# Ray-Tracing Methods and Simulations

### Ray-tracing methods use discrete rays to represent advancing wavefronts as they propagate from a transmitter through a scene.

Rays interact with geometry in the scene through reflections, diffractions, and transmissions.  Rays that reach a receiver represent the paths that waves may travel from the transmitter to the receiver.  The electric field, received power, and other electromagnetic quantities can be calculated through the superposition of the contributions from all of the propagating waves that reach that receiver point.

There are two dominant methods used in ray-tracing, explained below.

## Shooting-and-Bouncing Rays (SBR):

This approach shoots rays in all directions, usually with a fixed angular spacing, and follows them as they interact and split further into additional paths, reflecting from surfaces, transmitting through them, or diffracting from wedges.

## Image Theory:

From a predefined pair of end points (e.g., a transmitter and receiver), this approach finds all of the paths between the points, using the method of images to determine where ray-tracing interactions will occur.  The approach is then repeated for each subsequent pair of points in a calculation.

###### Figure 2: Image Theory

SBR is a relatively efficient approach for finding ray-tracing paths through a complex scene, but as rays propagate, they continuously spread, and they risk missing interactions with smaller objects while also incurring increasing error in the calculation of path length and phase.  Image theory, on the other hand, is a more precise approach, but because it must be repeated for each pair of Tx and Rx points, it can be very computationally intensive in a scene with large numbers of facets and large numbers of transmit and receive pairs.

For these reasons, Remcom’s most advanced ray-tracing models in Wireless InSite® and WaveFarer®, which are based on the X3D ray-tracer, combine the two techniques.  SBR is used to find the initial chains of interactions, using GPU-accelerated ray-tracing.  Image theory is then used to perform an exact path correction (EPC), finding the precise paths between each point pair.  The result is the capability to efficiently find propagation paths, while providing precise calculations of time of arrival, phase, and polarization.  Precise estimates of these quantities have become increasingly important, if not required, for many current problems of interest, including MIMO analysis, fading due to mobility, and Doppler.

The way in which rays are traced and the propagation paths used depends significantly on the physics techniques that will be used to calculate the electromagnetic fields and power at receiver antennas.  Two broad categories of techniques include (1) Geometric Optics and the Uniform Theory of Diffraction, and (2) Physical Optics augmented by the Method of Equivalent Currents or other similar techniques to adjust for edge effects.

#### Ray-Tracing with Geometric Optics and UTD

Geometric optics and the uniform theory of diffraction (GO/UTD) provide one of the dominant combined sets of methods used for calculating electromagnetic fields using ray-tracing.