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This example shows how to apply the basic toolbox workflow to the following scenario: Assume you have a single isotropic antenna operating at 4 GHz. Assume the antenna is located at the origin of your global coordinate system. There is a target with a nonfluctuating radar cross section of 0.5 square meters initially located at [7000; 5000; 0]. The target moves with a constant velocity vector of [-15;-10;0]. Your antenna transmits ten rectangular pulses with a duration of 1 microsecond at a pulse repetition frequency (PRF) of 5 kHz. The pulses propagate to the target, reflect off the target, propagate back to the antenna, and are collected by the antenna. The antenna operates in a monostatic mode, receiving only when the transmitter is inactive.
hwav = phased.RectangularWaveform('PulseWidth',1e-6,... 'PRF',5e3,'OutputFormat','Pulses','NumPulses',1);
See Rectangular Pulse Waveforms for more detailed examples on building waveform models.
To model the antenna described in Radar Scenario, use phased.IsotropicAntennaElement. Set the operating frequency range of the antenna to [1,10] GHz. The isotropic antenna radiates equal energy for azimuth angles from –180 to 180 degees and elevation angles from –90 to 90 degrees.
hant = phased.IsotropicAntennaElement('FrequencyRange',... [1e9 10e9]);
To model the target described in Radar Scenario, use phased.RadarTarget. The target has a nonfluctuating RCS of 0.5 square meters and the waveform incident on the target has a carrier frequency of 4 GHz. The waveform reflecting off the target propagates at the speed of light. Parameterize this information in defining your target.
htgt = phased.RadarTarget('Model','Nonfluctuating',... 'MeanRCS',0.5,'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9);
The antenna is stationary in this scenario and is located at the origin of the global coordinate system. The target is initially located at [7000; 5000; 0] and moves with a constant velocity vector of [-15;-10;0].
htxplat = phased.Platform('InitialPosition',[0;0;0],... 'Velocity',[0;0;0],'OrientationAxes',[1 0 0;0 1 0;0 0 1]); htgtplat = phased.Platform('InitialPosition',[7000; 5000; 0],... 'Velocity',[-15;-10;0]);
For definitions and conventions regarding global and local coordinates, see Global and Local Coordinate Systems.
Use rangeangle to determine the range and angle between the antenna and the target.
[tgtrng,tgtang] = rangeangle(htgtplat.InitialPosition,... htxplat.InitialPosition);
See Motion Modeling in Phased Array Systems for more details on modeling motion.
To model the transmitter specifications, use phased.Transmitter. A key parameter in modeling a transmitter is the peak transmit power. To determine the peak transmit power, assume that the desired probability of detection is 0.9 and the maximum tolerable false-alarm probability is 10–6. Assume that the ten rectangular pulses are noncoherently integrated at the receiver. You can use albersheim to determine the required signal-to-noise ratio (SNR).
Pd = 0.9; Pfa = 1e-6; numpulses = 10; SNR = albersheim(Pd,Pfa,10);
The required SNR is approximately 5 dB. Assume you want to set the peak transmit power in order to achieve the required SNR for your target at a range of up to 15 km. Assume that the transmitter has a 20 dB gain. You can use radareqpow to determine the required peak transmit power.
maxrange = 1.5e4; lambda = physconst('LightSpeed')/4e9; tau = hwav.PulseWidth; Pt = radareqpow(lambda,maxrange,SNR,tau,'RCS',0.5,'Gain',20);
The required peak transmit power is approximately 45 kilowatts. To be conservative, use a peak power of 50 kilowatts in modeling your transmitter. To maintain a constant phase in the pulse waveforms, set the CoherentOnTransmit property to true. Because you are operating the transmitter in a monostatic (transmit-receive) mode, set the InUseOutputPort property to true to keep a record of the transmitter status.
htx = phased.Transmitter('PeakPower',50e3,'Gain',20,... 'LossFactor',0,'InUseOutputPort',true,... 'CoherentOnTransmit',true);
To model waveform radiation from the array, use phased.Radiator. To model narrowband signal collection at the array, use phased.Collector. For wideband signal collection, use phased.WidebandCollector.
In this example, the pulse satisfies the narrowband assumption around the carrier frequency of 4 GHz. For the value of the Sensor property, use the handle for the isotropic antenna. In phased.Collector, setting the Wavefront property to 'Plane' assumes the waveform incident on the antenna is a plane wave.
hrad = phased.Radiator('Sensor',hant,... 'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9); hcol = phased.Collector('Sensor',hant,... 'PropagationSpeed',physconst('LightSpeed'),... 'Wavefront','Plane','OperatingFrequency',4e9);
To model the receiver in Radar Scenario, use phased.ReceiverPreamp. In the receiver, you specify the noise figure and reference temperature, which are key contributors to the internal noise of your system. In this example, set the noise figure to 2 dB and the reference temperature to 290 degrees kelvin. Seed the random number generator for reproducible results.
hrec = phased.ReceiverPreamp('Gain',20,'NoiseFigure',2,... 'ReferenceTemperature',290,'SampleRate',1e6,... 'EnableInputPort',true,'SeedSource','Property','Seed',1e3);
See Receiver Preamp for more details.
To model the propagation environment in Radar Scenario, use phased.FreeSpace. You can model one-way and two-propagation by setting the TwoWayPropagation property. In this example, set this property to false to model one-way propagation.
hspace = phased.FreeSpace(... 'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9,'TwoWayPropagation',false,... 'SampleRate',1e6);
See Free Space Path Loss for more details.
Having parameterized all the necessary components for the model outlined in Radar Scenario, you are ready to generate the pulses, propagate the pulses to and from the target, and collect the echoes.
The following code prepares for the main simulation loop.
% Time step between pulses T = 1/hwav.PRF; % Get antenna position txpos = htxplat.InitialPosition; % Allocate array for received echoes rxsig = zeros(hwav.SampleRate*T,numpulses);
You can execute the main simulation loop with the following code:
for n = 1:numpulses % Update the target position [tgtpos,tgtvel] = step(htgtplat,T); % Get the range and angle to the target [tgtrng,tgtang] = rangeangle(tgtpos,txpos); % Generate the pulse sig = step(hwav); % Transmit the pulse. Output transmitter status [sig,txstatus] = step(htx,sig); % Radiate the pulse toward the target sig = step(hrad,sig,tgtang); % Propagate the pulse to the target in free space sig = step(hspace,sig,txpos,tgtpos,[0;0;0],tgtvel); % Reflect the pulse off the target sig = step(htgt,sig); % Propagate the echo to the antenna in free space sig = step(hspace,sig,tgtpos,txpos,tgtvel,[0;0;0]); % Collect the echo from the incident angle at the antenna sig = step(hcol,sig,tgtang); % Receive the echo at the antenna when not transmitting rxsig(:,n) = step(hrec,sig,~txstatus); end
Noncoherently integrate the received echoes, create a vector of range gates, and plot the result. The red vertical line on the plot marks the range of the target.
rxsig = pulsint(rxsig,'noncoherent'); t = unigrid(0,1/hrec.SampleRate,T,'[)'); rangegates = (physconst('LightSpeed')*t)/2; plot(rangegates,rxsig); hold on; xlabel('Meters'); ylabel('Power'); ylim = get(gca,'YLim'); plot([tgtrng,tgtrng],[0 ylim(2)],'r');