Radio Wave Propagation and Parabolic Equation Modeling (eBook)

GÖKHAN APAYDIN, BSEE, MSEE, PHD, is a freelance electrical and electronics engineer. His research interests include analytical and numerical methods in electromagnetics, especially on electromagnetic computation of wave propagation, diffraction modeling, scattering, and related areas. LEVENT SEVGI, BSEE, MSEE, PHD, is a Professor in the Electrical and Electronics Engineering Department at Okan University, Istanbul, Turkey. His research has focused on propagation in complex environments, EMC/BEM modeling and measurements, analytical and numerical methods in electromagnetics, and radar systems.

Preface ix

Acronyms xi

Matlab Codes xiii

Chapter 1: INTRODUCTION 1

1.1 Electromagnetic Problems and Classification 1

1.2 Maxwell Equations 3

1.3 Guided Waves and Transverse/Longitudinal Decomposition 4

1.4 Two Dimensional Helmholtz's Equation 5

1.5 Validation, Verification, and Calibration Procedure 6

1.6 Fourier Transform, DFT and FFT 7

Chapter 2: WAVE PROPAGATION OVER FLAT EARTH 15

2.1 Flat Earth and GO Two-Ray Model 15

2.2 Single Knife Edge Problem and Four-Ray Model 16

2.3 Vertical Linear Refractivity Profile and Mode Summation 19

Chapter 3: PARABOLIC EQUATION MODELING 23

3.1 Introduction 23

3.2 Parabolic Wave Equation Form 24

3.3 Dirichlet, Neumann, and Cauchy Boundary Conditions 27

3.4 Antenna/Source Injection 28

3.5 Split-Step Parabolic Equation (SSPE) Model 29

3.5.1 Narrow-Angle and Wide-Angle SSPE 30

3.5.2 A MATLAB-Based Simple SSPE Code 30

3.6 FEM-Based Parabolic Equation Model 32

3.7 Atmospheric Refractivity Effects 40

Chapter 4: WAVE PROPAGATION AT SHORT RANGES 43

4.1 Introduction 43

4.2 Accurate Source Modeling 44

4.3 Wave Propagators in Two Dimensions 47

4.3.1 Flat Earth and Two-Ray Model 47

4.3.2 FEM-Based PE Wave Propagator 49

4.3.3 SSPE-Based PE Wave Propagator 49

4.3.4 Method of Moments Modeling 49

4.4 Knife Edge and Four Ray Model 49

4.5 Canonical Tests and Calibration 50

Chapter 5: PE AND TERRAIN MODELING 53

5.1 Irregular PEC Terrain 53

5.2 PE and Impedance Boundary Modeling 54

5.2.1 Discrete Mixed Fourier Transform (DMFT) 56

5.3 Numerical Results and Comparison 57

Chapter 6: ANALYTICAL EXACT AND APPROXIMATE MODELS 65

6.1 Wave Propagation in a Parallel Plate Waveguide 65

6.2 Green's Function in Terms of Mode Summation 68

6.3 Mode Summation for a Tilted Gaussian Source 70

6.4 A Hybrid Ray + Image Method 71

6.5 Numerical Models 73

6.5.1 Parabolic Equation Models: SSPE and FEMPE 73

6.5.2 Method of Moments 75

Chapter 7: WAVE PROPAGATION INSIDE THREE-DIMENSIONAL RECTANGULAR WAVEGUIDE 79

7.1 Introduction 79

7.2 Three-Dimensional Rectangular Waveguide Model 80

7.3 Three-Dimensional Parabolic Equation Models 81

7.3.1 SSPE Model 81

7.3.2 FEMPE Model 82

7.3.3 ADIPE Model 82

7.4 Tests and Calibration 83

Chapter 8: TWO WAY PE MODELS 89

8.1 Formulation of Two Way FEMPE Method 89

8.2 Formulation of Two Way SSPE Method 91

8.3 Flat Earth with Infinite Wall 91

8.4 Flat Earth with Single and Double Knife Edges 91

8.5 Two Way Propagation Modeling in Waveguides 96

8.6 Three-Dimensional Split-Step- and Finite-Element-Based Parabolic Equation Models 96

8.7 Tests and Calibration 97

Chapter 9: PETOOL VIRTUAL PROPAGATION PACKAGE 101

9.1 Introduction 101

9.2 PETOOL Software 103

9.3 Characteristic Examples 107

Chapter 10: FEMIX VIRTUAL PROPAGATION PACKAGE 113

10.1 Introduction 113

10.2 Analytical Surface-Wave Model 115

10.2.1 Path Loss 115

10.2.2 Norton's Model 115

10.2.3 Wait's Model 116

10.2.4 Millington's Curve Fitting Approach 117

10.3 Numerical Surface-Wave Model 118

10.4 FEMIX Package 119

10.5 Characteristic Examples 122

References 127

Index 135