# Swerling 3 Target Models

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 3 model. In this example, the radar and target are stationary.

### Swerling 3 versus Swerling 4 Models

In Swerling 3 and Swerling 4 target models, the total RCS arises from a target consisting of one large scattering surface with several other small scattering surfaces. The total RCS may vary with every pulse in a scan (Swerling 4) or may be constant over a complete scan consisting of multiple pulses (Swerling 3). In either case, the statistics obey a chi-squared probability density function with four degrees of freedom.

### Dwell Time and Radar Scan

For simplicity, start with a rotating radar having a rotation time of 5 seconds corresponding to a rotation or scan rate of 72 degrees/sec.

```Trot = 5.0; scanrate = 360/Trot; ```

The radar has a main half-power beam width (HPBW) of 3.0 degrees. During the time that a target is illuminated by the main beam, radar pulses strike the target and reflect back to the radar. The time period during which the target is illuminated is called the dwell time. This time is also called a scan. The radar will process 3 scans of the target.

```HPBW = 3.0; Tdwell = HPBW/scanrate; Nscan = 3; ```

The number of pulses that arrive on target during the dwell time depends upon the pulse repetition frequency (PRF). PRF is the inverse of the pulse repetition interval (PRI). Assume 5000 pulses are transmitted per second.

```prf = 5000.0; pri = 1/prf; ```

The number of pulses in one dwell time is

```Np = floor(Tdwell*prf); ```

### Set up Swerling 3 radar model

You create a Swerling 3 target by properly employing the `step` method of the `RadarTarget` System object™. To effect a Swerling 3 model, set the `Model` property of the `phased.RadarTarget` System object to either `'Swerling3'` or `'Swerling4'`. Both are equivalent. Then, at the first call to the `step` method at the beginning of the scan, set the `updatercs` argument to `true`. Set `updatercs` to `false` for the remaining calls to `step` during the scan. This means that the radar cross section is only updated at the beginning of a scan and remains constant for the remainder of the scan.

Set the target model to `'Swerling3'` .

```tgtmodel = 'Swerling3'; ```

### Set up radar model System object components

Set up the radiating antenna. Assume the operating frequency of the antenna is 1 GHz.

```fc = 1e9; antenna = phased.IsotropicAntennaElement('BackBaffled',true); radiator = phased.Radiator('OperatingFrequency',fc,'Sensor',antenna); ```

Specify the location of the stationary antenna.

```radarplatform = phased.Platform('InitialPosition',[0;0;0]); ```

Specify the location of a stationary target.

```targetplatform = phased.Platform('InitialPosition',[2000; 0; 0]); ```

The transmitted signal is a linear FM waveform. Transmit one pulse per call to the `step` method.

```waveform = phased.LinearFMWaveform('PulseWidth',50e-6,... 'OutputFormat','Pulses','NumPulses',1); ```

Set up the transmitting amplifier.

```transmitter = phased.Transmitter('PeakPower',1000.0,'Gain',40); ```

Set up the propagation environment to be free space.

```channel = phased.FreeSpace('OperatingFrequency',fc,... 'TwoWayPropagation',true); ```

Specify the radar target to have a mean RCS of 1 m2 and be of the Swerling model type 3 or 4. You can use Swerling 3 or 4 interchangeably.

```target = phased.RadarTarget('MeanRCS',1,'OperatingFrequency',fc,... 'Model',tgtmodel); ```

```collector = phased.Collector('OperatingFrequency',1e9,... 'Sensor',antenna); ```

Define a matched filter to process the incoming signal.

```wav = step(waveform); filter = phased.MatchedFilter('Coefficients',getMatchedFilter(waveform)); ```

### Processing loop for 3 scans of a Swerling 3 target

1. Generate waveform with unit amplitude

2. Amplify the transmit waveform

3. Radiate the waveform in the desired direction to the target

4. Propagate the waveform to and from the radar target

5. Reflect waveform from radar target

Provide memory for radar return amplitudes.

```z = zeros(Nscan,Np); tp = zeros(Nscan,Np); ```

Enter the loop. Set `updatercs` to `true` only for the first pulse of the scan.

```for m = 1:Nscan t0 = (m-1)*Trot; t = t0; for k = 1:Np ```
``` if k == 1 updatercs = true; else updatercs = false; end t = t + pri; txwav = transmitter(wav); ```

Find the radar and target positions

``` [xradar,vradar] = radarplatform(pri); [xtgt,vtgt] = targetplatform(pri); ```

``` [~,ang] = rangeangle(xtgt,xradar); radwav = radiator(txwav,ang); ```

Propagate waveform to and from the target

``` propwav = channel(radwav,xradar,xtgt,vradar,vtgt); ```

Reflect waveform from target. Set the `updatercs` flag.

``` reflwav = target(propwav,updatercs); ```

``` collwav = collector(reflwav,ang); ```

Apply matched filter to incoming signal

``` y = filter(collwav); z(m,k) = max(abs(y)); tp(m,k) = t; ```
``` end end ```

### Plot the pulse amplitudes

Plot the amplitudes of the pulses for the scan as a function of time.

```plot(tp(:),z(:),'.') xlabel('Time (sec)') ylabel('Pulse Amplitude') ```

Notice that the pulse amplitudes are constant within a scan.