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This example shows the design of a moving target indication (MTI) radar to mitigate the clutter and identify moving targets. For a radar system, *clutter* refers to the received echoes from environmental scatters other than targets, such as land, sea or rain. Clutter echoes can be many orders of magnitude larger than target echoes. An MTI radar exploits the relatively high Doppler frequencies of moving targets to suppress clutter echoes, which usually have zero or very low Doppler frequencies.

A typical MTI radar uses a high pass filter to remove energy at low Doppler frequencies. Since the frequency response of an FIR high pass filter is periodic, some energy at high Doppler frequencies is also removed. Targets at those high Doppler frequencies thus will not be detectable by the radar. This issue is called the *blind speed problem*. This example shows how to use a technique, called staggered PRFs, to address the blind speed problem.

First, define the components of a radar system. The focus of this example is on MTI processing, so we'll use the radar system built in the example Designing a Basic Monostatic Pulse Radar. Readers are encouraged to explore the details of the radar system design through that example. Change the antenna's height to 100 meters to simulate a radar mounted on top of a building. Notice that the PRF in the system is approximately 30 kHz, which corresponds to a maximum unambiguous range of 5 km.

```
load BasicMonostaticRadarExampleData;
sensorheight = 100;
sensormotion.InitialPosition = [0 0 sensorheight]';
prf = waveform.PRF;
```

Retrieve the sampling frequency, the operating frequency, and the propagation speed.

fs = waveform.SampleRate; fc = radiator.OperatingFrequency; wavespeed = radiator.PropagationSpeed;

In many MTI systems, especially low-end ones, the transmitter's power source is a magnetron. Thus, the transmitter adds a random phase to each transmitted pulse. Hence, it is often necessary to restore the coherence at the receiver. Such setup is referred to as *coherent on receive*. In these systems, the receiver locks onto the random phased added by transmitter for each pulse. Then, the receiver removes the phase impact from the received samples received within the corresponding pulse interval. We can simulate a coherent on receive system by setting the transmitter and receiver as following:

transmitter.CoherentOnTransmit = false; transmitter.PhaseNoiseOutputPort = true; receiver.PhaseNoiseInputPort = true;

Next, define two moving targets.

The first target is located at position [1600 0 1300]. Given the radar position shown in the preceding sections, it has a range of 2 km from the radar. The velocity of the target is [100 80 0], corresponding to a radial speed of -80 m/s relative to the radar. The target has a radar cross section of 25 square meters.

The second target is located at position [2900 0 800], corresponding to a range of 3 km from the radar. Set the speed of this target to a blind speed, where the target's Doppler signature is aliased to the pulse repetition frequency. This setting prevents the MTI radar from detecting the target. We use the dop2speed() function to calculate a blind speed which has a corresponding Doppler frequency equal to the pulse repetition frequency.

wavelength = wavespeed/fc; blindspd = dop2speed(prf,wavelength)/2; % half to compensate round trip tgtpos = [[1600 0 1300]',[2900 0 800]']; tgtvel = [[100 80 0]',[-blindspd 0 0]']; tgtmotion = phased.Platform('InitialPosition',tgtpos,'Velocity',tgtvel); tgtrcs = [25 25]; target = phased.RadarTarget('MeanRCS',tgtrcs,'OperatingFrequency',fc);

The clutter signal was generated using the simplest clutter model, the constant gamma model, with the gamma value set to -20 dB. Such a gamma value is typical for flatland clutter. Assume that the clutter patches exist at all ranges, and that each patch has an azimuth width of 10 degrees. Also assume that the main beam of the radar points horizontally. Note that the radar is not moving.

trgamma = surfacegamma('flatland'); clutter = phased.ConstantGammaClutter('Sensor',antenna,... 'PropagationSpeed',radiator.PropagationSpeed,... 'OperatingFrequency',radiator.OperatingFrequency,... 'SampleRate',waveform.SampleRate,'TransmitSignalInputPort',true,... 'PRF',waveform.PRF,'Gamma',trgamma,'PlatformHeight',sensorheight,... 'PlatformSpeed',0,'PlatformDirection',[0;0],... 'BroadsideDepressionAngle',0,'MaximumRange',5000,... 'AzimuthCoverage',360,'PatchAzimuthWidth',10,... 'SeedSource','Property','Seed',2011);

Now we simulate 10 received pulses for the radar and targets defined earlier.

pulsenum = 10; % Set the seed of the receiver to duplicate results receiver.SeedSource = 'Property'; receiver.Seed = 2010; rxPulse = helperMTISimulate(waveform,transmitter,receiver,... radiator,collector,sensormotion,... target,tgtmotion,clutter,pulsenum);

We then pass the received signal through a matched filter.

```
matchingcoeff = getMatchedFilter(waveform);
matchedfilter = phased.MatchedFilter('Coefficients',matchingcoeff);
mfiltOut = matchedfilter(rxPulse);
matchingdelay = size(matchingcoeff,1)-1;
mfiltOut = buffer(mfiltOut(matchingdelay+1:end),size(mfiltOut,1));
```

MTI processing uses MTI filters to remove low frequency components in slow time sequences. Because land clutter usually is not moving, removing low frequency components can effectively suppress it. The three-pulse canceller is a popular and simple MTI filter. The canceller is an all-zero FIR filter with filter coefficients [1 -2 1].

h = [1 -2 1]; mtiseq = filter(h,1,mfiltOut,[],2);

Use noncoherent pulse integration to combine the slow time sequences. Exclude the first two pulses because they are in the transient period of the MTI filter.

```
mtiseq = pulsint(mtiseq(:,3:end));
% For comparison, also integrate the matched filter output
mfiltOut = pulsint(mfiltOut(:,3:end));
```

% Calculate the range for each fast time sample fast_time_grid = (0:size(mfiltOut,1)-1)/fs; rangeidx = wavespeed*fast_time_grid/2; % Plot the received pulse energy again range plot(rangeidx,pow2db(mfiltOut.^2),'r--',... rangeidx,pow2db(mtiseq.^2),'b-' ); grid on; title('Fast Time Sequences Using a Uniform PRF'); xlabel('Range (m)'); ylabel('Power (dB)'); legend('Before MTI filter','After MTI filter');

Recall that there are two targets (at 2 km and 3 km). In the case before MTI filtering, both targets are buried in clutter returns. The peak at 100m is the direct path return from the ground right below the radar. Notice that the power is decreasing as the range increases, which is due to the signal propagation loss.

After MTI filtering, most clutter returns are removed except for the direct path peak. The noise floor is now no longer a function of range, so the noise is now receiver noise rather than clutter noise. This change shows the clutter suppression capability of the three-pulse canceller. At the 2 km range, we see a peak representing the first target. However, there is no peak at 3 km range to represent the second target. The peak disappears because the three-pulse canceller suppresses the second target which travels at the canceller's blind speed.

To better understand the blind speed problem, let us look at the frequency response of the three-pulse canceller.

f = linspace(0,prf*9,1000); hresp = freqz(h,1,f,prf); plot(f/1000,20*log10(abs(hresp))); grid on; xlabel('Doppler Frequency (kHz)'); ylabel('Magnitude (dB)'); title('Frequency Response of the Three-Pulse Canceller');

Notice the recurring nulls in the frequency response. The nulls correspond to the Doppler frequencies of the blind speeds. Targets with these Doppler frequencies are cancelled by the three-pulse canceller. The plot shows that the nulls occur at integer multiples of the PRF (approximately 30kHz, 60kHz,...). If we can remove these nulls or push them away from the Doppler frequency region of the radar specifications, we can avoid the blind speed problem.

One solution to the blind speed problem is to use a nonuniform PRF, or staggered PRFs. Adjacent pulses are transmitted at different pulse repetition frequencies. Such configuration pushes the lower bound of blind speeds to a much higher value. To illustrate this idea, we will use a two-staggered PRF, and plot the frequency response of the three-pulse canceller.

Let us choose a second PRF at around 25kHz, which corresponds to a maximum unambiguous range of 6 km.

prf = wavespeed./(2*[6000 5000]); % Calculate the magnitude frequency response for the three-pulse canceller pf1 = @(f)(1-2*exp(1j*2*pi/prf(1)*f)+exp(1j*2*pi/prf(1)*f)); pf2 = @(f)(1-2*exp(1j*2*pi/prf(2)*f)+exp(1j*2*pi/prf(2)*f)); sfq = (abs(pf1(f)).^2 + abs(pf2(f)).^2)/2; % Plot the frequency response hold on; plot(f/1000,pow2db(sfq),'r--'); ylim([-50, 30]); legend('Uniform PRF','2-staggered PRF');

From the plot of the staggered PRFs we can see the first blind speed corresponds to a Doppler frequency of 150 kHz, five times larger than the uniform PRF case. Thus the target with the 30 kHz Doppler frequency will not be suppressed.

Now, simulate the reflected signals from the targets using the staggered PRFs.

% Assign the new PRF release(waveform); waveform.PRF = prf; release(clutter); clutter.PRF = prf; % Reset noise seed release(receiver); receiver.Seed = 2010; % Reset platform position reset(sensormotion); reset(tgtmotion); % Simulate target return rxPulse = helperMTISimulate(waveform,transmitter,receiver,... radiator,collector,sensormotion,... target,tgtmotion,clutter,pulsenum);

We process the pulses as before by first passing them through a matched filter and then integrating the pulses noncoherently.

mfiltOut = matchedfilter(rxPulse); % Use the same three-pulse canceller to suppress the clutter. mtiseq = filter(h,1,mfiltOut,[],2); % Noncoherent integration mtiseq = pulsint(mtiseq(:,3:end)); mfiltOut = pulsint(mfiltOut(:,3:end)); % Calculate the range for each fast time sample fast_time_grid = (0:size(mfiltOut,1)-1)/fs; rangeidx = wavespeed*fast_time_grid/2; % Plot the fast time sequences against range. clf; plot(rangeidx,pow2db(mfiltOut.^2),'r--',... rangeidx,pow2db(mtiseq.^2),'b-' ); grid on; title('Fast Time Sequences Using Staggered PRFs'); xlabel('Range (m)'); ylabel('Power (dB)'); legend('Before MTI filter','After MTI filter');

The plot shows both targets are now detectable after MTI filtering, and the clutter is also removed.

With very simple operations, MTI processing can be effective at suppressing low speed clutter. A uniform PRF waveform will miss targets at blind speeds, but this issue can be addressed by using staggered PRFs. For clutters having a wide spectrum, the MTI processing could be poor. That type of clutter can be suppressed using space-time adaptive processing. See the example Introduction to Space-Time Adaptive Processing for details.

Reference: Mark A. Richards, *Fundamentals of Radar Signal Processing*, McGraw-Hill, 2005.

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