# Swerling 4 Target Models

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 4 model. In this example, the radar and target are stationary.

### Swerling 3 versus Swerling 4 Targets

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 a Swerling 4 model

You create a Swerling 4 target by properly employing the `step` method of the `RadarTarget` System object™. To effect a Swerling 4 model, set the `Model` property of the `phased.RadarTarget` System object to either `'Swerling3'` or `'Swerling4'`. Both are equivalent. Then, at every call to the `step` method, set the `updatercs` argument to `true`. This means that the radar cross section is updated for every pulse in the scan.

Set the target model to `'Swerling4'` .

```tgtmodel = 'Swerling4'; ```

### 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 1 or 2. You can use Swerling 1 or 2 interchangeably.

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

Set up the radar collector.

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

Define a matched filter to process the incoming signal.

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

### Processing loop for 3 scans of a Swerling 4 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.

6. Collect radiation to create received signal

7. Match filter received signal

Provide memory for radar return amplitudes.

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

Enter the loop. Set `updatercs` to `true` only for all pulses of the scan.

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

Find the radar and target positions

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

Radiate waveform to target

``` [~,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); ```

Collect the received waveform

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

Apply matched filter to incoming signal

``` y = step(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 vary within a scan.

### Histogram the received pulse amplitudes

```hist(z(:),25) xlabel('Pulse Amplitude') ``` 