without VSWR constraints 371 Global Positioning System (GPS) receiver 211 Green’s function 191, 192, 256, 257 H Hankel function 232, 239–242 Hartley–Nyquist–Tuller (HNT) channel capacity 53–56 optimization for 345–347 vs power delivery with VSWR constraints 368, 370 without VSWR constraints 372 Hata model 203–206 Hertzian dipole 28, 29, 61, 316 Ampere’s law 64 electric field intensity 64 magnetic field intensity 63 magnetic vector potential 63 Poynting vector 64–65 Hertzian vector 184, 234, 235 Hertz potential 184, 185, 255, 257 HOBBIES 182, 334, 341 I Idea Cellular Network 177 impulse radiating antenna (IRA) 313–316 information and power transmission broadband matching see broadband matching effect, in dipole antennas wireless antennas 338–355 internal impedance 61, 75, 76 L line‐of‐sight propagation 62 load impedance 61, 75, 76, 78, 80, 91, 138, 346, 365 log‐normal model 182, 203 M macro cell propagation measurements 175 maximum power transfer concept AC power distribution 80 antenna systems 76 AWAS analysis 81–84 in communication systems 81 damping factor 80 efficiency vs power transfer 79 Index efficiency vs RL and XL 79 electric and magnetic fields 80 energy transfer 75 external load resistance 78 internal impedance 76 load impedance 76 load resistance 80 radio circuits 80 S‐parameters 84–85 Thevenin/Norton resistance 75 maximum power transfer theorem 61 Maxwell’s equations 2–5 electric and magnetic field intensities 22 Fourier transform theory 24 frequency domain 22–23 Gauss’s law of magnetostatics 19 gradient of vector 19 Lorenz gauge condition 22 magnetic flux density 19 time and space variables 24 time domain representation 22 transmit and receive modes of operations 24 vector’s Laplacian 21 method of steepest descent 247–252 monopole antenna ultra wideband signal transmission 325–328 and wave‐guide horn antennas 318 multiple‐input‐multiple‐output (MIMO) 62, 100 simple input‐output relationship 128 SISO system conducting concentric cylinders 135 global positioning system (GPS) 134 2×2 MIMO system 135–137 multi‐moded wave guiding system 134 N spatial modes 138 orthogonal mode 132 Shannon channel capacities 132 Shannon’s theory 133–134 transmitting antennas 132 transmit/receive antennas 108 uncoupled parallel decomposition 129 N non‐foster matching networks 366– 367, 370, 372 non‐resonating tapered horn antenna 303–305 Norton surface wave 189, 202, 231, 256 O Okumura propagation measurements 192–199, 204 optical analog model 171, 173 Ott’s formulation 241 P passive radio frequency identification (RFID) 339, 373 physics based electromagnetic macro model 179–180 Poincaré asymptotic series 251 pole near the saddle point 252–254 Poynting vector 64–65 printed circuit broadband matched dipole configuration 373, 374 voltage standing wave ratios 374, 375 propagation path loss 171–172 antenna’s tilt 207–210 electromagnetic macro model 171, 184–190 numerically accurate macro model 192–199 Zenneck wave 227–233 proper route concept 210–211 387 388 Index Q Q‐factor 92 quarter‐wave transformer 373 R radiated far field antenna field pattern 67 antenna impedance 67 E & H fields 66 electric and the magnetic fields 67 finite‐sized dipole antenna binomial expansion 72 center‐fed dipole 74 diffraction theory 74 electromagnetic wave propagation 74 Fraunhoffer diffraction 74 maximum phase error 73 power flows 66 reactive power component 67 small circular loop complex power density 69 far field expressions 70 magnetic vector potential 68 peak values 69 transmission of energy 66 radiating elements antenna array direction of arrival (DOA) 120 impulse response 123 isotropic radiator 120 mutual coupling 122 phased array, of Hertzian dipoles 122 signal of interest (SOI) 120 vector electromagnetic problem 120 field, in dielectric room and conducting box absorption boundary condition 109 electromagnetic practitioners 109 frequency domain integral equation code 117 numerical electromagnetics code 117 probability theory 112 signal enhancement effect 110 transmitting and receiving dipoles 110 Wheeler‐Cap method 117 finite‐sized dipole current and field distribution 70 electric fields 71, 72 magnetic fields 71 near field 72 sinusoidal approximation 70 vector potential 70 Hertzian dipole Ampere’s law 64 electric field intensity 64 magnetic field intensity 63 magnetic vector potential 63 Poynting vector 64–65 maximum power transfer concept see maximum power transfer concept microwave relay link, antennas cellular wireless communication 105 communication distance 104 multipath fading 105–106 rule of thumb 105 TV transmission 104 multiple antennas, deployment of automatic gain control (AGC) 124 electromagnetic wave 123 impedance matching 127 MIMO system 132–138 M‐transmit and M‐receive antennas 129 multiple‐input‐multiple‐ output 125, 126 mutual coupling 131 Index near and far fields 131 non‐realistic systems 126 NT transmit and NR receive antenna systems 127 point source model 131 signal processing approach 127 single‐input‐single‐output (SISO) channels 128, 132–138 singular value decomposition (SVD) 128 space and time variables 131 statistical methodology 132 radiated far field see radiated far field reactive near field 65–66 signal enhancement methodology concentric cylinders 142 electromagnetic analysis code 143, 145 helical antenna transmit/receive system 143, 148 multiple‐user transmit/receive scenario 139 reciprocity principle 139 transmitter T2 and receiver R1 140 spatial antenna diversity central limit theorem 101 electromagnetic field components 104 line‐of‐sight (LOS) 103 physics‐based approach 102 probability distributions 101 probability theory 101 vector quantities 100 radiation efficiency, of antenna 279 ray tracing technique 112, 204 reactive near field power flows 65, 66 Poynting vector 66 scalar power density 65 resistive loaded dipole antennas monocycle pulse reception 288–290 radiation efficiency 288, 291 radiation from 288–290 Riemann sheets 239, 240, 244, 259 S saddle point 188, 193, 231, 242, 244, 245, 247–248 Schelkunoff formulation 192, 194, 195, 229–231 Shannon channel capacity 182 global positions system (GPS) 48 optimization for 342–344 vs power delivery with VSWR constraints 368, 369 without VSWR constraints 371 Poynting vector 49–51 Pulse Code Modulation 48 Pulse Position Modulation 48 satellite communication 47 Shannon’s theory 133–134 simplified real frequency technique (SRFT) 362–366 slow fading phenomenon 171, 217 Sommerfeld formulation 98, 184, 191, 234–247 Sommerfeld integrals 171, 173, 259 Sommerfeld tail problem 231 space division multiple access (SDMA) 151, 197 spatial antenna diversity central limit theorem 101 electromagnetic field components 104 line‐of‐sight (LOS) 103 physics‐based approach 102 probability distributions 101 probability theory 101 vector quantities 100 statistical based models 182, 203 superposition, principle of 26–28 surface plasmon polaritons (SPP) 260–261 surface waves 232, 259–261 389 390 Index T tapered horn antenna monocycle pulse reception 300, 303 radiation from 300, 302 structure 300, 302 Taylor series 248–250, 252 T‐pulse (Time limited pulse) design 329–331 distortionless transmission and reception 332–338 FCC UWB spectral mask criterion 331 Fourier transform theory 328 orthogonal Nyquist signals 329 transverse electromagnetic mode (TEM) horn antenna 299 monocycle reception 300, 301 radiation from 300, 301 structure 300 ultra wideband signal transmission 319–322 transverse magnetic (TM) plane wave 227, 228 travelling wave antennas 276–279 two‐ray model 203–205 U ultrawideband (UWB) signal transmission experimental verification conical antenna 318–322 D*dot antenna 323–325 Frii’s transmission formula 316, 317 impulse response 315–316 monopole antenna 325–328 TEM horn antenna 319–322 FCC spectral mask criterion discrete finite time domain pulse 327–328 T‐pulse design 328–338 W water‐filling algorithm 340, 344, 347–350 Wheeler‐Cap method 117 wireless antennas, information and power transmission additive white Gaussian noise channel 339 bandwidth allocation 341 channel capacity 339 electromagnetic simulation setup 340 frequency selective channel simulation 347–353 HOBBIES 341 optimization for 353–355 Gabor channel capacity 344–345 Hartley‐Nyquist‐Tuller channel capacity 345–347 Shannon channel capacity 342–344 passive RFID 339 water‐filling algorithm 340 wireless sensing system 339 wireless propagation mechanism base station antennas 217–227 electromagnetic macro model 171, 184–190 measured data, description and analysis of 173–184 models 203–207 numerical evaluation 190–192 Index Okumura et al.’s measurement data analysis 192–199 proper route 210–216 total fields near the interface 254–258 visualization 199–203 Xpol 45º model 207–210 Zenneck wave 227–233, 258–259 wireless sensing system (WSN) 339, 373 X Xpol 45º tilted antenna model 207–210 Y Yagi‐Uda antenna 192, 193 Z Zenneck/Sommerfeld wave type 229 Zenneck wave 227–233, 258–259 391 ... the Poynting’s theorem of electromagnetic energy transmission This introduces the principle of conservation of energy into the domain of signal analysis which is missing in the context of information... the input of the first stage of the radio frequency (RF) amplifier The reality is that if the signal of interest is not captured and available for processing at the input of the first stage of. .. of the subtle electromagnetic principles that are often overlooked in designing a cellular wireless system These involve both physics and mathematics of the concepts used in deploying antennas