Luận Văn Modeling electromagnetic wave propagation in electrically large structures

Existing unified numerical electromagnetic methods are often unable to
analyze electrically large structures due to the amount of memory and processing
power required, necessitating approximate analyses with limited applicability. In this
research a hybrid modeling methodology is adopted to solve these complex problems
more efficiently than unified numerical methods and more accurately than analytical
methods. Electromagnetic modeling problems are divided into two or more levels of
scale. Each level analyzes a specific level of detail and only promotes the required
information to the next level. The method is demonstrated by successful application
to three important problems: (1) remote sensing of snow, (2) modeling an optical
Bragg resonator, and (3) modeling the MIMO wireless channel. First, complex snow
media is analyzed with a hybrid FDTD/radiative transfer model. FDTD is used to
compute phase matrices and extinction coefficients required for radiative transfer.
Comparison with exact analytical methods proves the validity of the FDTD method
for modest domain sizes ([5¸]3) and number of Monte Carlo realizations (32). The
method is used to illustrate a penetrating sphere model, which is not possible with
existing analysis techniques. Backscatter from the resulting model is about 3 times
higher than that of existing dense-medium theories, underlying the importance of exact
characterization of the media. Second, a hybrid FD/FDTD/S-parameter analysis
is developed to model a large (104 section) optical Bragg resonator: a simple FD
method computes propagation constants and field profiles, FDTD analysis provides
reflection and transmission coefficients for the single section, and S-parameter analysis
combines the sections to obtain the complete device response. A detailed study
on error suggests that the method provides better than 2% accuracy in reflection and
transmission response. Third, a hybrid electromagnetic/SVA model is developed to
study the indoor MIMO wireless channel. A MIMO measurement platform is discussed
for simultaneous probing of up to 16 transmit and receive antennas, which
was required to assess the validity of later modeling. FDTD or MOM antenna analysis
coupled with the SVA model gives capacity predictions which match measured
data. The model is used to explore the impact of antenna spacing, directivity, and
polarization on channel capacity. Closely spaced antennas lead to an approximate
halving of receive power. Directivity effectively doubles receive power for aligned
transmit and receive. Dual polarization increases system capacity anywhere from
10% to 70%, depending on the spacing of elements and the amount of multipath richness.
This analysis of MIMO systems underlines the need for models that describe
both multipath richness and average receive power.
Contents
List of Tables xv
List of Figures xxii
1 Introduction 1
1.1 Problem: Limitations of Conventional Modeling . . . . . . . . . . . . 3
1.2 Solution: The Hybrid Method . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Problem 1: Modeling of Snow for Remote Sensing . . . . . . . . . . . 6
1.4 Problem 2: Modeling an Optical Bragg Resonator . . . . . . . . . . . 7
1.5 Problem 3: Indoor MIMO Channel Modeling . . . . . . . . . . . . . . 8
1.6 Limitations of the Hybrid Method . . . . . . . . . . . . . . . . . . . . 9
1.7 New Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . 10
2 Finite-Difference Methods 13
2.1 Finite-Difference Mode Solutions . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Discretization of Maxwell’s Equations . . . . . . . . . . . . . . 15
2.1.2 Boundary Truncation Conditions . . . . . . . . . . . . . . . . 16
2.1.3 Eigenvalue/Eigenvector Method . . . . . . . . . . . . . . . . . 17
2.1.4 Iterative Linear Method . . . . . . . . . . . . . . . . . . . . . 19
2.1.5 Method Validation . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.6 Compatibility of Modal Solutions and FDTD . . . . . . . . . 20
2.2 Finite-Difference Time-Domain . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Simulation Domain . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 23
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2.2.3 Scattered Field Formulation . . . . . . . . . . . . . . . . . . . 24
2.2.4 Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . . 26
2.2.5 The Perfectly Matched Layer and Modal Propagation . . . . . 28
2.2.6 FDTD Volume Averaging . . . . . . . . . . . . . . . . . . . . 32
2.3 One-dimensional FDTD PML Solutions . . . . . . . . . . . . . . . . . 35
2.3.1 Functional Representation of Fields . . . . . . . . . . . . . . . 35
2.3.2 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Radiative Transfer 41
3.1 Specific Intensity and Stokes Parameters . . . . . . . . . . . . . . . . 42
3.2 Equation of Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Extinction Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.1 Absorption Coefficient . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Scattering Coefficient . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Emission Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Phase Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6.1 Fresnel Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Snow Modeling for Remote Sensing 53
4.1 Numerical Computation of Radiative Transfer Quantities . . . . . . . 56
4.1.1 Phase Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.2 Extinction Coefficients . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Finite Volume and Realization Effects . . . . . . . . . . . . . . . . . . 59
4.2.1 Phase Matrix Convergence . . . . . . . . . . . . . . . . . . . . 60
4.2.2 Error Quantification . . . . . . . . . . . . . . . . . . . . . . . 62
4.3 FDTD Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.1 FDTD Phase Matrices . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Penetrating Spheres . . . . . . . . . . . . . . . . . . . . . . . 68
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4.3.3 Extinction Coefficients . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Remote Sensing Simulations . . . . . . . . . . . . . . . . . . . . . . . 70
4.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Modeling of an Optical Bragg Resonator 73
5.1 Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Accuracy of the Mode Solution . . . . . . . . . . . . . . . . . 75
5.1.2 Bragg Resonator Guided Mode Solution . . . . . . . . . . . . 83
5.2 3D Simulations of Bragg Resonator Section . . . . . . . . . . . . . . . 84
5.2.1 Mode Extraction . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.2 Finite Difference Approximations . . . . . . . . . . . . . . . . 88
5.2.3 Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4 ABC Performance . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 Bragg Resonator Response . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.1 Error Quantification . . . . . . . . . . . . . . . . . . . . . . . 97
5.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 MIMO Measurement System 105
6.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.1.1 High-level System Diagram . . . . . . . . . . . . . . . . . . . 108
6.1.2 Hardware Components . . . . . . . . . . . . . . . . . . . . . . 109
6.1.3 RF Chassis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.1.4 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.5 Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . 123
6.1.6 Antenna Pattern Coverage . . . . . . . . . . . . . . . . . . . . 130
6.2 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.2.1 Data Storage Format . . . . . . . . . . . . . . . . . . . . . . . 134
6.2.2 Code Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.2.3 Carrier Recovery . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2.4 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.5 Estimation Error . . . . . . . . . . . . . . . . . . . . . . . . . 142
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6.2.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7 MIMO Data Collection 149
7.1 Measurement Locations and Parameters . . . . . . . . . . . . . . . . 150
7.1.1 Collection 4x4(a) . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.1.2 Collection 4x4(b) . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.1.3 Collection 10x10(a) . . . . . . . . . . . . . . . . . . . . . . . . 154
7.1.4 Collection 10x10(b) . . . . . . . . . . . . . . . . . . . . . . . . 154
7.1.5 Collection 10x10(c) . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2 Marginal PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.3 Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.4 Temporal Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.5 Capacity Per Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.6 Capacity vs. Polarization . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.7 Capacity vs. Directivity . . . . . . . . . . . . . . . . . . . . . . . . . 170
7.8 Multipath Richness vs. SNR . . . . . . . . . . . . . . . . . . . . . . . 171
7.9 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
8 MIMO Channel Modeling 175
8.1 Antenna Characterization . . . . . . . . . . . . . . . . . . . . . . . . 178
8.1.1 Patch Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8.1.2 Monopole Array . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.2 SVA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.2.1 Full Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.2.2 Narrowband Simplifications . . . . . . . . . . . . . . . . . . . 193
8.2.3 Complex Normal Approximation . . . . . . . . . . . . . . . . 195
8.2.4 Shift-Invariance and Separability . . . . . . . . . . . . . . . . 198
8.2.5 Comparison of Measured Data and SVA Model Predictions . . 198
8.2.6 Comparison of SVA and Multivariate Complex Normal Models 199
8.2.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 203
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8.3 Dual-Polarization Model . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.3.1 Independent Subchannel Method . . . . . . . . . . . . . . . . 211
8.3.2 SVA Model Parameters . . . . . . . . . . . . . . . . . . . . . . 214
8.3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 215
8.4 SVA Model Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.4.1 Mutual Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.4.2 Antenna Directivity . . . . . . . . . . . . . . . . . . . . . . . . 221
8.4.3 Dual Polarization . . . . . . . . . . . . . . . . . . . . . . . . . 225
8.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
9 Conclusion 231
9.1 Remote Sensing of Snow . . . . . . . . . . . . . . . . . . . . . . . . . 231
9.2 Analysis of an Optical Bragg Resonator . . . . . . . . . . . . . . . . . 233
9.3 MIMO Wireless Channel Modeling . . . . . . . . . . . . . . . . . . . 234
9.4 Ideas for Future Research . . . . . . . . . . . . . . . . . . . . . . . . 235
A Exact Mode Solutions For Cylindrical Dielectric Waveguides 239
A.1 Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
A.2 Transcendental Mode Relationship . . . . . . . . . . . . . . . . . . . 241
A.3 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
B Plane Wave Scattering from an Infinite Dielectric Cylinder 245
B.1 Case I: On-Axis Polarization . . . . . . . . . . . . . . . . . . . . . . . 245
B.2 Case II: Off-Axis Polarization . . . . . . . . . . . . . . . . . . . . . . 246
C Plane Wave Scattering from a Dielectric Sphere (Mie Solution) 247
C.1 Scatter for Horizontal and Vertical Polarization . . . . . . . . . . . . 248
C.2 Numerical Computation . . . . . . . . . . . . . . . . . . . . . . . . . 249
D Numerical Solutions to Radiative Transfer 253
D.1 Discrete Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
D.2 Active Remote Sensing Solution . . . . . . . . . . . . . . . . . . . . . 257
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D.2.1 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 258
D.3 Matrix Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
D.3.1 Bistatic and Backscatter Coefficient Computation . . . . . . . 261
D.4 Passive Remote Sensing Solution . . . . . . . . . . . . . . . . . . . . 263
D.4.1 Homogeneous Solution . . . . . . . . . . . . . . . . . . . . . . 264
D.4.2 Particular Solution . . . . . . . . . . . . . . . . . . . . . . . . 264
D.4.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 267
D.4.4 Intermediate Interfaces . . . . . . . . . . . . . . . . . . . . . . 269
D.4.5 Half-Space Condition . . . . . . . . . . . . . . . . . . . . . . . 270
D.5 Matrix Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
E Computation of Phase Matrices 273
E.1 Complete Phase Matrix Computation . . . . . . . . . . . . . . . . . . 273
E.2 Rayleigh Phase Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 278
E.3 Mie Phase Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
E.4 QCA/QCA-CP Scaled Phase Matrix . . . . . . . . . . . . . . . . . . 280
F Quasicrystalline Approximation (QCA/QCA-CP) 283
F.1 QCA Low-Frequency Solution . . . . . . . . . . . . . . . . . . . . . . 283
F.2 QCA General Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 284
F.2.1 T-Matrix Coefficients for Spheres . . . . . . . . . . . . . . . . 285
F.2.2 L and M Functions . . . . . . . . . . . . . . . . . . . . . . . . 285
F.2.3 Percus-Yevick Pairwise Distribution Function . . . . . . . . . 285
F.2.4 Multiple Scattering Equations . . . . . . . . . . . . . . . . . . 289
F.3 QCA-CP Low Frequency Solution . . . . . . . . . . . . . . . . . . . . 290
F.4 Computation of Extinction Coefficients and Effective Permittivity . . 291
G The Multivariate Complex Normal Distribution 293
G.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
G.2 Pairwise PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
G.3 Covariance Matrices and Simplifying Assumptions . . . . . . . . . . . 297
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G.4 Computer Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
G.5 Joint Complex Normal Models . . . . . . . . . . . . . . . . . . . . . . 298
G.5.1 Complex Correlation Method . . . . . . . . . . . . . . . . . . 299
G.5.2 Power Correlation Method . . . . . . . . . . . . . . . . . . . . 299
H MIMO Channel Normalization 301
H.1 Fixed Average SISO SNR . . . . . . . . . . . . . . . . . . . . . . . . 301
H.2 Fixed Average Receive SNR . . . . . . . . . . . . . . . . . . . . . . . 302
I MIMO Channel Capacity Computation 305
I.1 Informed Transmit and Receive . . . . . . . . . . . . . . . . . . . . . 305
I.2 Uninformed Transmit Capacity . . . . . . . . . . . . . . . . . . . . . 307
J Approximating Arbitrary Metal Surfaces in FDTD 311
K Far Field E-Field Computation with an Infinite Ground Plane 313
Bibliography 325
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