Advanced Electromagnetic Ray Tracing Methods

Advanced Ray-Tracing Algorithms

Fig 1: Visualization of ray paths in a simulation for characterizing wireless link in an urban environment

Ray-tracing is a convenient method to characterize wave propagation in electrically large and complex environments.
Computational costs much smaller compared to full-wave solvers such as FEM or MoM.
No increase in run-time or memory with increasing frequency.
Great potential for parallelization with GPU: Fast simulations.
Typical applications:
- Radar cross section (RCS) computations.
- Wireless network simulations in virtual environments.
- Automotive applications: radar, communication.
- Planning of indoor/outdoor mobile systems.

Fig 2: Vitual environment for V2V communication

Fig 3: RCS calculation and accuracy comparsion with ray-tracing and MoM

Principles

Mostly based on Geometrical Optics and Uniform Theory of Diffraction (GO/UTD).
Physical Optics (PO) for scattering problems.

Geometrical Optics Approach

Fig 4: Asymptotic ray tubes with caustics

Approximation of Maxwell’s equations for high-frequency (ω→∞).
Propagation of energy along straight lines, i.e, the rays.
Conservation of energy: Diverging ray tubes.
Propagation path satisfies the principle of least time (Fermat’s principle).

Reflection & Refractions (Snell’s Law)

Fig 5a: Illustration of Snell’s Law for TE polarized incident waves.

Fig 5b: Illustration of Snell’s Law for TM polarized incident waves.

Uniform Theory of Diffraction

Fig 6: Illustration of Keller cone (Keller, 1962)

Fields in shadow regions are ignored in GO.
UTD is utilized to compute those contributions.
Straight edges are considered.
A single incident ray upon the edge may create thousands of new rays on Keller cone.

Generation of Rays

Two approaches

1. Method of Images

All feasible ray paths between receiver-transmitter are obtained deterministically by image theory.

Preprocessing required.

Complexity increases exponentially with the number of the interactions.

Fig 7a: Illustration of Method of Images

2. Shooting and Bouncing Rays (SBR)

Launch many rays in arbitrary directions.

Rays are traced until stopping criteria is met.

No preprocessing required.

Linear increase in complexity with the number of interactions.

Reception of Rays

Fig 8: Illustration of the effects of different reception sphere sizes. Large sphere (Rx1) captures presumably incorrect rays while small sphere (Rx3) captures nothing. Rx2 is the optimal sphere.

Spheres are placed at receiver locations.
Rays are collected if they hit the sphere.
Sphere size should be chosen carefully.
Large spheres: Many incorrect contributions might be captured.
Small spheres: Relevant contributions might be missed.
Number of ray launches should be large if the environment is large and complex.

Novel Approaches

Typical Problems of Traditional Ray-Tracing Techniques

Problems with reception spheres:
- Reception spheres should typically be small to prevent incorrect rays to be captured.
- Small spheres implies a large number of ray launches to ensure relevant contributions are captured.
- Large number of ray launches → increase in complexity.
Problems with UTD-based diffraction computations:
- The number of rays may grow rapidly, especially when multiple diffractions are involved.
- Accuracy problems with multiple diffraction scenarios when the propagation path is at the optical boundaries.

TUM HFT Approach

Instead of launching rays from a single antenna (unidirectional), both antennas are used for ray launching (bidirectional).
Rays are captured on a large interaction surface, instead of small spheres.
Coupling is computed by evaluating reciprocity integrals on the surface.

Fig 9a: Illustration of Bidirectional ray-tracing methods

Fig 9b: Illustration of Unidirectional ray-tracing methods

Bidirectional Ray-Tracing for Diffraction Scenarios

A large, open surface is placed above the diffraction edge(s) where the antennas can directly hit the surface.
No new rays are generated, computation time does not increase.

Fig 10a: Illustration of single diffraction scenarios

Fig 10b: Illustration of double diffraction scenarios

Examples & Results

The bidirectional ray-tracing method demonstrates a better accuracy than unidirectional ray-tracing when the scenario grows in size, i.e., the distance between the antennas.

Fig 11a: Schema of a Two Ray Ground Reflection Model

Fig 11b: Diagram of a Two Ray Ground Reflection Model

Double knife-edge diffractions near optical boundaries can be simulated with a better accuracy and by tracing a smaller number of rays, hence, with a smaller computational effort.

Fig 13: Path Gain Difference with Vogler

Application Examples

Characterization of Channel Aging Effects in Massive MIMO

Massive MIMO relies on accurate channel information for beamforming.
Channel state information becomes quickly obsolete when users are mobile. Channel aging → reduced performance.
Small urban scenario with 64 mobile users (vehicles).
Channel state information is not updated.
Decline of the average data rate has been investigated.
Comparisons with a statistical channel aging model.
Utilizing large number of TX antennas (256 vs. 64) alleviates the drastic decay.

Fig 14: Average user data rate with 256 antennas

Fig 15: Average user data rate with 64 antennas

Conclusion

Improvements over the state-of-the-art in terms of computational speed and accuracy.

Useful in practically relevant propagation environments, e.g., urban, suburban.

Various application areas: Massive MIMO, Radar, V2X communications.

Literature

Z. Yun and M. F. Iskander, "Ray Tracing for Radio Propagation Modeling: Principles and Applications", IEEE Access, vol. 3, pp. 1089-1100, 2015.
R. Kouyoumjian, P. Pathak, "A Uniform Geometrical theory of Diffraction for an Edge in a Perfectly Conducting Surface", Proceedings of the IEEE, vol. 62, no. 11, 1974.
R. Brem and T. F. Eibert, "A Shooting and Bouncing Ray (SBR) Modeling Framework Involving Dielectrics and Perfect Conductors", IEEE Transactions on Antennas and Propagation, vol. 63, no. 8, pp. 3599-3609, 2015.
M. S. L. Mocker, M. Schiller, R. Brem, Z. Sun, H. Tazi, T. F. Eibert and A. Knoll, "Combination of a Full-Wave Method and Ray Tracing for Radiation Pattern Simulations of Antennas on Vehicle Roofs", European Conference on Antennas and Propagation (EuCAP), Lisbon, 2015.
M. M. Taygur, I. O. Sukharevsky and T. F. Eibert, "A Bidirectional Ray-Tracing Method for Antenna Coupling Evaluation Based on the Reciprocity Theorem", IEEE Transactions on Antennas and Propagation, vol. 66, no. 12, pp. 6654-6664, 2018.
M. M. Taygur, I. O. Sukharevsky and T. F. Eibert, "Computation of Antenna Transfer Functions with a Bidirectional Ray-Tracing Algorithm Utilizing Antenna Reciprocity," URSI Atlantic Radio Science Conference, Gran Canaria, 2018.