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Efficient Ray-Tracing Algorithms for Radio Wave Propagation in Urban Environments

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Efficient Ray-Tracing Algorithms for Radio Wave Propagation in Urban Environments Sajjad Hussain BSc. MSc. Supervisor: Dr. Conor Brennan School of Electronic Engineering Dublin City University This dissertation is submitted for the degree of Doctor of Philosophy September 2017 To my parents for their love and encouragement, my loving and supportive wife Akasha for always standing beside me and our beautiful son Muhammad Hashir. Declaration I hereby certify that this material, which I now submit for assessment on the programme of study leading to the award of PhD is entirely my own work, and that I have exercised reasonable care to ensure that the work is original, and does not to the best of my knowl- edge breach any law of copyright, and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged within the text of my work. Signed: ID No.: 13212215 Date: 05/09/2017 Acknowledgements I would like to express special appreciation and thanks to my supervisor, Dr. Conor Brennan, for his continuous support and confidence in my work. His patience and encouragement were invaluable to me throughout the course of my PhD. He pushed me to perform to the best of my abilities. I would also like to thank my examiners, Dr. Jean-Frédéric and Dr. Prince Anandarajah for their brilliant comments and suggestions that has really improved the quality of this thesis. I would especially like to thank my colleagues including Ian Kavanagh, Vinh Pham-Xuan and Dung Trinh-Xuan for their help and support. I thank, from the bottom of my heart, those who have supported me throughout my stay at DCU through their true friendship and thoughtfulness. A special thanks to my family. Your prayer for me was what sustained me thus far. At the end, I would like to express appreciation to my beloved wife Akasha and our son Muhammad Hashir for their love, support and patience. Table of Contents List of Figures viii List of Tables xii 1 Introduction3 1.1 Motivation for Radio Channel Modeling . .4 1.2 Contribution and Overview . .4 2 Electromagnetic Theory6 2.1 Constitutive Parameters . .7 2.2 Types of Materials . .7 2.3 Classification Of Media . .8 2.4 Mathematical Formulation . .9 2.5 Ray Properties . 10 2.6 Ray Interaction with Surfaces . 11 2.6.1 Reflection . 12 2.6.2 Diffraction . 14 2.7 Scattering . 19 2.8 Application of UTD . 20 2.8.1 2-D fields from a wedge . 20 2.8.2 3-D fields from a cube . 21 2.9 Conclusion . 21 3 General Methods in Ray Tracing 24 3.1 Ray Tracing Techniques . 25 3.1.1 Shooting and Bouncing Ray (SBR) . 25 3.1.2 Image Method . 26 3.1.3 Hybrid Method . 26 3.2 Modeling of Objects . 27 3.2.1 Buildings . 27 3.2.2 Vegetation . 29 3.2.3 Pedestrians and Vehicular Traffic . 30 3.3 Visibility Algorithms . 32 Table of Contents 3.3.1 Dimensional Reduction Technique . 33 3.3.2 BSP Algorithm . 34 3.3.3 Polar Sweep Algorithm . 38 3.4 Image-Tree . 39 3.5 Ray-Object Intersection . 40 3.6 Characterization of the Radio Channel . 44 3.6.1 Path Loss . 44 3.6.2 Channel Impulse Response (CIR) . 45 3.6.3 Time Dispersion Parameters . 45 3.6.4 Frequency Dispersion Parameters . 46 3.7 Conclusion . 47 4 Literature Review 48 4.1 Empirical Models . 49 4.1.1 Okumura Model . 50 4.1.2 Hata Model . 51 4.1.3 Lee Model . 52 4.1.4 Erceg Model . 52 4.2 Vertical Plane Models . 54 4.2.1 COST-231 Walfisch Ikegami Model . 54 4.2.2 Vogler Model . 57 4.2.3 Flat Edge Model . 58 4.2.4 Saunders and Bonar Hybrid Model . 59 4.2.5 Knife-Edge Diffraction Models . 60 4.3 Ray Tracing Models . 63 4.4 Efficient RT Techniques . 64 4.4.1 Space Division Methods . 64 4.4.2 Transmitter Dependant Methods . 67 4.4.3 Receiver Dependant Methods . 71 4.4.4 2-D/2.5-D Simplification Methods . 72 4.4.5 Exhaustive Pre-Processing Methods . 75 4.4.6 Hybrid Methods . 77 4.4.7 Interpolation Methods . 78 4.4.8 Parallel Computing and GPUs . 80 4.4.9 Commercial Tools . 81 4.4.10 Other Methods . 83 4.5 Ray Tracing Limitations . 83 4.6 Future Trends . 84 vi Table of Contents 5 Ray Tracing Acceleration for a Mobile Receiver 86 5.1 Introduction . 87 5.2 Lit and Shadow Polygons . 89 5.3 Fast Ray-Object Intersection Test . 92 5.4 Performance of Initial Model . 97 5.4.1 Measured Data . 98 5.4.2 Initial Results . 100 5.4.3 Analysis of Propagation Mechanisms . 103 5.5 Mapping of Lit Polygons . 110 5.5.1 Selection of Grid Resolution . 116 5.5.2 Results . 118 5.6 RT for a Mobile Route . 119 5.6.1 Selection of Route Length . 122 5.6.2 Results . 126 5.7 Mapping of Shadow Polygons . 126 5.7.1 Results . 128 5.8 Summary of Acceleration Techniques . 128 5.9 Conclusion . 130 6 Ray Tracing Acceleration for a Mobile Transmitter 132 6.1 Introduction . 133 6.2 Intra-Visibility Matrix . 134 6.3 Initial Model . 140 6.4 Ray tracing for a Mobile Transmitter . 142 6.5 The Ray Tracing Algorithm . 145 6.5.1 First order visible nodes . 145 6.5.2 Visible nodes for wall reflection . 147 6.5.3 Direction of the Mobile Transmitter . 154 6.5.4 Visible nodes for edge diffraction . 156 6.5.5 Image-tree computation . 156 6.6 Results . 161 6.6.1 Run Time Comparison . 161 6.6.2 Results Validation . 164 6.6.3 Selection of Transmitter Route Length . 166 6.7 Conclusion . 167 7 Conclusions and Future Work 168 7.1 Conclusions . 168 7.2 Future Work . 169 Bibliography 171 vii Table of Contents Appendix A Publications 184 viii List of Figures 2.1 A diverging astigmatic ray tube [11]. 10 2.2 Incident and reflected ray at a point on a surface. 12 2.3 The planes of incidence and reflection in ray-fixed coordinate system. 13 2.4 Cone of diffracted rays [11]. ...................... 15 2.5 Geometry for scattering from a wedge [11]. 16 2.6 Edge fixed coordinate system for oblique incidence wedge diffraction [13].................................... 17 2.7 Geometry of a wedge illuminated by a line source [21]. 21 2.8 Comparison of electric field (dB) along a line of receivers using UTD and VEFIE [21].............................. 22 2.9 Geometry of a PEC cube illuminated by a dipole source. 23 2.10 Comparison of electric field along a line of receivers using UTD and Method of Moment. 23 3.1 Shooting and bouncing ray (SBR) technique. 25 3.2 Use of image method to compute accurate ray trajectories. 27 3.3 Representation of a building in Cartesian coordinate system in 3-D space. 28 3.4 3-D model of a tree used in ray-tracing to account for the vegetation loss[32]................................. 29 3.5 Two ray ground reflection model. 30 3.6 Comparison of two ray path loss with free space path loss. 31 3.7 Change in effective ground height due to pedestrian and vehicular traffic. 32 3.8 Lit region of a wall reflection can be found using image theory. 32 3.9 The region exterior to the walls that make up the edge forms the lit region of a diffracting edge. 33 3.10 Faces are projected onto a projection plane from transmitter perspective after back face culling [48]........................ 34 3.11 A sweep line with polygon subtraction algorithm is applied to obtain the visible surfaces in 2-D [48]...................... 35 3.12 An outdoor scenario for which BSP tree is computed [50]. 36 ix List of Figures 3.13 Step by step BSP tree computation for example in Figure 3.12. a) Division of scene in two planes with respect to root node 9. b) BSP tree computation for all nodes on right side of root node 9. c) Complete BSP tree [50]............................... 37 3.14 Computation of visible faces in horizontal plane using polar sweep algorithm [56]. ............................. 38 3.15 An example of a typical image tree. 39 3.16 Top view of a test environment for ray-object intersection test. 41 3.17 Ray-object intersection test to show how a ray is validated for example in Figure 3.16. a) Ray-object intersection test for ray segment between receiver and second order reflection image. b) Ray-object intersection test for ray segment between second order reflection image and first order diffraction image. c) Ray-object intersection.
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