IP Library › Granted Patent US 12,731,324
Granted Patent B2
US 12,731,324 · App. 18/653,088 · Granted Sep 8, 2026

Neural components for differentiable ray tracing of radio propagation

Inventors: Jakob Richard Hoydis (Paris, FR); Faycal Ait Aoudia (Santa Clara, CA); Sebastian Cammerer (Tuebingen, DE); Alexander Georg Keller (Berlin, DE); Merlin Nimier-David (Nyon, CH); Nikolaus Binder (Berlin, DE); Guillermo Anibal Marcus Martinez (Berlin, DE)
Assignee: NVIDIA Corporation
G06T15/06G06T17/05H04W16/18G06T2207/20081G06T2207/20084
View Patent ↗
Loading inventors, assignments & file history…
Monitor This Case
Get email alerts when status or documents change.
Order Certified Copies
Most orders are placed with the USPTO same day — all within 24 business hours.
Order via The Patent Place →
Pre-filled with this patent's details
Quick Facts
Patent No.
US 12,731,324
App. No.
18/653,088
Granted
Sep 8, 2026
Kind
B2
Abstract

Apparatuses, systems, and techniques relate to neural components for differentiable ray tracing of radio propagation. Differentiable ray tracing may be used to refine the scene geometry of the physical environment, to learn or optimize the scene properties of objects in the scene, to learn or optimize the scene properties of antennas, and to learn or optimize antenna patterns, array geometries, and orientations and positions of transmitters and receivers. Once scene properties have been learned or optimized, the differentiable ray tracer may further be used to simulate the performance of different configurations of the transmitters, receivers, and scene geometry. In an embodiment, one or more of the scene geometry, scene properties, and antenna characteristics are computed by a differentiable parametric function, such as a neural network, etc. and parameters of the differentiable parametric function are learned using the differentiable ray tracing.

Claims (31)

1 . A computer-implemented method, comprising:

computing, by a differentiable ray tracer, simulated radio characteristics for a three-dimensional (3D) scene based on configured parameters and at least one trainable parameter corresponding to a scene property, wherein for each ray intersection point in the 3D scene, a neural component estimates the at least one trainable parameter; and

updating weights applied by the neural component to estimate the at least one trainable parameter using gradient-based optimization to minimize a loss function of the simulated radio characteristics and reference radio characteristics, wherein the at least one trainable parameter comprises a scattering pattern that is modeled as a linear combination of components on a hemisphere.

2 . The computer-implemented method of claim 1 , wherein the neural component generates an embedding vector used to estimate the at least one trainable parameter.

3 . The computer-implemented method of claim 1 , wherein each ray intersection point is encoded into a higher dimension space for input to the neural component.

4 . The computer-implemented method of claim 1 , wherein each ray intersection point is encoded using a multiresolution hash grid for input to the neural component.

5 . The computer-implemented method of claim 1 , wherein each ray intersection point is normalized to a unit cube and encoded into a higher dimension space for input to the neural component.

6 . The computer-implemented method of claim 1 , wherein each ray intersection point comprises at least one angle relative to a surface in the 3D scene at the intersection point.

7 . The computer-implemented method of claim 1 , further comprising updating the weights to modify at least one of a meta material, a reconfigurable intelligent surface, an antenna pattern, an antenna orientation, and an antenna position.

8 . The computer-implemented method of claim 1 , wherein the configured parameters or the at least one trainable parameter include one or more of scene geometry, configuration of reconfigurable intelligent surfaces and meta materials, antenna patterns, array geometries, and transmitter and receiver orientations and positions.

9 . The computer-implemented method of claim 1 , wherein the scene property comprises at least one of relative permittivity, reflection coefficients, transmission coefficients, conductivity, effective roughness, and permeability of object surfaces and scattering functions.

10 . The computer-implemented method of claim 1 , wherein the at least one trainable parameter comprises an antenna pattern that is modeled as a mixture of spherical Gaussian distributions.

11 . The computer-implemented method of claim 1 , wherein the differentiable ray tracer computes paths of electromagnetic waves.

12 . The computer-implemented method of claim 1 , wherein the simulated radio characteristics estimate qualities of a transmitted electromagnetic wave at a receiver.

13 . The computer-implemented method of claim 1 , wherein the simulated radio characteristics comprise one or more of channel impulse responses, channel frequency responses, path delays, path losses, angles of arrival, angles of departure, amplitudes, powers, delay spread, Doppler spread, angular spread, power-delay-angular profile, and a number of paths.

14 . The computer-implemented method of claim 1 , wherein the reference radio characteristics are measurements taken at different locations in the 3D scene.

15 . The computer-implemented method of claim 1 , wherein at least one of the steps of computing or updating is performed on a server or in a data center and the simulated radio characteristics or an image generated from the simulated radio characteristics is streamed to a user device.

16 . The computer-implemented method of claim 1 , wherein at least one of the steps of computing or updating is performed within a cloud computing environment.

17 . The computer-implemented method of claim 1 , wherein at least one of the steps of computing or updating is performed for training, testing, or certifying a neural network employed in a machine, robot, or autonomous vehicle.

18 . The computer-implemented method of claim 1 , wherein at least one of the steps of computing or updating is performed on a virtual machine comprising a portion of a graphics processing unit.

19 . A system, comprising:

a memory that stores reference radio characteristics; and

a processor that is connected to the memory, wherein the processor is configured to

produce simulated radio characteristics for a three-dimensional scene (3D) by:

computing, by a differentiable ray tracer, the simulated radio characteristics for the 3D scene based on configured parameters and at least one trainable parameter corresponding to a scene property, wherein for each ray intersection point in the 3D scene, a neural component estimates the at least one trainable parameter; and

updating weights applied by the neural component to estimate the at least one trainable parameter using gradient-based optimization to minimize a loss function of the simulated radio characteristics and the reference radio characteristics, wherein the at least one trainable parameter comprises a scattering pattern that is modeled as a linear combination of components on a hemisphere.

20 . The system of claim 19 , wherein the differentiable ray tracer computes paths of electromagnetic waves.

21 . A non-transitory computer-readable mediummedia storing computer instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of:

computing, by a differentiable ray tracer, simulated radio characteristics for a three-dimensional (3D) scene based on configured parameters and at least one trainable parameter corresponding to a scene property, wherein for each ray intersection point in the 3D scene, a neural component estimates the at least one trainable parameter; and

updating weights applied by the neural component to estimate the at least one trainable parameter using gradient-based optimization to minimize a loss function of the simulated radio characteristics and reference radio characteristics, wherein the at least one trainable parameter comprises a scattering pattern that is modeled as a linear combination of components on a hemisphere.

22 . The non-transitory computer-readable medium of claim 21 , wherein the differentiable ray tracer computes paths of electromagnetic waves.

Assignments (1)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded May 3, 2024
From: HOYDIS, JAKOB RICHARD; AOUDIA, FAYCAL AIT; CAMMERER, SEBASTIAN; KELLER, ALEXANDER GEORGE; NIMIER-DAVID, MERLIN; BINDER, NIKOLAUS; MARCUS MARTINEZ, GUILLERMO ANIBAL
To: NVIDIA CORPORATION
Reel/Frame 067304/0389 →
Continuity (2)
Provisional Application 63585914 · Sep 27, 2023
Related Publication 20250104329A1 · Mar 27, 2025
References Cited (196)
US 6249252B1 · Dupray et al. · 2001 [cited by applicant]
US 6487417B1 · Rossoni et al. · 2002 [cited by applicant]
US 6636743B1 · Vicharelli et al. · 2003 [cited by applicant]
US 7274332B1 · Dupray et al. · 2007 [cited by applicant]
US 7313402B1 · Rahman et al. · 2007 [cited by applicant]
US 8509809B2 · Hirsch et al. · 2013 [cited by applicant]
US 8768344B2 · Naguib et al. · 2014 [cited by applicant]
US 8948742B2 · Horton et al. · 2015 [cited by applicant]
US 8994591B2 · Dupray et al. · 2015 [cited by applicant]
US 9080889B2 · Shrum et al. · 2015 [cited by applicant]
US 10224991B2 · Nair et al. · 2019 [cited by applicant]
US 11252731B1 · Levitsky · 2022 [cited by applicant]
US 11863266B2 · Mo et al. · 2024 [cited by applicant]
US 12119914B2 · Chawa et al. · 2024 [cited by applicant]
US 12339366B2 · Chai et al. · 2025 [cited by applicant]
US 12348983B1 · Lin et al. · 2025 [cited by applicant]
US 12362472B2 · McCandless et al. · 2025 [cited by applicant]
US 12425987B2 · Black et al. · 2025 [cited by applicant]
US 20010022558A1 · Karr et al. · 2001 [cited by applicant]
US 20020002046A1 · Okanoue et al. · 2002 [cited by applicant]
US 20040266457A1 · Dupray et al. · 2004 [cited by applicant]
US 20060070113A1 · Bhagwat et al. · 2006 [cited by applicant]
US 20070019769A1 · Green et al. · 2007 [cited by applicant]
US 20070177680A1 · Green et al. · 2007 [cited by applicant]
US 20090076788A1 · Sugahara et al. · 2009 [cited by applicant]
US 20100003991A1 · Pao et al. · 2010 [cited by applicant]
US 20110021156A1 · Kobayashi et al. · 2011 [cited by applicant]
US 20110156957A1 · Waite et al. · 2011 [cited by applicant]
US 20110244901A1 · Sugahara et al. · 2011 [cited by applicant]
US 20110287778A1 · Levin et al. · 2011 [cited by applicant]
US 20110287784A1 · Levin et al. · 2011 [cited by applicant]
US 20110287801A1 · Levin et al. · 2011 [cited by applicant]
US 20130155102A1 · Gonia et al. · 2013 [cited by applicant]
US 20130285855A1 · Dupray et al. · 2013 [cited by applicant]
US 20130342565A1 · Sridhara et al. · 2013 [cited by applicant]
US 20140179340A1 · Do et al. · 2014 [cited by applicant]
US 20140320348A1 · Ly Nguyen et al. · 2014 [cited by applicant]
US 20150133167A1 · Edge et al. · 2015 [cited by applicant]
US 20160077190A1 · Julian · 2016 [cited by applicant]
US 20160088440A1 · Palanki et al. · 2016 [cited by applicant]
US 20160188631A1 · Deb et al. · 2016 [cited by applicant]
US 20180093183A1 · Leblanc · 2018 [cited by examiner]
US 20180138996A1 · Lee et al. · 2018 [cited by applicant]
US 20180139623A1 · Parlk et al. · 2018 [cited by applicant]
US 20180164400A1 · Wirola et al. · 2018 [cited by applicant]
US 20180266826A1 · Wang et al. · 2018 [cited by applicant]
US 20190005166A1 · Yamauchi et al. · 2019 [cited by applicant]
US 20190021068A1 · Yuan et al. · 2019 [cited by applicant]
US 20190150006A1 · Yang et al. · 2019 [cited by applicant]
US 20190222652A1 · Graefe et al. · 2019 [cited by applicant]
US 20190253900A1 · Narasimha et al. · 2019 [cited by applicant]
US 20190342763A1 · Jung et al. · 2019 [cited by applicant]
US 20190357056A1 · An et al. · 2019 [cited by applicant]
US 20190372644A1 · Chen et al. · 2019 [cited by applicant]
US 20190373595A1 · Sadiq et al. · 2019 [cited by applicant]
US 20190380090A1 · Kim et al. · 2019 [cited by applicant]
US 20200106477A1 · Nanni et al. · 2020 [cited by applicant]
US 20200311985A1 · Jeong et al. · 2020 [cited by applicant]
US 20200372699A1 · Raposo Subtil · 2020 [cited by examiner]
US 20200405393A1 · Villongco · 2020 [cited by applicant]
US 20210044366A1 · Cody et al. · 2021 [cited by applicant]
US 20210044988A1 · Park et al. · 2021 [cited by applicant]
US 20210051678A1 · Suzaki et al. · 2021 [cited by applicant]
US 20210068170A1 · Sadhu et al. · 2021 [cited by applicant]
US 20210167878A1 · Lee et al. · 2021 [cited by applicant]
US 20210263128A1 · Smith et al. · 2021 [cited by applicant]
US 20210266758A1 · Fujiwaka et al. · 2021 [cited by applicant]
US 20210329478A1 · Nishikawa et al. · 2021 [cited by applicant]
US 20210360456A1 · Ratnam et al. · 2021 [cited by applicant]
US 20210376905A1 · Zhou et al. · 2021 [cited by applicant]
US 20210409966A1 · Lee et al. · 2021 [cited by applicant]
US 20220076061A1 · Fiterman · 2022 [cited by applicant]
US 20220103272A1 · Dietrich et al. · 2022 [cited by applicant]
US 20220107383A1 · Rappaport et al. · 2022 [cited by applicant]
US 20220121789A1 · Kanza et al. · 2022 [cited by applicant]
US 20220174520A1 · Sakamoto et al. · 2022 [cited by applicant]
US 20220182840A1 · Ohtsuji et al. · 2022 [cited by applicant]
US 20220264514A1 · Butt et al. · 2022 [cited by applicant]
US 20220345185A1 · Michalopoulos et al. · 2022 [cited by applicant]
US 20220352933A1 · Rakib et al. · 2022 [cited by applicant]
US 20220377568A1 · Kanza et al. · 2022 [cited by applicant]
US 20220383118A1 · Nair et al. · 2022 [cited by applicant]
US 20230037893A1 · Vankayala et al. · 2023 [cited by applicant]
US 20230059198A1 · Moriuchi et al. · 2023 [cited by applicant]
US 20230062443A1 · Chakraborty et al. · 2023 [cited by applicant]
US 20230075165A1 · Lindquist et al. · 2023 [cited by applicant]
US 20230096553A1 · Metwaly Saad et al. · 2023 [cited by applicant]
US 20230147351A1 · Machin et al. · 2023 [cited by applicant]
US 20230147767A1 · Hiraoka et al. · 2023 [cited by applicant]
US 20230154145A1 · Zakharov et al. · 2023 [cited by applicant]
US 20230155662A1 · Barbu et al. · 2023 [cited by applicant]
US 20230169241A1 · Liu et al. · 2023 [cited by applicant]
US 20230177327A1 · Pillai et al. · 2023 [cited by applicant]
US 20230194279A1 · Kakosyan et al. · 2023 [cited by applicant]
US 20230231635A1 · Okamoto et al. · 2023 [cited by applicant]
US 20230284074A1 · Kundu et al. · 2023 [cited by applicant]
US 20230316062A1 · Balevi et al. · 2023 [cited by applicant]
US 20230324501A1 · Feigl et al. · 2023 [cited by applicant]
US 20230361897A1 · Racz et al. · 2023 [cited by applicant]
US 20230403672A1 · Takeuchi et al. · 2023 [cited by applicant]
US 20240070353A1 · Wang et al. · 2024 [cited by applicant]
US 20240095473A1 · Sakurai et al. · 2024 [cited by applicant]
US 20240111937A1 · Jaiswal et al. · 2024 [cited by applicant]
US 20240112009A1 · Orekondy et al. · 2024 [cited by applicant]
US 20240118954A1 · Boccuzzi et al. · 2024 [cited by applicant]
US 20240129751A1 · Belgiovine et al. · 2024 [cited by applicant]
US 20240155369A1 · Inomata et al. · 2024 [cited by applicant]
US 20240155385A1 · Inomata et al. · 2024 [cited by applicant]
US 20240214093A1 · Kim et al. · 2024 [cited by applicant]
US 20240265619A1 · Aoudia et al. · 2024 [cited by applicant]
US 20240267173A1 · Paz et al. · 2024 [cited by applicant]
US 20240284522A1 · Dutta et al. · 2024 [cited by applicant]
US 20240323719A1 · Corgan · 2024 [cited by examiner]
US 20240361469A1 · Dupray et al. · 2024 [cited by applicant]
US 20240364437A1 · Hehn et al. · 2024 [cited by applicant]
US 20240364565A1 · Gilbert et al. · 2024 [cited by applicant]
US 20240388472A1 · Hirzallah et al. · 2024 [cited by applicant]
US 20240411471A1 · Luo et al. · 2024 [cited by applicant]
US 20240430719A1 · Higuchi et al. · 2024 [cited by applicant]
US 20250005856A1 · Qiu et al. · 2025 [cited by applicant]
US 20250067897A1 · Gan et al. · 2025 [cited by applicant]
US 20250078723A1 · Chen · 2025 [cited by applicant]
US 20250104329A1 · Hoydis et al. · 2025 [cited by applicant]
US 20250113234A1 · Alanen et al. · 2025 [cited by applicant]
US 20250175272A1 · Hehn et al. · 2025 [cited by applicant]
US 20250182379A1 · Cammerer et al. · 2025 [cited by applicant]
US 20250183943A1 · Wong et al. · 2025 [cited by applicant]
US 20250184875A1 · Krunz et al. · 2025 [cited by applicant]
US 20250192853A1 · Cho et al. · 2025 [cited by applicant]
US 20250192855A1 · Cho et al. · 2025 [cited by applicant]
US 20250234331A1 · Alkhateeb et al. · 2025 [cited by applicant]
US 20250240765A1 · Hirzallah et al. · 2025 [cited by applicant]
US 20250245392A1 · Park et al. · 2025 [cited by applicant]
US 20250251480A1 · Lin et al. · 2025 [cited by applicant]
US 20250259374A1 · Fazal et al. · 2025 [cited by applicant]
US 20250260948A1 · Hill et al. · 2025 [cited by applicant]
US 20250280383A1 · Reddy et al. · 2025 [cited by applicant]
US 20250300751A1 · Zhang et al. · 2025 [cited by applicant]
US 20250310784A1 · Nakahira et al. · 2025 [cited by applicant]
US 20250316016A1 · Nguyen et al. · 2025 [cited by applicant]
US 20250317224A1 · Shah et al. · 2025 [cited by applicant]
US 20250327895A1 · Popov et al. · 2025 [cited by applicant]
Yun, Z., et al., “Ray tracing for radio propagation modeling: Principles and applications,” IEEE Access, vol. 3, Jul. 2015. [cited by applicant]
Bourdoux, A., et al., “6G White Paper on Localization and Sensing,” University of Oulu: 6G Research Visions, Jun. 2020. [cited by applicant]
Alkhateeb, A., et al., “DeepSense 6G: A large-scale real-world multi-model sensing and communication dataset,” arXiv Preprint arXiv:2211.09769, 2022. [cited by applicant]
Renzo, M.D., et al., “Smart radio environments empowered by reconfigurable AI meta-surfaces: An idea whose time has come,” vol. 2019, No. 1, p. 129, May 2019. [cited by applicant]
Studer, C., et al., “Channel charting: Locating users within the radio environment using channel state information,” IEEE Access, vol. 6, pp. 47 682-47 698, 2018. [cited by applicant]
Hoydis, J., et al., “Toward a 6G AI-Native Air Interface,” IEEE Commun. Mag., vol. 59, No. 5, pp. 76-81, May 2021. [cited by applicant]
Alkhateeb, A., et al., “Real-time digital twins: Vision and research directions for 6G and beyond,” arXiv e-prints, pp. arXiv-2301, 2023. [cited by applicant]
Lin, X., et al., “6G Digital Twin Networks: From Theory to Practice,” arXiv preprint arXiv:2212.02032, 2022. [cited by applicant]
Bakirtzis, S., et al., “DeepRay: Deep Learning Meets Ray-Tracing,” in 16th European Conf. Ant. Prop. (EuCAP), Madrid, Spain, Mar. 2022, pp. 1-5. [cited by applicant]
Azpilicueta, L., et al., “A ray launching-neural network approach for radio wave propagation analysis in complex indoor environments,” IEEE TRans. Antennas Propag. vol. 62, No. 5, pp. 2777-2786, Feb. 2014. [cited by applicant]
Zhang, X., et al., “Cellular network radio propagation modeling with deep convolutional neural networks,” in Proc. 26th ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining, Aug. 2020, pp. 2378-2386. [cited by applicant]
Levie, R., et al., “RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks,” IEEE Trans. Wireless Commun., vol. 20, No. 6, pp. 4001-4015, Feb. 2021. [cited by applicant]
Eller, L., et al., “A Deep Learning Network Planner: Propagation Modeling Using Real-World Measurements and a 3D City Model,” IEEE Access, vol. 10, pp. 122 182-122 196, Nov. 2022. [cited by applicant]
Gupta, A., et al., “Machine Learning-Based Urban Canyon Path Loss Prediction Using 28 GHz Manhattan Measurements,” IEEE Trans. Antennas Propag., vol. 70, No. 6, pp. 4096-4111, Feb. 2022. [cited by applicant]
Orekondy, T., et al., “WiNeRT: Towards neural ray tracing for wireless channel modelling an differentiable simulations,” In International Conference on Learning Representations, 2023. [cited by applicant]
Muller, T., et al., “Instant neural graphics primitives with a multiresolution hash encoding,” ACM Trans. Graph., vol. 41, No. 4, pp. 102:1-102:15, Jul. 2022. [cited by applicant]
Li, T.M., et al., “Differentiable Monte Carlo ray tracing through edge sampling,” ACM Trans. Graph, vol. 37, No. 6, Dec. 2018. [cited by applicant]
Jakob, W., et al., “Dr. Jit: A just-in-time compiler for differentiable rendering,” Transactions on Graphics (Proceedings of SIGGRAPH), vol. 41, No. 4, Jul. 2022. [cited by applicant]
Li, Z., et al., “Neuralangelo: High-fidelity neural surface reconstruction,” in IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2023. [cited by applicant]
Kanhere, O., et al., “Calibration of NYURay, a 3D mmWave and sub-THz ray tracer using indoor, outdoor, and factory channel measurements,” arXiv preprint arXiv:2302.12380, Feb. 2023. [cited by applicant]
Jemai, J., et al., “Calibration of a UWB sub-band channel model using simulated annealing,” IEEE Trans. Antennas Propag. vol. 57, No. 10, pp. 3439-3443, Oct. 2009. [cited by applicant]
Gan, M., et al., “Calibration of indoor UWB sub-band divided ray tracing using multiobjective simulated annealing,” in IEEE Int. Conf. Commun. (ICC), Sydney, NSW, Australia, Jun. 2014, pp. 4844-4849. [cited by applicant]
Charbonnier, R., et al., “Calibration of ray-tracing with diffuse scattering against 28-GHz directional urban channel measurements,” IEEE Trans. Veh. Technol., vol. 69, No. 12, pp. 14 264-14 276, Oct. 2020. [cited by applicant]
Bhatia, G.S., et al., “Tuning of ray-based channel model for 5G indoor industrial scenarios,” in IEEE Int. Mediterranean Conf. Commun. Network (MeditCom), Dubrovnik, Croatia, Sep. 2023, pp. 311-316. [cited by applicant]
Hoydis, J., et al., “Sionna RT: Differentiable Ray Tracing for Radio Propagation Modeling,” arXiv preprint, Mar. 2023. [cited by applicant]
Kingma, D.P., et al., “Adam: A method for stochastic optimization,” arxiv preprint arXiv:1412.6980, 2014. [cited by applicant]
Raissi, M., et al., “Physics-informed neural networks: A deep learning framework for solving forward an dinverse problems involving nonlinear partial differential equations,” Journal of Computational physics, vol. 378, … [cited by applicant]
Hoydis, J., et al., “Learning radio environments by differentiable ray tracing,” Dec. 2023. [cited by applicant]
Fugen, T., et al., “Capability of 3D ray tracing for defining parameter sets for the specification of future mobile communications systems,” IEEE Trans. Antennas Propag., vol. 54, No. 11, pp. 3125-3137, Nov. 2006. [cited by applicant]
Degli-Esposti, V., et al., “Measurement and modelling of scattering from buildings,” IEEE Trans. Antennas Propag., vol. 55, No. 1, pp. 143-153, Jan. 2007. [cited by applicant]
Degli-Esposti, V., et al., “Analysis and modeling on co-and cross-polarized urban radio propagation for dual-polarized MOMO wireless systems,” IEEE Trans. Antennas Propag., vol. 59, No. 11, pp. 4247-4256, Aug. 2011. [cited by applicant]
Deschamps, G.A., et al., “Ray techniques in electromagnetics,” Proc. IEEE, vol. 60, No. 9, pp. 1022-1035, Sep. 1972. [cited by applicant]
Kouyoumjian, R.G., et al., “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE, vol. 62, No. 11, pp. 1448-1461, Nov. 1974. [cited by applicant]
Luebbers, R., et al., “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE TRans. Anennas Propag., vol. 32, No. 1, pp. 70-76, Jan. 1984. [cited by applicant]
Keller, J.B., et al., “Geometrical theory of diffraction,” Journal of the Optical Society of America, vol. 52, No. 2, pp. 116-130, Feb. 1962. [cited by applicant]
Nicolet, B., et al., “Large steps in inverse rendering of geometry,” ACM Trans. Graph., vol. 40, No. 6, Dec. 2021. [cited by applicant]
Meder, J., et al., “Hemispherical Gaussians for accurate light integration,” in Proc. Int. Conf. Computer Vision and Graphics (ICCVG), Warsaw, Poland, Step. 2018, pp. 3-15. [cited by applicant]
Choromanska, A., et al., “The loss surfaces of multilayer networks,” in Proc. Int. Conf. Artificial Intelligence and Statistics (PMLR), vol. 38, San Diego, CA, USA, May 9-12, 2015, pp. 192-204. [cited by applicant]
Mildenhall, B., et al., “NeRF: Representing scenes as neural radiance fields for view synthesis,” Communications of the ACM, vol. 65, No. 1, pp. 1-6, Jan. 2021. [cited by applicant]
Tancik, M., et al., “Fourier features let networks learn high frequency functions in low dimensional domains,” In Advances in Neural Information Processing Systems, vol. 33, Curran Associates, Inc., Aug. 2020, pp. 7537-… [cited by applicant]
Euchner, F., et al., A distributed massive MIMO channel counder for “Big CSI Data-driven machine learning,” arXiv:2206.15302v1, Jun. 30, 2022. [cited by applicant]
Yun, R., et al., “Ray Tracing for Radio Propagation Modeling: Principles and Applications,” IEEE Access, vol. 3, 2015, pp. 1089-1100. [cited by applicant]
ITU, “Recommendation ITU-R, P.2040-3: Effects of building materials and structures on radiowave propagation above about 100 MHz,” Tech Rep., Aug. 2023. [cited by applicant]
ITU, “Recommendation ITU-R, P.526-15: Propagation by diffraction,” Tech. Rep., Oct. 2019. [cited by applicant]
Euchner, F., et al., “dichasus-dcxx:Institute hallway with known 3D model, distributed antennas,” https://dichasus.inue.uni-stuttgart.de/datasets/data/dichasus-dcxx/, Dec. 2023. [cited by applicant]
McKown et al., “Ray tracing as a design tool for radio networks,” in IEEE Networlk, vol. 5, No. 6, pp. 27-30, Nov. 1991. [cited by applicant]
Sheikh et al., “Measurements and Ray Tracing Simulations: Impact of Different Antenna Positions on Meeting Room Coverage at 60 GHz,” 2020 European Conference on Networlks and Communications (EuCNC), Dubrovnik, Croatia, … [cited by applicant]
Rustako et al., “Radio propagation at microwave frequencies for line-of-sight microcellular mobile and personal communications,” in IEEE Transactions on Vehicular Technology, vol. 40, No. 1, pp. 203-210, Feb. 1991. [cited by applicant]
Fugen et al., “Capability of 3-D Ray Tracing for Defining Parameter Sets for the Specification of Future Mobile Communications Systems,” in IEEE Transactions on Antennas and Propagation, vol. 54, No. 11, pp. 3125-3137, … [cited by applicant]
Christensen et al., “Ray differentials and multiresolution geometry caching for distribution ray tracing in complex scenes,” Computer Graphics Forum. vol. 22. No. 3. Oxford, UK: Blackwell Publishing, Inc, 2003. [cited by applicant]
Chatterjee et al., “Convergence of gradient descent for deep neural networks,” arXiv preprint arXiv, Dec. 17, 2022. [cited by applicant]
Hou et al., “A new method for radio wave propagation prediction based on finite integral method and machine learning,” 2017 IEEE 5th International Symposium on Electromagnetic Compatibility (EMC—Beijing), Beijing, China… [cited by applicant]
Chang et al., “Propagation Analysis with Ray Tracing Method for High Speed Trains Environment at 60 GHz,” IEEE 81st Vehicular Technology Conference (VTC Spring), Glasgow, UK, pp. 1-5, 2015. [cited by applicant]
Lgehy, “Tracing ray differentials,” In Proceedings of the 26th annual conference on Computer graphics and interactive techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., USA, 179-186, 1999. [cited by applicant]