# RayTracing

Ray tracing propagation model

## Description

Ray tracing models compute propagation paths using 3-D environment geometry [1][2] . Represent a ray tracing model by
using a `RayTracing`

object.

Ray tracing models:

Are valid from 100 MHz to 100 GHz.

Compute multiple propagation paths. Other propagation models compute only single propagation paths.

Support 3-D outdoor and indoor environments.

Determine the path loss and phase shift of each ray using electromagnetic analysis, including tracing the horizontal and vertical polarizations of a signal through the propagation path. The path loss includes free-space loss and reflection losses. For each reflection, the model calculates losses on the horizontal and vertical polarizations by using the Fresnel equation, the incident angle, and the relative permittivity and conductivity of the surface material [3][4] at the specified frequency.

You can create ray tracing models that use either the shooting and bouncing rays (SBR) method or the image method.

## Creation

Create a `RayTracing`

object by using the `propagationModel`

function.

## Properties

### Ray Tracing

`Method`

— Ray tracing method

`"sbr"`

(default) | `"image"`

Ray tracing method, specified as one of these values:

`"sbr"`

— Use the shooting and bouncing rays (SBR) method, which supports up to 10 path reflections. The SBR method calculates an approximate number of propagation paths with exact geometric accuracy. The SBR method is generally faster than the image method. The model calculates path loss from free-space loss plus reflection losses due to material and antenna polarizations.`"image"`

— Use the image method, which supports up to 2 path reflections. The image method calculates an exact number of propagation paths with exact geometric accuracy. The model calculates path loss from free-space loss plus reflection losses due to material and antenna polarizations.

Specify the maximum number of path reflections by using the `MaxNumReflections`

property.

When both the image and SBR methods find the same path, the points along the path are the same within a tolerance of machine precision for single-precision floating-point values. For more information about differences between the image and SBR methods, see Choose a Propagation Model.

**Data Types: **`char`

| `string`

`AngularSeparation`

— Average number of degrees between launched rays

`"medium"`

(default) | `"high"`

| `"low"`

| numeric scalar in degrees in the range [0.05, 10]

Average number of degrees between launched rays, specified as
`"high"`

, `"medium"`

, `"low"`

, or
a numeric scalar in degrees in the range [0.05, 10]. If you specify a numeric value,
then the ray tracing algorithm might use a lower value than the value you
specify.

This table describes the behavior of the `"high"`

,
`"medium"`

, and `"low"`

options.

Option | Approximate Numeric Equivalent | Range of Numeric Values | Number of Launched Rays |
---|---|---|---|

`"high"` | 1.0781 | [0.9912, 1.1845] | 40,962 |

`"medium"` | 0.5391 | [0.4956, 0.5923] | 163,842 |

`"low"` | 0.2695 | [0.2478, 0.2961] | 655,362 |

To improve the accuracy of the number of paths found by the SBR method, decrease
the value of `AngularSeparation`

. Decreasing the value of
`AngularSeparation`

can increase the amount of time MATLAB^{®} requires to perform the analysis.

When you first use a given value of `AngularSeparation`

in a
MATLAB session, MATLAB caches the geodesic sphere associated with that value for the duration
of the session. As a result, the first use of that value of
`AngularSeparation`

takes longer than subsequent uses within the
same session. For more information about geodesic spheres, see Shooting and Bouncing Rays Method.

#### Tips

When creating coverage maps using the `coverage`

function, you can improve the results by choosing a lower angular separation.

#### Dependencies

To enable this argument, you must specify the `Method`

property
as `"sbr"`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `char`

| `string`

`MaxNumReflections`

— Maximum number of path reflections

`2`

(default) | integer in the range [0,10]

Maximum number of path reflections to search for using ray tracing, specified as
an integer. Supported values depend on the value of the `Method`

property.

When

`Method`

is`"image"`

, supported values are`0`

,`1`

, and`2`

.When

`Method`

is`"sbr"`

, supported values are in the range [0, 10].

**Data Types: **`double`

`CoordinateSystem`

— Coordinate system of map and site location

`"geographic"`

(default) | `"cartesian"`

Coordinate system of the site location, specified as
`"geographic"`

or `"cartesian"`

. If you specify
`"geographic"`

, define material types by using the `BuildingsMaterial`

and `TerrainMaterial`

properties. If you specify `"cartesian"`

, define material types by
using the `SurfaceMaterial`

property.

**Data Types: **`string`

| `char`

### Buildings Material

`BuildingsMaterial`

— Surface material of geographic buildings

`"concrete"`

(default) | `"perfect-reflector"`

| `"brick"`

| `"wood"`

| `"glass"`

| `"metal"`

| `"custom"`

Surface material of geographic buildings, specified as one of these values:
`"perfect-reflector"`

, `"concrete"`

,
`"brick"`

, `"wood"`

, `"glass"`

,
`"metal"`

, or `"custom"`

. The model uses the
material type to calculate reflection loss where propagation paths reflect off of
building surfaces. For more information, see ITU Permittivity and Conductivity Values for Common Materials.

When `BuildingsMaterial`

is `"custom"`

,
specify the material permittivity and conductivity by using the `BuildingsMaterialPermittivity`

and `BuildingsMaterialConductivity`

properties.

#### Dependencies

To enable `BuildingsMaterial`

, you must set `CoordinateSystem`

to `"geographic"`

.

**Data Types: **`char`

| `string`

`BuildingsMaterialPermittivity`

— Relative permittivity of surface materials of buildings

`5.31`

(default) | nonnegative scalar

Relative permittivity of the surface materials of the buildings, specified as a nonnegative scalar. Relative permittivity is expressed as a ratio of absolute material permittivity to the permittivity of vacuum. The model uses this value to calculate path loss due to reflection. The default value corresponds to concrete at 1.9 GHz.

#### Dependencies

To enable `BuildingsMaterialPermittivity`

, you must set
`CoordinateSystem`

to `"geographic"`

and `BuildingsMaterial`

to `"custom"`

.

**Data Types: **`double`

`BuildingsMaterialConductivity`

— Conductivity of surface materials of buildings

`0.0548`

(default) | nonnegative scalar

Conductivity of the surface materials of the buildings, specified as a nonnegative scalar in siemens per meter (S/m). The model uses this value to calculate path loss due to reflection. The default value corresponds to concrete at 1.9 GHz.

#### Dependencies

To enable `BuildingsMaterialConductivity`

, you must set
`CoordinateSystem`

to `"geographic"`

and `BuildingsMaterial`

to `"custom"`

.

**Data Types: **`double`

### Terrain Material

`TerrainMaterial`

— Surface material of geographic terrain

`"concrete"`

(default) | `"perfect-reflector"`

| `"brick"`

| `"water"`

| `"vegetation"`

| `"loam"`

| `"custom"`

Surface material of the geographic terrain, specified as one of these values:
`"perfect-reflector"`

, `"concrete"`

,
`"brick"`

, `"water"`

,
`"vegetation"`

, `"loam"`

, or
`"custom"`

. The model uses the material type to calculate
reflection loss where propagation paths reflect off of terrain surfaces. For more
information, see ITU Permittivity and Conductivity Values for Common Materials.

When `TerrainMaterial`

is `"custom"`

, specify
the material permittivity and conductivity by using the `TerrainMaterialPermittivity`

and `TerrainMaterialConductivity`

properties.

#### Dependencies

To enable `TerrainMaterial`

, you must set `CoordinateSystem`

to `"geographic"`

.

**Data Types: **`char`

| `string`

`TerrainMaterialPermittivity`

— Relative permittivity of terrain materials

`5.31`

(default) | nonnegative scalar

Relative permittivity of the terrain material, specified as a nonnegative scalar. Relative permittivity is expressed as a ratio of absolute material permittivity to the permittivity of vacuum. The model uses this value to calculate path loss due to reflection. The default value corresponds to concrete at 1.9 GHz.

#### Dependencies

To enable `TerrainMaterialPermittivity`

, you must set
`CoordinateSystem`

to `"geographic"`

and `TerrainMaterial`

to `"custom"`

.

**Data Types: **`double`

`TerrainMaterialConductivity`

— Conductivity of terrain materials

`0.0548`

(default) | nonnegative scalar

Conductivity of the terrain material, specified as a nonnegative scalar in siemens per meter (S/m). The model uses this value to calculate path loss due to reflection. The default value corresponds to concrete at 1.9 GHz.

#### Dependencies

To enable `TerrainMaterialConductivity`

, you must set
`CoordinateSystem`

to `"geographic"`

and set `TerrainMaterial`

to `"custom"`

.

**Data Types: **`double`

### Surface Material

`SurfaceMaterial`

— Surface material of Cartesian map surface

`"plasterboard"`

(default) | `"perfect-reflector"`

| `"ceilingboard"`

| `"chipboard"`

| `"floorboard"`

| `"concrete"`

| `"brick"`

| `"wood"`

| `"glass"`

| `"metal"`

| `"water"`

| `"vegetation"`

| `"loam"`

| `"custom"`

Surface material of Cartesian map surface, specified as one of these values:
`"plasterboard"`

,`"perfect-reflector"`

,
`"ceilingboard"`

, `"chipboard"`

,
`"floorboard"`

, `"concrete"`

,
`"brick"`

, `"wood"`

, `"glass"`

,
`"metal"`

, `"water"`

,
`"vegetation"`

, `"loam"`

, or
`"custom"`

. The model uses the material type to calculate
reflection loss where propagation paths reflect off of surfaces. For more information,
see ITU Permittivity and Conductivity Values for Common Materials.

When `SurfaceMaterial`

is `"custom"`

, specify
the material permittivity and conductivity by using the `SurfaceMaterialPermittivity`

and `SurfaceMaterialConductivity`

properties.

#### Dependencies

To enable `SurfaceMaterial`

, you must set `CoordinateSystem`

to `"cartesian"`

.

**Data Types: **`char`

| `string`

`SurfaceMaterialPermittivity`

— Relative permittivity of surface materials

`2.94`

(default) | nonnegative scalar

Relative permittivity of the surface material, specified as a nonnegative scalar. Relative permittivity is expressed as a ratio of absolute material permittivity to the permittivity of vacuum. The model uses this value to calculate path loss due to reflection. The default value corresponds to plaster board at 1.9 GHz.

#### Dependencies

To enable `SurfaceMaterialPermittivity`

, you must set
`CoordinateSystem`

to `"cartesian"`

and `SurfaceMaterial`

to `"custom"`

.

**Data Types: **`double`

`SurfaceMaterialConductivity`

— Conductivity of surface materials

`0.0183`

(default) | nonnegative scalar

Conductivity of the surface material, specified as a nonnegative scalar in siemens per meter (S/m). The model uses this value to calculate path loss due to reflection. The default value corresponds to plaster board at 1.9 GHz.

#### Dependencies

To enable `SurfaceMaterialConductivity`

, you must set
`CoordinateSystem`

to `"cartesian"`

and set `SurfaceMaterial`

to `"custom"`

.

**Data Types: **`double`

## Examples

### Model Propagation Paths Using SBR and Image Methods

Show reflected propagation paths in Chicago by using the SBR and image methods.

Create a Site Viewer with buildings in Chicago. For more information about the osm file, see [1].

viewer = siteviewer("Buildings","chicago.osm");

Create a transmitter site on a building and a receiver site near another building.

tx = txsite("Latitude",41.8800, ... "Longitude",-87.6295, ... "TransmitterFrequency",2.5e9); show(tx) rx = rxsite("Latitude",41.8813452, ... "Longitude",-87.629771, ... "AntennaHeight",30); show(rx)

Create a ray tracing model. Use the image method and calculate paths with up to one reflection. Then, display the propagation paths.

pm = propagationModel("raytracing","Method","image", ... "MaxNumReflections",1); raytrace(tx,rx,pm)

For this ray tracing model, there is one propagation path from the transmitter to the receiver.

Update the ray tracing model to use the SBR method and to calculate paths with up to two reflections. Display the propagation paths.

```
pm.Method = "sbr";
pm.MaxNumReflections = 2;
clearMap(viewer)
raytrace(tx,rx,pm)
```

The updated ray tracing model shows three propagation paths from the transmitter to the receiver.

**Appendix**

[1] The osm file is downloaded from https://www.openstreetmap.org, which provides access to crowd-sourced map data all over the world. The data is licensed under the Open Data Commons Open Database License (ODbL), https://opendatacommons.org/licenses/odbl/.

### Model Coverage Using Ray Tracing

Create a Site Viewer with buildings in Chicago. For more information about the `.osm`

file, see [1].

viewer = siteviewer("Buildings","chicago.osm");

Create a transmitter site on a building and a receiver site near another building.

tx = txsite("Latitude",41.8800, ... "Longitude",-87.6295, ... "TransmitterFrequency",2.5e9); show(tx)

Create a ray tracing model. By default, ray tracing models use the SBR method. Set the maximum number of reflections to `2`

. Then, display the coverage map.

pm = propagationModel("raytracing","Method","sbr", ... "MaxNumReflections",2); coverage(tx,pm,"SignalStrengths",-100:5)

**Appendix**

[1] The `.osm`

file is downloaded from https://www.openstreetmap.org, which provides access to crowd-sourced map data all over the world. The data is licensed under the Open Data Commons Open Database License (ODbL), https://opendatacommons.org/licenses/odbl/.

## More About

### Shooting and Bouncing Rays Method

The shooting and bouncing rays (SBR) method finds an approximate number of propagation paths with exact geometric accuracy. You can use this method to find paths with up to 10 path reflections.

The computational complexity of the SBR method increases linearly with the number of reflections. As a result, the SBR method is generally faster than the image method.

This figure illustrates the SBR method for calculating propagation paths from a transmitter, *Tx*, to a receiver, *Rx*.

The SBR method launches many rays from a geodesic sphere centered at *Tx*. The geodesic sphere enables the model to launch rays that are approximately uniformly spaced.

Then, the method traces every ray from *Tx* and can model different types of interactions between the rays and surrounding objects, such as reflections, diffractions, refractions, and scattering. Note that the current implementation of the SBR method considers only reflections.

When a ray hits a flat surface, shown as

*R*, the ray reflects based on the law of reflection.When a ray hits an edge, shown as

*D*, the ray spawns many diffracted rays based on the law of diffraction [5][6]. Each diffracted ray has the same angle with the diffracting edge as the incident ray. The diffraction point then becomes a new launching point and the SBR method traces the diffracted rays in the same way as the rays launched from*Tx*. A continuum of diffracted rays forms a cone around the diffracting edge, which is commonly known as a*Keller cone*[6]. The current implementation of the SBR method does not consider edge diffractions.

For each launched ray, the SBR method surrounds *Rx* with a sphere, called a reception sphere, with a radius that is proportional to the distance the ray travels and the average number of degrees between the launched rays. If the ray intersects the sphere, then the model considers the ray a valid path from *Tx* to *Rx*. The SBR method corrects the valid paths so that the paths have exact geometric accuracy.

When you increase the number of rays by decreasing the number of degrees between rays, the reception sphere becomes smaller. As a result, in some cases, launching more rays results in fewer or different paths. This situation is more likely to occur with custom 3-D scenarios created from STL files or triangulation objects than with scenarios that are automatically generated from OpenStreetMap^{®} buildings and terrain data.

The SBR method finds paths using single-precision floating-point computations.

### Image Method

The image method finds an exact number of propagation paths with exact geometric accuracy. You can use this method to find paths with up to 2 path reflections. The computational complexity of the image method increases exponentially with the number of reflections.

This figure illustrates the image method for calculating the propagation path of a single
reflection ray for the same transmitter and receiver as the SBR method. The image method
locates the image of *Tx* with respect to a planar reflection surface,
*Tx'*. Then, the method connects *Tx'* and
*Rx* with a line segment. If the line segment intersects the planar
reflection surface, shown as *R* in the figure, then a valid path from
*Tx* to *Rx* exists. The method determines paths with
multiple reflections by recursively extending these steps. The image method finds paths
using single-precision floating-point computations.

### ITU Permittivity and Conductivity Values for Common Materials

ITU-R P.2040-1 [3] and ITU-R P.527-5 [4] present methods, equations, and values used to calculate real relative permittivity, conductivity, and complex relative permittivity for common materials.

For information about the values computed for building materials specified in ITU-R P.2040-1, see

`buildingMaterialPermittivity`

.For information about the values computed for terrain materials specified in ITU-R P.527-5, see

`earthSurfacePermittivity`

.

## References

[1] Yun, Zhengqing, and Magdy F. Iskander. “Ray Tracing for Radio Propagation Modeling: Principles and Applications.” *IEEE Access* 3 (2015): 1089–1100. https://doi.org/10.1109/ACCESS.2015.2453991.

[2] Schaubach, K.R., N.J. Davis, and T.S. Rappaport. “A Ray Tracing Method for Predicting Path Loss and Delay Spread in Microcellular Environments.” In *[1992 Proceedings] Vehicular Technology Society 42nd VTS Conference - Frontiers of Technology*, 932–35. Denver, CO, USA: IEEE, 1992. https://doi.org/10.1109/VETEC.1992.245274.

[3] International Telecommunications Union Radiocommunication
Sector. *Effects of building materials and structures on radiowave propagation above
about 100MHz.* Recommendation P.2040-1. ITU-R, approved July 29, 2015.
https://www.itu.int/rec/R-REC-P.2040-1-201507-I/en.

[4] International Telecommunications Union Radiocommunication
Sector. *Electrical characteristics of the surface of the Earth*.
Recommendation P.527-5. ITU-R, approved August 14, 2019.
https://www.itu.int/rec/R-REC-P.527-5-201908-I/en.

[5] International Telecommunications Union Radiocommunication Sector. *Propagation by diffraction*. Recommendation P.526-15. ITU-R, approved October 21, 2019. https://www.itu.int/rec/R-REC-P.526-15-201910-I/en.

[6] Keller, Joseph B. “Geometrical Theory of Diffraction.” *Journal of the Optical Society of America* 52, no. 2 (February 1, 1962): 116. https://doi.org/10.1364/JOSA.52.000116.

## Version History

**Introduced in R2019b**

### R2022b: Customize spacing of launched rays for ray tracing with SBR method

When performing ray tracing using the SBR method, you can customize the spacing of
launched rays by specifying the `AngularSeparation`

property of the
`RayTracing`

object as a numeric value in degrees. In previous releases,
the `AngularSeparation`

property supported only the options
`"high"`

, `"medium"`

, and
`"low"`

.

### R2022b: SBR method calculates propagation paths with exact geometric accuracy

When you find propagation paths using the SBR method, MATLAB corrects the results so that the geometric accuracy of each path is exact. In previous releases, the paths have approximate geometric accuracy.

### R2021b: Default modeling method is shooting and bouncing rays method

Starting in R2021b, when you create a propagation model using the syntax
`propagationModel("raytracing")`

, MATLAB returns a `RayTracing`

model with the
`Method`

value set to `"sbr"`

and two reflections
(instead of `"image"`

and one reflection, as in previous releases).

To create ray tracing propagation models that use the image method, use the syntax
`propagationModel("raytracing","Method","image")`

.

## See Also

### Functions

`propagationModel`

|`raytrace`

|`coverage`

|`sigstrength`

|`buildingMaterialPermittivity`

|`earthSurfacePermittivity`

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