RF Propagation Models

The following sections provide an overview of propagation models and simulation capabilities for applications at the power-level, measurement-level, and waveform-level, including performance analysis, system optimization, algorithm design, tracker tuning, and end-to-end analysis.

Topics include:

Propagation Geometry Functions

Propagation geometry functions return geometric aspects of the path and do not include loss-related terms. Power-level, measurement-level, and waveform-level application rely on geometry models.

Propagation through a free-space or uniform atmosphere results in a straight-line propagation path.
Propagation through a layered atmosphere results in a curved refracted propagation path (see How? — Propagation Geometry).

Radar Toolbox Feature	Primary Output	Path Geometry: Straight	Path Geometry: Curved	CRPL Model
`llarangeangle`	Range to target (one-way) [m]		✔
`slant2range`	Range to target (one-way) [m]		✔	✔
`height2range`	Range to target (one-way) [m]	✔	✔	✔
`range2height`	Height of target [m]	✔	✔	✔
`el2height`	Height of target [m]	✔	✔	✔
`height2grndrange`	Ground range to target [m]	✔	✔	✔
`horizonrange`	Range to radar horizon [m]		✔
`height2el`	Elevation angle of radar [deg]	✔	✔
`grazingang`	Grazing angle, relative to surface [deg]		✔

Note that the curved refracted path length or propagated range is longer than the corresponding slant range geometric distance (see How? — Propagation Geometry).

How to choose a propagation geometry function:

llarangeangle accepts coordinate positions as input and returns the propagated range (path length) as output.
slant2range returns the propagated range given a slant range, target height, and antenna height, where slant range is the corresponding straight-line geometric path length.
height2range and range2height inter-convert target height and propagated range given slant range, antenna height, and elevation angle.
height2grndrange returns the ground range to a target given the target height, antenna height, and elevation angle.
horizonrange returns the Radar Horizon range of the radar given antenna height.
height2el and el2height inter-convert target height and elevation angle given slant range and antenna height.
grazingang returns the grazing angle of the propagated path relative to the surface.

When a curved refracted path is modeled, the large-scale curvature of the Earth surface is also considered, otherwise a flat Earth surface is assumed.

You can select the refracted path model:

The functions listed in the table above assume a Curved Earth Model with an Effective Earth Radius factor of 4/3 by default. A 4/3 effective radius is a good approximation for low altitude antenna heights. The figure below shows the effective Earth radius factor as a function of antenna height for different models. You can see that for low altitude antenna heights, a 4/3 approximation is similar to the CRPL model and is roughly equivalent to the Effective Earth Radius from Average Radius of Curvature near 1 km.

See Compare Effective Earth Radius Factors for more information.

Propagation Losses and Power-Level Models

Power-level applications, including link budget and performance analysis, depend on underlying loss models and visualization tools.

Propagation loss models predict one-way path loss between sites and return individual loss quantities that depend on propagation distance (path length) and frequency.
Propagation models and visualization tools incorporate mechanisms like atmospheric refraction and multipath interference and return results that are expressed relative to ideal free‑space propagation.

The Radar Designer app is an interactive system design tool that has many capabilities for link budget and performance analysis, and only the propagation-related plots are discussed below.

Propagation Loss Models

Losses models in the following table return individual distance-dependent loss quantities at a given frequency. You need to additively combine multiple losses to get a total path loss quantity.

Radar Toolbox Feature	Primary Output	Path Geometry: Straight	Path Geometry: Curved	Algorithms
`fspl`	Path loss from free space spreading (far field) [dB]	★	★	Free Space Path Loss
`gaspl`	Path loss from atmospheric gas absorption in a single, homogenous layer [dB]	★	★	Atmospheric Gas Attenuation Model
`fogpl`	Path loss from fog [dB]	★	★	Fog and Cloud Attenuation Model
`cranerainpl`	Path loss from rainfall regions [dB]	★	★	Crane Rainfall Attenuation Model
`rainpl`	Path loss from uniform rainfall [dB]	★	★	Rainfall Attenuation Model
`snowpl`	Path loss from snow [dB]	★	★	Gunn, K. L. S., and T. W. R. East. “The Microwave Properties of Precipitation Particles.” Quarterly Journal of the Royal Meteorological Society 80, no. 346 (October 1954): 522–45.
`tropopl`	Path loss from atmospheric gas absorption in a layered atmosphere \| optional lensing loss [dB]		✔	Layered Atmosphere
`lenspl`	Path loss from refraction-based lensing [dB]		✔	Layered Atmosphere
Radar Designer Environmental Losses plot	Path loss components from precipitation, gas absorption, lensing – plot	✔	✔	Incorporates losses from functions detailed in this table.

[★] Loss depends on the propagated distance (path length) and frequency – the path geometry is not considered.

Combining multiple losses:

For two-way propagation, make sure to account for all propagation segments in the total propagation distance.
You may choose to model localized weather‑related attenuation over only a portion of the path length.
Make sure that you properly consider path length when combining multiple distributed losses.
- For example, to add fspl (Phased Array System Toolbox™) loss to the tropopl loss, make sure to use the refracted curved path length calculated by slant2range – instead of the slant range – as the fslp propagation distance.

You can readily combine multiple loss sources using the Radar Designer app.

See Radar Link Budget Analysis for more information.

Reference atmospheres:

You can find the relevant International Telecommunication Union (ITU) reference atmosphere standard in the References section of each function page.
Atmospheric parameters (temperature, pressure, and water vapor) applicable to gaspl can be calculated using the atmositu function.
For low antenna heights, you may want to assume average gas parameters that correspond to the radar antenna height.

The figure below shows atmospheric variability as a function of altitude.

See Modeling Target Position Errors Due to Refraction for more information.

Propagation Models and Visualization Tools

Propagation models and visualization tools listed in the table below are expressed relative to ideal free-space propagation and are used to assess radar range for target detection.

The Radar Designer app is an interactive system design tool that has many capabilities for link budget and performance analysis, and only the propagation-related plots are listed in the table below.

Radar Toolbox Feature	Primary Output	Multipath Fading (Multi-Bounce Path)	Path Geometry: Straight	Path Geometry: Curved
`radarpropfactor`	Radar propagation factor	✔		✔
Radar Designer app Environmental Losses plot	Radar propagation factor plot	✔	✔	✔
`radarvcd`	Vertical coverage pattern	✔		✔
`blakechart`	Range-angle-height (Blake) chart	✔		✔
Radar Designer app Vertical Coverage plot	Range-angle-height (Blake) chart	✔	✔	✔

The radarpropfactor quantifies how the strength of a received radar signal differs from what would be expected in free-space conditions, and is expressed as a ratio relative to ideal free‑space propagation. A radar propagation factor is included in some forms of the Radar Equation.

What radarpropfactor accounts for:

Refracted path from the CRPL model.
Surface properties including dielectric constant, surface height standard deviation, vegetation cover, and surface slope.
Multipath fading (interference between direct single-bounce path and ground‑reflected rays).
Over the horizon diffraction (see Radar Horizon).

You can see in the figures below that multipath fading is frequency dependent and does not contribute to the diffraction region.

See Modeling the Propagation of Radar Signals for more information.
Also See Passive Bistatic Radar Performance Assessment, which uses radarpropfactor in the context of a passive bistatic scenario.

What a Blake chart shows:

blakechart produces a range-angle-height diagram that shows the relationship between the range to a target, the height of the target, and the initial elevation angle of the transmitted signal for a specified antenna height. In other words, the plot shows the maximum radar range as a function of elevation, with lines of constant range and height.
blakechart relies on the vertical coverage pattern generated using radarvcd, which contains the maximum radar detection range as a function of elevation angle, expressed relative to ideal free‑space propagation.
Note that you can plot a Blake chart directly from radarvcd using a convenience syntax, but the blakechart function has additional properties.
The Radar Designer Vertical Coverage plot also produces a range-angle-height diagram, but may include additional contributions related to vertical coverage.
blakechart models:
- Refracted path from the CRPL model.
- Multipath fading (interference between direct single-bounce path and ground‑reflected rays), assuming surface properties defined in radarvcd: dielectric constant, surface height standard deviation, vegetation cover, and surface slope.
The vertical coverage pattern underlying blakechart (generated using radarvcd) is generally considered to be valid for antenna heights that are within a few hundred feet of the surface and with targets at altitudes that are not too close to the radar horizon.

In the figure below, you can see the effects of multipath fading in the presence of heavy clutter as lobes in the Blake chart.

See Radar Vertical Coverage over Terrain for more information.

Detection and I/Q Simulators

Measurement-level detection models incorporate processing chain gains and losses to simulate target detections. Applications include tracker design and tuning, algorithm design, and system optimization.

Waveform-level I/Q models account for the full signal and processing chain gains and losses to simulate realistic I/Q signals. Applications include algorithm design, system optimization, and end-to-end analysis

Fidelity	Radar Toolbox Feature	Primary Output	Surface Reflection (Single-Bounce Path)	Target Reflection (Single-Bounce Path)	Multipath Fading (Multi-Bounce Path)	Multipath Ghosts (Multi-Bounce Path)	Path Geometry: Straight	Path Geometry: Curved
Measurement-Level	`radarDataGenerator` attached to a `radarScenario`	Detections Track reports	✔	✔	✔	✔	✔	✔
Waveform-Level	`freeSpacePath` \| `bistaticFreeSpacePath`	Propagation path configuration `struct`		✔			✔
	`radarTransceiver` attached to a `radarScenario`	I/Q signals	✔	✔			✔	✔
	`bistaticTransmitter` and `bistaticReceiver`	I/Q signals		✔			✔
	`weatherTimeSeries`	I/Q signals as complex voltages					✔

What is radarScenario:

radarScenario simulates a 3-D environment, or radar scenario, that contains (multiple) platform objects that support:
- Trajectories.
- Target signatures.
- Sensors, including radarDataGenerator and radarTransceiver objects.
radarScenario supports a Cartesian or Earth-centered frame:
- Set the IsEarthCentered property to the default value of false to assume a straight-line, free-space propagation path.
- Set the IsEarthCentered property to true to enable a curved, refracted propagation path.
radarScenario allows an atmosphere object that supports:
- Free-space loss for a curved refracted path determined using:
  - EffectiveEarth Curved Earth Model.
  - CRPL CRPL Exponential Reference Atmosphere Model.
  - RefractivityGradient model.
radarScenario allows land, sea, or custom surfaces (specified as landSurface. seaSurface, or customSurface objects) that:
- Contain surface properties, including reflectivity and terrain.
- Are used to model terrain and object occlusion, multipath reflections, and to generate clutter (see Radar Surface Clutter Simulation).
radarScenario includes SurfaceManager, which enables:
- Occlusion modeling.
- Multiple surface patches.
- Multipath reflections (available for radarDataGenerator sensors – see below).
See Radar Scenario Tutorial for more information.

The figure below shows target error relative to the predicted error for a refracted curved path model using radarTransceiver (labeled waveform-level) and radarDataGenerator (labeled measurement-level) simulations.

See Simulating Radar Systems with Atmospheric Refraction for more information.

How to model multipath interference with radarDataGenerator (straight-line path only):

Set the IsEarthCentered property of radarScenario to the default value of false or set the IsEarthCentered property of radarScenario to true and set the model property of the atmosphere object to the default value of "FreeSpace".
Set the EnableMultipath property of SurfaceManager to true to model:
- Multipath reflections from surfaces (up to three bounces).
- Multipath reflections from targets (up to three bounces).
  - The radarDataGenerator HasGhosts property is automatically set to true to enable target multipath.
See Airborne Target Height Estimation Using Multipath Over Sea and Land for more information.

What freeSpacePath and bistaticFreeSpacePath are used for:

freeSpacePath and bistaticFreeSpacePath are channel path generators that return path configurations that capture target interactions and path‑losses, but do not apply those effects (see Channel Models).
Path configurations are returned as an array of propPaths structs.
Each propPaths struct contains these fields: PathLength, PathLoss, ReflectionCoefficient, AngleOfDeparture, AngleOfArrival, and DopplerShift.
You can manually add atmospheric attenuation to propPaths by editing the PathLoss field.
You can define radarTransceiver propagation channels using propPaths returned by freeSpacePath (see Parallel Simulation of Target, Clutter, and Interference Signals).
- For the monostatic case, the same antenna is used for transmit and receive, the antennas are co-located. Therefore, the departure and arrival angles on the paths are the same and the direct path is not included.
You can define bistaticTransmitter transmit propagation channels using propPaths returned by bistaticFreeSpacePath (see Parallel Simulation of Target, Clutter, and Interference Signals).
- For the bistatic case, each path is from the bistatic transmitter to the target and from the target to the bistatic receiver, labeled as R_T and R_R in the figure below. You can optionally include the direct path between the bistatic transmitter and receiver.
  - See Cooperative Bistatic Radar I/Q Simulation and Processing for more information.

How weatherTimeSeries works:

Each weatherTimeSeries simulation produces an independent radar return from a particular resolution volume, or cell, that is modeled as a complex stationary Gaussian random process using a Monte Carlo method.
See Improving Weather Radar Moment Estimation with Convolutional Neural Networks for more information.

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Channel Models

Channel models are waveform-level models that take in a waveform, apply channel effects, and return the modified waveform. Channel effects can include range-dependent time delays, gains, phase shifts, and Doppler shifts.

Most channel models listed in the table below are part of the Phased Array System Toolbox. radarScenario enables higher-fidelity I/Q simulation capabilities and is therefore the recommended Radar Toolbox workflow.

Radar Toolbox Feature	Primary Output	Multipath Fading (Multi-Bounce Path)	Path Geometry: Straight
`phased.FreeSpace` \| `phased.WidebandFreeSpace`	I/Q signals		✔
`phased.LOSChannel` \| `phased.WidebandLOSChannel`	I/Q signals		✔
`twoRayChannel` \| `widebandTwoRayChannel`	I/Q signals	✔	✔

How to choose a channel model::

All the listed channel models apply a Doppler shift when either the source or destination is moving.
phased.FreeSpace / phased.WidebandFreeSpace is a free-space channel model that applies angle-dependent time delays, gains and losses, and phase shifts to a narrowband / wideband input signal.
- You can model one-way or two-way propagation.
phased.LOSChannel / phased.WidebandLOSChannel is a free-space or uniform atmosphere line-of-sight channel model that applies range-dependent time delays and gains or losses to a narrowband / wideband input signal.
- You can model the propagation of signals between multiple points simultaneously.
twoRayChannel / widebandTwoRayChannel is a free-space or uniform atmosphere line-of-sight channel model that applies range-dependent time delays, gains or losses, phase shifts, and boundary reflection loss to a narrowband / wideband input signal.
- A two-ray propagation channel is the simplest type of multipath channel and includes a line-of-sight (direct single-bounce) propagation path from one point to another and a ray path reflected from a surface (see Two-Ray Propagation Paths).