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# Documentation

The phased.RadarTarget object models a reflected signal from a target with 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

Create a radar target with a nonfluctuating RCS of 1 square meter and an operating frequency of 300 MHz. Specify a wave propagation speed equal to the speed of light.

```hr = phased.RadarTarget('Model','nonfluctuating','MeanRCS',1,...
'PropagationSpeed',physconst('LightSpeed'),...
'OperatingFrequency',3e8);```

The waveform incident on the target is scaled by the factor:

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

Here, σ represents the target mean RCS, and λ is the wavelength of the operating frequency. Each element of the signal incident on the target is scaled by the preceding factor.

Create a target with a nonfluctuating RCS of 1 square meter. Set the operating frequency to 1 GHz. Set the signal incident on the target to be a vector of ones to demonstrate the gain factor.

```hr = phased.RadarTarget('MeanRCS',1,'OperatingFrequency',1e9);
x = ones(10,1);
y = step(hr,x);```

The output vector y is equal to 11.8245*ones(10,1). The amplitude scaling factor equals:

```lambda = hr.PropagationSpeed/hr.OperatingFrequency;
G = sqrt(4*pi*1/lambda^2)```

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 NumberDescription
IScan-to-scan decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer.
IIPulse-to-pulse decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer.
IIIScan-to-scan decorrelation — Chi-square PDF with 4 degrees of freedom. A number of scatterers with one scatterer dominant.
IVPulse-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. Use the step method and set the UPDATERCS input argument 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 a 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 approximately 1414 meters from the antenna at an angle of 45 degrees azimuth and 0 degrees elevation.

```% Create objects and assign property values
% Isotropic antenna element
hant = phased.IsotropicAntennaElement('BackBaffled',true);
% Location of the antenna
harraypos = phased.Platform('InitialPosition',[0;0;0]);
% Location of the radar target
hrfpos = phased.Platform('InitialPosition',[1000; 1000; 0]);
% Linear FM waveform
hwav = phased.LinearFMWaveform('PulseWidth',100e-6);
% Transmitter
htx = phased.Transmitter('PeakPower',1e3,'Gain',40);
'Sensor',hant);
% Propagation environment to and from the RadarTarget
hspace = phased.FreeSpace('OperatingFrequency',1e9,...
'TwoWayPropagation',true);
% Collector
hc = phased.Collector('OperatingFrequency',1e9,...
'Sensor',hant);

% Implement system
wf = step(hwav);  % generate waveform
txwf = step(htx,wf);  % transmit waveform