# Basic Radar Using Phase-Coded Waveform

Instead of the rectangular waveform used in the End-to-End Radar System example, you can use a phase-coded waveform. To do so, replace the `phased.RectangularWaveform` System object™ with `phased.PhaseCodedWaveform`.

```waveform = phased.PhaseCodedWaveform('Code','Frank','NumChips',4,... 'ChipWidth',1e-6,'PRF',5e3,'OutputFormat','Pulses',... 'NumPulses',1);```

Then, redefine the pulse width, `tau` , using the properties of the new waveform.

`tau = waveform.ChipWidth*waveform.NumChips;`

The remainder of the code is almost identical to the code in the original examples and is presented here without comments. For a detailed explanation of how the code works, see the original End-to-End Radar System example.

```antenna = phased.IsotropicAntennaElement('FrequencyRange',[1e9 10e9]); target = phased.RadarTarget('Model','Nonfluctuating',... 'MeanRCS',0.5,'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9); transmitterplatform = phased.Platform('InitialPosition',[0;0;0],... 'Velocity',[0;0;0]); targetplatform = phased.Platform('InitialPosition',[7000; 5000; 0],... 'Velocity',[-15;-10;0]); [tgtrng,tgtang] = rangeangle(targetplatform.InitialPosition,... transmitterplatform.InitialPosition); % Use the radar equation to compute the transmitted power needed for a given Pd and Pfa. numpulses = 10; Pd = 0.9; Pfa = 1e-6; maxrange = 1.5e4; lambda = physconst('LightSpeed')/target.OperatingFrequency; RCS = 0.5; Ts = 290; SNR = albersheim(Pd,Pfa,10); Gain = 20; dbterms = db2pow(SNR - 2*Gain); Pt = (4*pi)^3*physconst('Boltzmann')*Ts/tau/RCS/(lambda^2)*maxrange^4*dbterms; transmitter = phased.Transmitter('PeakPower',50e3,'Gain',20,... 'LossFactor',0,'InUseOutputPort',true,... 'CoherentOnTransmit',true); radiator = phased.Radiator('Sensor',antenna,... 'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9); collector = phased.Collector('Sensor',antenna,... 'PropagationSpeed',physconst('LightSpeed'),... 'Wavefront','Plane','OperatingFrequency',4e9); receiver = phased.ReceiverPreamp('Gain',20,'NoiseFigure',2,... 'ReferenceTemperature',290,'SampleRate',1e6,... 'EnableInputPort',true,'SeedSource','Property','Seed',1e3); channel = phased.FreeSpace(... 'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',4e9,'TwoWayPropagation',false,... 'SampleRate',1e6);```
```T = 1/waveform.PRF; txpos = transmitterplatform.InitialPosition;```
```rxsig = zeros(waveform.SampleRate*T,numpulses); for n = 1:numpulses [tgtpos,tgtvel] = targetplatform(T); [tgtrng,tgtang] = rangeangle(tgtpos,txpos); sig = waveform(); [sig,txstatus] = transmitter(sig); sig = radiator(sig,tgtang); sig = channel(sig,txpos,tgtpos,[0;0;0],tgtvel); sig = target(sig); sig = channel(sig,tgtpos,txpos,tgtvel,[0;0;0]); sig = collector(sig,tgtang); rxsig(:,n) = receiver(sig,~txstatus); end rxsig = pulsint(rxsig,'noncoherent'); t = unigrid(0,1/receiver.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') hold off```