Swerling 1 Target Models

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The example presents a scenario consisting of a rotating monostatic radar and a target with a radar cross-section described by a Swerling 1 model. In this example, the radar and target are stationary.

Swerling 1 versus Swerling 2 Models

For Swerling 1 and Swerling 2 target models, the total RCS arises from many independent small scatterers of approximately equal individual RCS. The total RCS may vary with every pulse in a scan (Swerling 2) or may be constant over a complete scan consisting of multiple pulses (Swerling 1). In either case, the statistics obey a chi-squared probability density function with two 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 rate or scan rate of 72 degrees/sec.

Trot = 5.0;
rotrate = 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 period is also called a scan. The example will process 3 scans of the target.

HPBW = 3.0;
Tdwell = HPBW/rotrate;
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 1 radar model

You create a Swerling 1 target by using the RadarTarget System object™. To effect a Swerling 1 model, set the Model property of the phased.RadarTarget System object to either 'Swerling1' or 'Swerling2'. Both are equivalent. Then, at the first call to the object at the beginning of the scan, set the updatercs argument to true. Set updatercs to false for the remaining calls to the object during the scan. This procedure 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 'Swerling1'.

tgtmodel = 'Swerling1';

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 object.

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 1 target

Generate waveform with unit amplitude
Amplify the transmit waveform
Radiate the waveform in the desired direction to the target
Propagate the waveform to and from the target
Reflect waveform from radar target
Collect radiation to create received signal
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 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(t);
        [xtgt,vtgt] = targetplatform(t);

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 = 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 Amplitudes')

Notice that the pulse amplitudes are constant within a scan.