Radio Wave Propagation and Parabolic Equation Modeling

147 Pages·2017·22.222 MB·english

by  Gökhan Apaydin, Levent Sevgi

RADIO WAVE PROPAGATION
AND PARABOLIC EQUATION
MODELING
GÖKHAN APAYDIN
LEVENT SEVGI
Copyright © 2017 by The Institute of Electrical and Electronics Engineers, Inc.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
Library of Congress Cataloging-in-Publication Data is available.

ISBN: 978-1-119-43211-1
PrintedintheUnitedStatesofAmerica.
Contents
Preface ix
Acronyms xi
MatlabCodes xiii
Chapter1 INTRODUCTION 1
1.1 ElectromagneticProblemsandClassification 1
1.2 MaxwellEquations 3
1.3 GuidedWavesandTransverse/LongitudinalDecomposition 4
1.4 TwoDimensionalHelmholtz’sEquation 5
1.5 Validation,Verification,andCalibrationProcedure 6
1.6 FourierTransform,DFTandFFT 7
Chapter2 WAVEPROPAGATIONOVERFLATEARTH 15
2.1 FlatEarthandGOTwo-RayModel 15
2.2 SingleKnifeEdgeProblemandFour-RayModel 16
2.3 VerticalLinearRefractivityProfileandModeSummation 19
Chapter3 PARABOLICEQUATIONMODELING 23
3.1 Introduction 23
3.2 ParabolicWaveEquationForm 24
3.3 Dirichlet,Neumann,andCauchyBoundaryConditions 27
3.4 Antenna/SourceInjection 28
3.5 Split-StepParabolicEquation(SSPE)Model 29
3.5.1 Narrow-AngleandWide-AngleSSPE 30
3.5.2 AMATLAB-BasedSimpleSSPECode 30
3.6 FEM-BasedParabolicEquationModel 32
3.7 AtmosphericRefractivityEffects 40
Chapter4 WAVEPROPAGATIONATSHORTRANGES 43
4.1 Introduction 43
4.2 AccurateSourceModeling 44
4.3 WavePropagatorsinTwoDimensions 47
4.3.1 FlatEarthandTwo-RayModel 47
4.3.2 FEM-BasedPEWavePropagator 49
4.3.3 SSPE-BasedPEWavePropagator 49
4.3.4 MethodofMomentsModeling 49
4.4 KnifeEdgeandFourRayModel 49
4.5 CanonicalTestsandCalibration 50
Chapter5 PEANDTERRAINMODELING 53
5.1 IrregularPECTerrain 53
5.2 PEandImpedanceBoundaryModeling 54
5.2.1 DiscreteMixedFourierTransform(DMFT) 56
5.3 NumericalResultsandComparison 57
Chapter6 ANALYTICALEXACTANDAPPROXIMATEMODELS 65
6.1 WavePropagationinaParallelPlateWaveguide 65
6.2 Green’sFunctioninTermsofModeSummation 68
6.3 ModeSummationforaTiltedGaussianSource 70
6.4 AHybridRay+ImageMethod 71
6.5 NumericalModels 73
6.5.1 ParabolicEquationModels: SSPEandFEMPE 73
6.5.2 MethodofMoments 75
Chapter7 WAVEPROPAGATIONINSIDETHREE-DIMENSIONAL
RECTANGULARWAVEGUIDE 79
7.1 Introduction 79
7.2 Three-DimensionalRectangularWaveguideModel 80
7.3 Three-DimensionalParabolicEquationModels 81
7.3.1 SSPEModel 81
7.3.2 FEMPEModel 82
7.3.3 ADIPEModel 82
7.4 TestsandCalibration 83
Chapter8 TWOWAYPEMODELS 89
8.1 FormulationofTwoWayFEMPEMethod 89
8.2 FormulationofTwoWaySSPEMethod 91
8.3 FlatEarthwithInfiniteWall 91
8.4 FlatEarthwithSingleandDoubleKnifeEdges 91
8.5 TwoWayPropagationModelinginWaveguides 96
8.6 Three-Dimensional Split-Step- and Finite-Element-Based
ParabolicEquationModels 96
8.7 TestsandCalibration 97
Chapter9 PETOOLVIRTUALPROPAGATIONPACKAGE 101
9.1 Introduction 101
9.2 PETOOLSoftware 103
9.3 CharacteristicExamples 107
Chapter10 FEMIXVIRTUALPROPAGATIONPACKAGE 113
10.1 Introduction 113
10.2 AnalyticalSurface-WaveModel 115
10.2.1 PathLoss 115
10.2.2 Norton’sModel 115
10.2.3 Wait’sModel 116
10.2.4 Millington’sCurveFittingApproach 117
10.3 NumericalSurface-WaveModel 118
10.4 FEMIXPackage 119
10.5 CharacteristicExamples 122
References 127
Index 135
PREFACE
Wavepropagationinandthroughcomplexenvironmentshaslongbeenahottopic.
Oneneedstounderstand/model/simulateelectromagneticwavepropagationinorder
toestablishareliablecommunicationlink,toearlydetecttargetsinradarsystems,to
continuouslycoveranoperationalgroundandairareas,etc.Thesameisalsotruefor
underwateracousticwaves. Establishingacommunicationlinkbetweenashipanda
submarine,betweentwosubmarines,etc.,andearlydetectingnuclearsubmarinesin
deepaswellasshallowwaters,etc.,isachallenge. Thesearealsocriticalinoptical
wavepropagationthroughfibercablesandtheatmosphere.
Realisticelectromagnetic/acoustic/opticalwavepropagationmodelsinandthrough
complexenvironmentshavelongbeeninvestigatedanddeveloped. Oneoftheear-
liest and the most effective models, used in electromagnetic/acoustic/optical wave
propagation,istheparabolicequationmethod. Thisbookisacontinuationofbook
ParabolicEquationMethodsforElectromagneticWavePropagationwrittenbyLevy
in 2000 and presents the application of analytical and numerical methods for wave
propagation. The powerful numerical methods are given with several scenarios
arounduswhileconsideringtheeffectsofenvironmentonradiowavepropagation.
This book is written for electrical, electronics, communication, computer engi-
neersinindustry,aswellasforuniversitystudents,researchers,andprofessors. The
goalistodiscussfundamentalsofelectromagneticwavepropagation,especiallyon
radio wave propagation, groundwave propagation, maritime communication, inte-
gratedmaritimesurveillancesystems, submarinecommunication, defenseindustry,
radar applications, etc. The topics listed in the contents are re-visited in terms of
radiowaveengineering.ThebookalsointroducessomesimpleMATLABscriptsfor
severalwell-knownelectromagneticpropagationproblems.
Thefirstchapterintroducessomefundamentalconceptsofelectromagneticprob-
lems. Maxwell equations, transverse electric and magnetic models in guided wave
representation, Fourier transform, validation, verification, and calibration are re-
viewedbriefly. Thesecondchapterpresentsthesimplestpropagationscenarioused
in analytical modeling to investigate wave propagation over flat Earth. The part is
importantforvalidation, verification, andcalibration. Chapter3presentsparabolic
equation modeling based on the Fourier split-step and the finite-element methods.
SimpleMATLAB-basedpropagationtoolsareintroduced. Systematiccomparisons
on some canonical test scenarios are performed, and the propagation tools are cal-
ibratedagainstthemathematicallyexactsolutions. Atmosphericrefractivityeffects
arealsodiscussedattheendofthispart. Accuratesourcemodelingandvalidation,
verification,andcalibrationofdifferentpropagatorsarediscussedinChapter4. The
SSPE, FEMPE, and MoM propagators are validated and calibrated at short ranges
against the two-ray model over flat Earth and the single knife edge problem with
the four-ray model. Irregular terrain modeling and impedance boundary modeling
arepresentedinChapter5. Wavepropagationinsideasimplecanonicalstructure,a
parallelplatewaveguide,isinvestigatedinChapter6. Analyticalsolutionsinterms
of mode summation as well as image method are discussed and simple MATLAB
scripts are developed. In Chapter 7, the classical rectangular waveguide problem
ischosenforthree-dimensionalparabolicequationpropagation. Propagationinside
thiswaveguidecanbeexactlymodeledintermsofmodalsummationandanygiven
sourcedistributioncanbeanalyticallyrepresentedasaccuratelyasdesired. Theal-
gorithms are developed, tested against analytically exact data, and calibrated here.
Chapter 8 improves parabolic equation modeling with backward propagation, con-
sideredastwo-wayparabolicequationmodeling. SimpleMATLAB-basedpropaga-
tiontoolswhichusetwo-wayparabolicequationaredevelopedandtested. Chapter
9 presents a novel software tool (PETOOL), developed in MATLAB with graphi-
cal user interface (GUI), for the analysis and visualization of radio wave propaga-
tion through the homogeneous and inhomogeneous atmosphere, by incorporating
variable terrain effects with the aid of the two-way split-step algorithm employing
wide-angle propagator. The last chapter presents a novel MATLAB software tool
(FEMIX)fortheanalysisandvisualizationofsurface-wavepropagationovertheir-
regularEarth’ssurfacethroughahomogeneousandaninhomogeneousatmosphere.
SomeofthecontentsofthisbookhavebeenpublishedinIEEEpublicationssuch
asIEEETransactionsonAntennasandPropagation,andIEEEAntennasandProp-
agationMagazineforthelastcoupleofyears.
This book uses a MATLAB license under the MathWorks Book Program in de-
velopingbookmaterials.
GÖKHAN APAYDIN, LEVENT SEVGI
ACRONYMS
ADIPE alternatedirectionimplicitparabolicequation
BC boundarycondition
CBC Cauchyboundarycondition
DBC Dirichletboundarycondition
DCT discretecosinetransform
DFT discreteFouriertransform
DMFT discretemixedFouriertransform
DST discretesinetransform
EM electromagnetic
FDTD finite-differencetimedomain
FEM finite-elementmethod
FEMIX FEM-basedPEalgorithmwithmixedpaths
FEMPE FEM-basedparabolicequation
GO geometricoptics
GTD geometrictheoryofdiffraction
GUI graphicaluserinterface
HFA high-frequencyasymptotics
FFT fastFouriertransform
IM imagemethod
ITU InternationalTelecommunicationUnion
LOS lineofsight
MODSIM modelingandsimulation
MoM methodofmoments
NBC Neumannboundarycondition
PDE partialdifferentialequation
PE parabolicequation
PEC perfectelectricconductor
PF propagationfactor
PL pathloss
PO physicaloptics
PWE parabolicwaveequation
PTD physicaltheoryofdiffraction
RCS radarcross-section
SSPE split-stepparabolicequation
TE transverseelectric
TEM transverseelectromagnetic
TM transversemagnetic
TLM transmissionlinematrix
UTD uniformtheoryofdiffraction
VV&C validation,verification,andcalibration
1D one-dimensional
2D two-dimensional
3D three-dimensional
MATLAB CODES
Page CodeName Purpose
9 dft_sin.m ComputesdiscreteFouriertransformoftwosinusoids
10 fft_sin.m ComputesfastFouriertransformoftwosinusoids
12 Fseries.m ComputesFourierseriesrepresentationofagivenfunction
14 fft_dst_dct.m ComparesdiscreteFouriertransformanddiscretesine/cosine
transformofaGaussianfieldprofile
16 Ray2.m Computesfieldsover2Dflatgroundusingtwo-raymodel
16 Ray2PF.m Computespropagationfactorover2Dflatground
19 Ray4.m Computespropagationfactorover2Dflatground
usingfour-raymodel
22 Linear.m Computesfieldsusingmodesummationover2Dflatground
forlinearlydecreasingrefractivity
34 sspe.m Computesfieldsover2DflatgroundusingSSPEmodel
34 fempe.m Computesfieldsover2DflatgroundusingFEMPEmodel
48 Fearth1.m Computesfieldsover2DflatEarthusingtwo-raymodel
withrayexcitationcoefficients