## Radar Target

### Radar Target Properties

The `phased.RadarTarget`

System object™ models
a reflected signal from a target. The target may have a nonfluctuating
or fluctuating radar cross section (RCS). This object has the following
modifiable properties:

`MeanRCSSource`

— Source of the target's mean radar cross section`MeanRCS`

— Target's mean RCS`Model`

— Statistical model for the target's RCS`PropagationSpeed`

— Signal propagation speed`OperatingFrequency`

— Operating frequency`SeedSource`

— Source of the seed for the random number generator to generate the target's random RCS values`Seed`

— Seed for the random number generator

### Gain for Nonfluctuating RCS Target

Create a radar target with a nonfluctuating RCS of 1 square meter and an operating frequency of 1 GHz. Specify a wave propagation speed equal to the speed of light.

sigma = 1.0; target = phased.RadarTarget('Model','nonfluctuating','MeanRCS',sigma,... 'PropagationSpeed',physconst('LightSpeed'),'OperatingFrequency',1e9);

For a nonfluctuation target, the reflected waveform equals the incident waveform scaled by the gain

$$G=\sqrt{\frac{4\pi \sigma}{{\lambda}^{2}}}$$

Here, σ represents the mean target RCS, and λ is the wavelength of the operating frequency.

Set the signal incident on the target to be a vector of ones to obtain the gain factor used by the `phased.RadarTarget`

System object™.

x = ones(10,1); y = target(x)

`y = `*10×1*
11.8245
11.8245
11.8245
11.8245
11.8245
11.8245
11.8245
11.8245
11.8245
11.8245

Compute the gain from the formula to verify that the output of the System object equals the theoretical value.

lambda = target.PropagationSpeed/target.OperatingFrequency; G = sqrt(4*pi*sigma/lambda^2)

G = 11.8245

### Fluctuating RCS Targets

The previous examples used nonfluctuating values for the target's RCS. This model is not valid in many scenarios. There are several cases where the RCS exhibits relatively small or large magnitude fluctuations. These fluctuations can occur rapidly on pulse-to-pulse, or more slowly, on scan-to-scan time scales:

**Several small randomly distributed reflectors with no dominant reflector**— This target, at close range or when the radar uses pulse-to-pulse frequency agility, can exhibit large magnitude rapid (pulse-to-pulse) fluctuations in the RCS. That same complex reflector at long range with no frequency agility can exhibit large magnitude fluctuations in the RCS over a longer time scale (scan-to-scan).**Dominant reflector along with several small reflectors**— The reflectors in this target can exhibit small magnitude fluctuations on pulse-to-pulse or scan-to-scan time scales, subject to:How rapidly the aspect changes

Whether the radar uses frequency agility

To account for significant fluctuations in the RCS, you need
to use statistical models. The four *Swerling* models,
described in the following table, are widely used to cover these kinds
of fluctuating-RCS cases.

Swerling Case Number | Description |
---|---|

I | Scan-to-scan decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer. |

II | Pulse-to-pulse decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer. |

III | Scan-to-scan decorrelation — Chi-square PDF with 4 degrees of freedom. A number of scatterers with one scatterer dominant. |

IV | Pulse-to-pulse decorrelation — Chi-square PDF with 4 degrees of freedom. A number of scatterers with one scatterer dominant. |

You can simulate a Swerling target model by setting the `Model`

property.
Call the object with the `UPDATERCS`

input argument set to
`true`

or `false`

. Setting
`UPDATERCS`

to `true`

updates the RCS value
according to the specified probability model each time you call `step`

. If you set `UPDATERCS`

to
`false`

, the previous RCS value is used.

### Model Pulse Reflection from Nonfluctuating Target

This example creates and transmits a linear FM waveform with a 1 GHz carrier frequency. The waveform is transmitted and collected by an isotropic antenna with a back-baffled response. The waveform propagates to and from a target with a nonfluctuating RCS of 1 square meter. The target is located at a range of 1.414 km from the antenna at an azimuth angle of 45° and an elevation of 0°.

Set up the radar system.

antenna = phased.IsotropicAntennaElement('BackBaffled',true); antennapos = phased.Platform('InitialPosition',[0;0;0]); targetpos = phased.Platform('InitialPosition',[1000; 1000; 0]); waveform = phased.LinearFMWaveform('PulseWidth',100e-6); transmitter = phased.Transmitter('PeakPower',1e3,'Gain',40); radiator = phased.Radiator('OperatingFrequency',1e9, ... 'Sensor',antenna); channel = phased.FreeSpace('OperatingFrequency',1e9,... 'TwoWayPropagation',true); target = phased.RadarTarget('MeanRCS',1,'OperatingFrequency',1e9); collector = phased.Collector('OperatingFrequency',1e9,... 'Sensor',antenna);

Compute the transmitted and received waveforms.

```
wav = waveform();
txwav = transmitter(wav);
radwav = radiator(txwav,[0 0]');
propwav = channel(radwav,antennapos.InitialPosition,...
targetpos.InitialPosition,[0;0;0],[0;0;0]);
reflwav = target(propwav);
collwav = collector(reflwav,[45 0]');
```