Differentiable Ray Tracing for Radio Propagation Modeling
Wireless communications are the foundation of modern technologies, such as smartphones, Wi-Fi networks, connected vehicles, and future infrastructures. The design of these technologies relies on accurate models predicting radio wave propagation in complex environments shaped by obstacles, reflections, diffraction, and interference.
This book explores differentiable ray tracing for radio propagation modeling, an approach inspired by computer graphics and acoustics. By tracing radio waves through virtual environments and integrating differentiability into the simulation pipeline, this approach enables channel prediction and gradient computation for optimization, inverse problems, and machine learning workflows.
The book is organized into three parts: Understanding, Building, and Using. The first part covers the fundamentals of radio wave propagation, including electromagnetic theory, geometrical optics, and diffraction. The second part presents ray tracing algorithms, including GPU-accelerated path tracing and discontinuity smoothing techniques for differentiable simulations. The third part demonstrates applications to channel modeling, localization, material calibration, dynamic propagation via the multipath lifetime map, and machine-learning-assisted generative path sampling.
Additionally, the book highlights the link between scientific research and software development through open-source tools and reproducible implementations, showing how modern scientific computing can advance radio propagation modeling and support the design of future wireless systems.
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Spécifications
- Éditeur
- Presses universitaires de Louvain
- Auteur
- Jérome Eertmans,
- Collection
- Thèses de l'École polytechnique de Louvain | n° 1143
- Langue
- anglais
- Catégorie (éditeur)
- Sciences appliquées > Informatique > Réseaux et télécommunication
- Catégorie (éditeur)
- Sciences appliquées
- BISAC Subject Heading
- TEC000000 TECHNOLOGY & ENGINEERING
- BIC subject category (UK)
- T Technology, engineering, agriculture > TJ Electronics & communications engineering
- Code publique Onix
- 06 Professionnel et académique
- CLIL (Version 2013-2019 )
- 3069 TECHNIQUES ET SCIENCES APPLIQUEES
- Date de première publication du titre
- 15 juillet 2026
- Type d'ouvrage
- Thèse
Livre broché
- Date de publication
- 15 juillet 2026
- ISBN-13
- 978-2-39061-716-7
- Ampleur
- Nombre de pages de contenu principal : 364
- Dépôt Légal
- D/2026/9964/25 Louvain-la-Neuve, Belgique
- Code interne
- 110550
- Format
- 16 x 24 cm
- Poids
- 579 grammes
- Type de packaging
- Aucun emballage extérieur
- Prix
- 41,00 €
- ONIX XML
- Version 2.1, Version 3
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Sommaire
Acknowledgments v
Preface vii
Contributions ix
1 Core Methodological Contributions . . . . . . . . . . . . . . . . ix
2 Scientific Publications . . . . . . . . . . . . . . . . . . . . . . . . x
3 Conferences, Scientific Workshops, Seminars, and Visits . . . . xii
4 Open Source Software . . . . . . . . . . . . . . . . . . . . . . . . xiii
5 Peer Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
6 In This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Understanding 1
1 The Propagation of Radio Waves 3
1.1 Fundamentals of the Wireless Channel . . . . . . . . . . . . . . . 4
1.2 Electromagnetic Foundations . . . . . . . . . . . . . . . . . . . . 8
1.3 Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Fundamentals of Antennas . . . . . . . . . . . . . . . . . . . . . 18
1.5 Wave Interactions at Boundaries . . . . . . . . . . . . . . . . . . 23
1.6 Path Loss Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2 Ray Tracing Fundamentals 43
2.1 History of Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2 The High-Frequency Approximation . . . . . . . . . . . . . . . . 48
2.3 Antenna Modeling in Ray Tracing . . . . . . . . . . . . . . . . . 63
2.4 Introduction to Jones Calculus . . . . . . . . . . . . . . . . . . . 69
2.5 Geometrical Optics Reflected Fields . . . . . . . . . . . . . . . . 72
2.6 The Uniform Theory of Diffraction . . . . . . . . . . . . . . . . . 79
2.7 Scattering from Rough Surfaces . . . . . . . . . . . . . . . . . . . 96
2.8 Reconfigurable Intelligent Surfaces . . . . . . . . . . . . . . . . . 101
2.9 Modeling Transmitted Waves . . . . . . . . . . . . . . . . . . . . 107
2.10 Computing the Total Channel . . . . . . . . . . . . . . . . . . . . 111
2.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3 How To Trace Paths 121
3.1 Exact Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.2 Inexact Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4 Differentiable Ray Tracing 151
4.1 The Paradigm Shift to Inverse Electromagnetic Design . . . . . 152
4.2 Automatic Differentiation . . . . . . . . . . . . . . . . . . . . . . 154
4.3 Building a Differentiable Ray Tracing Pipeline . . . . . . . . . . 161
4.4 Resolving Geometric Discontinuities and Topological Transitions 170
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5 Efficient Path Tracing 181
5.1 Scene Representation in Modern Ray Tracing Pipelines . . . . . 182
5.2 The Challenge of Exponential Path Generation . . . . . . . . . . 184
5.3 Pruning Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.4 Dynamic Scenarios and Continuous Updates . . . . . . . . . . . 194
5.5 Efficient Ray–Object Intersection . . . . . . . . . . . . . . . . . . 197
5.6 Hardware Acceleration and GPU Execution Paradigms . . . . . 203
5.7 Efficacy of Exact Path Tracing Methods . . . . . . . . . . . . . . 208
5.8 Software Landscape and Recommendations . . . . . . . . . . . . 212
5.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Using 219
6 Applications 221
6.2 Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
7 Advanced Topics in Propagation Modeling 243
7.1 Machine-Learning-Assisted Ray Tracing . . . . . . . . . . . . . . 243
7.2 Study of the Multipath Lifetime Map . . . . . . . . . . . . . . . . 273
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
8 Conclusion and Perspectives 281
8.1 Summary of What We Have Seen . . . . . . . . . . . . . . . . . . 281
8.2 Limitations and Future Directions . . . . . . . . . . . . . . . . . 283
8.3 Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Appendix 287
A Getting Started with Path Tracing: Tutorial 289
A.1 Example on a Simple Scene . . . . . . . . . . . . . . . . . . . . . 289
A.2 Scaling to Complex Scenes . . . . . . . . . . . . . . . . . . . . . . 298
A.3 An Alternative: Ray Launching . . . . . . . . . . . . . . . . . . . 301
A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
B Generating Path Candidates 309
B.1 Scene with Known Visibility . . . . . . . . . . . . . . . . . . . . 309
B.2 Scene with Unknown Visibility . . . . . . . . . . . . . . . . . . . 312
B.3 Beware of the Number of Path Candidates . . . . . . . . . . . . . 314
Contents xxi
Bibliography 317
Nomenclature 331
Acronyms 335
Glossary 339