# clutterSurfaceRCS

## Syntax

``rcs = clutterSurfaceRCS(nrcs,range,azimuth,elevation,graz,tau)``
``rcs = clutterSurfaceRCS(___,C)``
``rcs = clutterSurfaceRCS(___,'BeamLoss',Lp)``

## Description

example

````rcs = clutterSurfaceRCS(nrcs,range,azimuth,elevation,graz,tau)` returns the radar cross section, `rcs`, of the surface clutter patch as an M-length row vector in meters squared.`rcs = clutterSurfaceRCS(___,C)` returns the surface clutter radar cross-section with the propagation speed `C`.`rcs = clutterSurfaceRCS(___,'BeamLoss',Lp)` returns the surface clutter radar cross section using the beamshape loss.```

## Examples

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Calculate the radar cross section of a clutter patch and estimate the clutter-to-noise ratio at the receiver. Assume that the patch is `1000` meters away from the radar system and the azimuth and elevation beamwidths are `1` degree and `3` degrees, respectively. Also assume that the grazing angle is 2`0` degrees, the pulse width is `10` microseconds, and the radar is operated at a wavelength of `1` cm with a peak power of `5` kw.

```rng = 1000; bwAz = 1; bwEl = 3; graz = 20; tau = 10e-6; lambda = 0.01; ppow = 5000; ```

Calculate the NRCS.

`nrcs = landreflectivity('Mountains',graz)`
```nrcs = 0.1082 ```

Calculate clutter RCS using the calculated NRCS.

`rcs = clutterSurfaceRCS(nrcs,rng,bwAz,bwEl,graz,tau)`
```rcs = 288.9855 ```

Calculate clutter-to-noise ratio using the calculated RCS.

`cnr = radareqsnr(lambda,rng,ppow,tau,'rcs',rcs)`
```cnr = 62.5974 ```

## Input Arguments

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The normalized radar cross section (NRCS) of a clutter patch is specified as either a nonnegative scalar or an M-length vector of nonnegative values in meters squared. The NRCS is also known as the reflectivity or σ0.

Example: `nrcs = 1`

The clutter patch range, specified as either a nonnegative scalar or an M-length vector of nonnegative values in meters.

Example: `range = 1000;`

The azimuth beamwidth of the radar, specified as a positive scalar or a 1-by-2 vector in degrees. Use with the `elevation` argument.

• When the transmit and receive beamwidths are the same, specify `azimuth` as a positive scalar .

• When the transmit and receive azimuth beamwidths are not the same, specify `azimuth` as a 1-by-2 positive vector `[azimuth_Tx,azimuth_Rx]`, where the first element is the transmit azimuth beamwidth in degrees and the second element is the receive azimuth beamwidth in degrees.

The function uses these two beamwidths to create an effective azimuth beamwidth. See Effective Beamwidth.

Example: `bwAz = 1`

The elevation beamwidth of the radar, specified as a positive scalar or a 1-by-2 vector in degrees. Use with the `azimuth` argument.

• When the transmit and receive beamwidths are the same, specify `elevation` as a positive scalar .

• When the transmit and receive elevation beamwidths are not the same, specify `elevation` as a 1-by-2 positive vector `[elevation_Tx,elevation_Rx]`, where the first element is the transmit azimuth beamwidth in degrees and the second element is the receive azimuth beamwidth in degrees.

The function uses these two beamwidths to create an effective elevation beamwidth. See Effective Beamwidth.

Example: `bwEl = 3`

Grazing angle, specified as a nonnegative scalar or an N-length row vector of nonnegative values. This argument specifies the grazing angles of the clutter patch relative to the radar. Units are in degrees. See `grazingang`.

Pulse width of the transmitted signal, specified as a nonnegative scalar in seconds.

Example: `tau = 10e-6`

The propagation speed specified as a positive scalar in meters per second.

The beamshape loss, specified as a nonnegative scalar in decibels. The beamshape loss accounts for the reduced two-way antenna gain of off-axis scatterers.

Use this property when the elevation beamwidth (`elevation`) for the transmitter and receiver are not the same.

Example: `loss = 0`

## Output Arguments

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The radar cross section of a surface cluster patch, returned as an M-length vector in meters squared.

## Algorithms

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### Effective Beamwidth

The effective beamwidth is used for the effective azimuth θazimutheff and effective elevation θelevationeff calculation when the transmitter and receiver beamwidths are not equal.

`$\begin{array}{l}{\theta }_{azimutheff}=\frac{\sqrt{2{\theta }_{at}{\theta }_{ar}}}{\sqrt{{\theta }_{at}{}^{2}+{\theta }_{ar}{}^{2}}}\\ {\theta }_{elvationeff}=\frac{\sqrt{2{\theta }_{et}{\theta }_{er}}}{\sqrt{{\theta }_{et}{}^{2}+{\theta }_{er}{}^{2}}}\end{array}$`

• at is the azimuth transmitter elevation beamwidth in degrees.

• ar is the azimuth receiver elevation beamwidth in degrees.

• et is the elevation transmitter elevation beamwidth in degrees.

• er is the elevation receiver elevation beamwidth in degrees.

## References

[1] Barton, David K. Radar Equations for Modern Radar. Norwood, MA: Artech House, 2013.

[2] Long, Maurice W. Radar Reflectivity of Land and Sea. Boston: Artech House, 2001.

[3] Nathanson, Fred E., J. Patrick Reilly, and Marvin N. Cohen. Radar Design Principles. Mendham, NJ: SciTech Publishing, 1999.

## Version History

Introduced in R2021a