# Advanced Electromagnetic Ray Tracing Methods

## Advanced Ray-Tracing Algorithms

- 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.

## Principles

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

### Geometrical Optics Approach

**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)

### Uniform Theory of Diffraction

- 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 pathsbetween receiver-transmitter are obtaineddeterministicallybyimage theory.Preprocessingrequired.Complexityincreasesexponentiallywith the number of the interactions.

2. **Shooting and Bouncing Rays (SBR)**

- Launch
many raysinarbitrarydirections.- Rays are traced until stopping criteria is met.
No preprocessingrequired.Linearincrease incomplexitywith the number of interactions.

### Reception of Rays

**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**.

- The number of rays may grow rapidly, especially when

### 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.

### 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.

### 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.

- 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.**

## 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.

## 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.