References

  • [1] J. Hoydis, F. Aït Aoudia, S. Cammerer, M. Nimier-David, N. Binder, G. Marcus, and A. Keller, “Sionna RT: Differentiable ray tracing for radio propagation modeling,” arXiv:2303.11103, 2023. [Online]. Available: https://arxiv.org/abs/2303.11103
  • [2] J. Hoydis, S. Cammerer, F. Aït Aoudia, A. Vem, N. Binder, G. Marcus, and A. Keller, “Sionna: An open-source library for next-generation physical layer research,” arXiv:2203.11854, 2022. [Online]. Available: https://arxiv.org/abs/2203.11854
  • [3] W. Jakob, S. Speierer, N. Roussel, and D. Vicini, “Dr.Jit: A just-in-time compiler for differentiable rendering,” Transactions on Graphics (Proceedings of SIGGRAPH), vol. 41, no. 4, Jul. 2022.
  • [4] W. Jakob, S. Speierer, N. Roussel, M. Nimier-David, D. Vicini, T. Zeltner, B. Nicolet, M. Crespo, V. Leroy, and Z. Zhang, “Mitsuba 3 Physically Based Renderer,” 2022. [Online]. Available: https://mitsuba-renderer.org
  • [5] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems,” 2015. [Online]. Available: https://www.tensorflow.org/
  • [6] A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köf, E. Yang, Z. DeVito, M. Raison, , A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, “PyTorch: An imperative style, high-performance deep learning library,” 2019. [Online]. Available: https://pytorch.org
  • [7] M. Pharr, W. Jakob, and G. Humphreys, Physically Based Rendering: From Theory to Implementation, 4th ed.   The MIT Press, 2023.
  • [8] OpenStreetMap, “Planet dump retrieved from https://planet.osm.org ,” https://www.openstreetmap.org, 2017.
  • [9] Prochitecture, “Blosm for Blender: OpenStreetMap, Google 3D cities, terrain,” accessed 18-February-2025. [Online]. Available: https://github.com/vvoovv/blosm
  • [10] J. B. Keller, “Geometrical Theory of Diffraction,” J. Opt. Soc. Am., vol. 52, no. 2, pp. 116–130, Feb 1962.
  • [11] Wikipedia. Diffuse reflection. [Online]. Available: https://en.wikipedia.org/wiki/Diffuse_reflection
  • [12] D. A. McNamara, C. W. I. Pistorius, and J. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction.   Artech House, 1990.
  • [13] Á. González, “Measurement of areas on a sphere using Fibonacci and latitude–longitude lattices,” Mathematical Geosciences, vol. 42, pp. 49–64, 2010.
  • [14] J. Hannay and J. Nye, “Fibonacci numerical integration on a sphere,” Journal of Physics A: Mathematical and General, vol. 37, no. 48, p. 11591, 2004.
  • [15] T. Kloek and H. K. van Dijk, “Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo,” Econometrica, vol. 46, no. 1, pp. 1–19, 1978.
  • [16] Wikipedia. Importance sampling. Accessed November-2025. [Online]. Available: https://en.wikipedia.org/wiki/Importance_sampling
  • [17] G. Fowler and L. C. Noll and K. P. Vo, “Fowler–noll–vo hash function,” http://www.isthe.com/chongo/tech/comp/fnv/#FNV-1a, accessed: 2025-02-18.
  • [18] Wikipedia. Rolling hash. [Online]. Available: https://en.wikipedia.org/wiki/Rolling_hash
  • [19] ——. Locality-sensitive hashing. Accessed November-2025. [Online]. Available: https://en.wikipedia.org/wiki/Locality-sensitive_hashing
  • [20] F. Puggelli, G. Carluccio, and M. Albani, “A novel ray tracing algorithm for scenarios comprising pre-ordered multiple planar reflectors, straight wedges, and vertexes,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 8, pp. 4336–4341, 2014.
  • [21] 3rd Generation Partnership Project (3GPP), “Study on channel model for frequencies from 0.5 to 100 GHz,” 3GPP, Technical Report TR 38.901, 2024, Release 18.0.0. [Online]. Available: https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3173
  • [22] P. Bagnerini, A. Buffa, and A. Cangiani, “A fast algorithm for determining the propagation path of multiple diffracted rays,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 5, pp. 1416–1422, 2007.
  • [23] J. T. Kajiya, “The Rendering Equation,” SIGGRAPH Comput. Graph., vol. 20, no. 4, p. 143–150, Aug. 1986. [Online]. Available: https://doi.org/10.1145/15886.15902
  • [24] E. Veach, “Robust monte carlo methods for light transport simulation,” Ph.D. dissertation, Stanford University, December 1997.
  • [25] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.   Cambridge University Press, 2005. [Online]. Available: https://web.stanford.edu/~dntse/wireless_book.html
  • [26] Wikipedia. Surface integral. Accessed November-2025. [Online]. Available: https://en.wikipedia.org/wiki/Surface_integral
  • [27] F. Aït Aoudia, J. Hoydis, M. Nimier-David, S. Cammerer, and A. Keller, “Instant radio maps,” 2024. [Online]. Available: https://github.com/NVlabs/instant-rm
  • [28] N. Geng and W. Wiesbeck, Planungsmethoden für die Mobilkommunikation: Funknetzplanung unter realen physikalischen Ausbreitungsbedingungen.   Springer-Verlag, 2013.
  • [29] Wikipedia. atan2. Accessed 10-February-2025. [Online]. Available: https://en.wikipedia.org/wiki/Atan2
  • [30] ——. Rodrigues’ rotation formula. Accessed 10-February-2025. [Online]. Available: https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
  • [31] C. A. Balanis, Advanced Engineering Electromagnetics.   John Wiley & Sons, 2012.
  • [32] Wikipedia. Maximum power transfer theorem. Accessed 10-February-2025. [Online]. Available: https://en.wikipedia.org/wiki/Maximum_power_transfer_theorem
  • [33] ITU, “Recommendation ITU-R P.2040-3: Effects of building materials and structures on radiowave propagation above about 100 MHz,” International Telecommunication Union, Recommendation ITU-R P.2040-3, August 2023. [Online]. Available: https://www.itu.int/rec/R-REC-P.2040/en
  • [34] M. Kline, “An asymptotic solution of maxwell’s equations,” Communications on Pure and Applied Mathematics, vol. 4, no. 2-3, pp. 225–262, 1951.
  • [35] R. K. Luneburg and M. Herzberger, Mathematical Theory of Optics, 1st ed.   University of California Press, 1964. [Online]. Available: http://www.jstor.org/stable/jj.8501483
  • [36] R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proceedings of the IEEE, vol. 62, no. 11, pp. 1448–1461, 1974.
  • [37] R. Luebbers, “Finite conductivity uniform gtd versus knife edge diffraction in prediction of propagation path loss,” IEEE Transactions on Antennas and Propagation, vol. 32, no. 1, pp. 70–76, 1984.
  • [38] ITU, “Recommendation ITU-R P.526-15: Propagation by diffraction,” International Telecommunication Union, Recommendation ITU-R P.526-15, October 2019. [Online]. Available: https://www.itu.int/rec/R-REC-P.526/en
  • [39] METIS Project, “METIS Channel Models,” Mobile and wireless communications Enablers for Twenty-twenty (2020) Information Society (METIS), Deliverable D1.4, February 2015. [Online]. Available: https://metis2020.com/wp-content/uploads/deliverables/METIS_D1.4_v1.0.pdf
  • [40] Wikipedia. Fresnel integral. Accessed 21-April-2023. [Online]. Available: https://en.wikipedia.org/wiki/Fresnel_integral
  • [41] V. Degli-Esposti, F. Fuschini, E. M. Vitucci, and G. Falciasecca, “Measurement and modelling of scattering from buildings,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 1, pp. 143–153, 2007.
  • [42] V. Degli-Esposti, V.-M. Kolmonen, E. M. Vitucci, and P. Vainikainen, “Analysis and modeling on co- and cross-polarized urban radio propagation for dual-polarized MIMO wireless systems,” IEEE Transactions on Antennas and Propagation, vol. 59, no. 11, pp. 4247–4256, 2011.