Range Doppler Response has a linear bias

The range doppler response of matlab's phased array system toolbox seems to have a linear bias for doppler frequency. The system is a moving radar platform (at certain altitude) and a stationary ground target and ground clutter (modeled as phased.ConstantGammaClutter object). In my particular case, 0 velocity will have everything in correct frequency (0 Hz for ground clutter and target), however for 10 m/s velocity, the frequency is 88 Hz more than what it should be (for both ground clutter and ground target), for 20 m/s it is 88*2 Hz more and so on. I am not sure if I'm missing some parameters, my phased.RangeDopplerResponse object is defined as follows

myResponse = phased.RangeDopplerResponse('RangeMethod','Matched Filter', ...
                                         'PropagationSpeed',c, 'DopplerOutput','speed',...
                                         'SampleRate', fs,'OperatingFrequency',fc,...
                                         'DopplerFFTLengthSource','Property', ...
                                         'DopplerFFTLength',1024);

Also, the limit on doppler frequency is supposed to be -PRF/2 to PRF/2 but it is a bit beyond that. This is not of too much concern, but the bias on doppler frequency is an issue. Any help or clarification is greatly appreciated. thanks

Answer 1

[Honglei Chen]

Hi Ramesh,

Is it possible for you to provide a little more details? Like what are the fs and fc? What are the position and velocity of the radar and the target? Otherwise it's hard to guess the issue.

[ramesh]

thank you for the reply. sorry, I didn't think those were relevant. fs is 10 MHz (sampling freq), fc is 10 GHz (carrier freq), the waveform is linear chirp with bandwidth of 2 MHz. The radar is placed at [0;0;3000] and the target is at [8.5e3; 0; 0], radar velocity is [50; 0; 0] and target's velocity is [0; 0; 0]. The elevation angle is -19 degrees. with all those parameters, my doppler frequency should be about 597 Hz, but I get 686 Hz. However, if I do my own fft and calculate the range doppler response,it shows correct doppler. Interestingly, the phased.AngleDopplerResponse also produces correct doppler frequency. I don't think the fft length (in phased.RangeDopplerResponse) is an issue as changing it changes the resolution, not the doppler shift.

[Honglei Chen]

I don't quite get why you say the correct Doppler frequency is 597 Hz. In fact I get neither 597 Hz nor 686 Hz. Based on what you have

rpos = [0;0;3000];
tpos = [8.5e3;0;0];
rvel = [50;0;0];
tvel = [0;0;0];

The relative speed I get is

rspeed = radialspeed(tpos,tvel,rpos,rvel)

About 47.15 m/s. So the corresponding Doppler is

c = 3e8;
Fc = 10e9;
fd = 2*tvel/(c/Fc)

This turns out to be about 3.14 kHz.

The following code shows a simple example I made based on your description. The PRF is made up but it should work for other values too. The figure I get correctly identifies the speed at about 47.15 m/s. Maybe you can take a look and see what I missed?

c = 3e8;
Fs = 10e6;
Fc = 10e9;
rpos = [0;0;3000];
tpos = [8.5e3;0;0];
rvel = [50;0;0];
tvel = [0;0;0];
dmax = 12e3;

prf = c/(2*dmax);

bw = 2e6;
myWav = phased.LinearFMWaveform('SampleRate',Fs,'PRF',prf,...
    'SweepBandwidth',bw,'PulseWidth',0.1/prf);

myRadarPlat = phased.Platform('InitialPosition',rpos,'Velocity',rvel);
myTargetPlat = phased.Platform('InitialPosition',tpos,'Velocity',tvel);
myChannel = phased.FreeSpace('SampleRate',Fs,'PropagationSpeed',c,...
    'OperatingFrequency',Fc,'TwoWayPropagation',true);

N = 64;
tstep = 1/prf;
for m = 1:64
    [rpos,rvel] = step(myRadarPlat,tstep);
    [tpos,tvel] = step(myTargetPlat,tstep);

      x = step(myWav);
      y(:,m) = step(myChannel,x,rpos,tpos,rvel,tvel);
  end

myResponse = phased.RangeDopplerResponse(...
        'RangeMethod','Matched Filter', ...
        'PropagationSpeed',c, 'DopplerOutput','speed',...
        'SampleRate', Fs,'OperatingFrequency',Fc,...
        'DopplerFFTLengthSource','Property', ...
        'DopplerFFTLength',1024);
plotResponse(myResponse,y,getMatchedFilter(myWav));

[ramesh]

Hi Honglei,

I think I figured out what was happening. It is partly my fault. My PRF was 10 KHz which gives me about 15 km of unambiguous range, my targets were at around 9 km so I didn't need to sample beyond a particular index and my code did exactly that. But when I used matlab's RangeDopplerResponse, I think it assumed that my ranges went from 0 to 15 km which caused my limit on doppler frequency to go beyond prf/2 (in negative and positive side) like I mentioned in my original post. I think that is what caused the doppler frequency to be incorrect. Now that I have removed the max-range limit, the problem is rectified.

I greatly appreciate your help. thank you