This example shows how to set a 2-D CFAR threshold based upon a required probability of false alarm (pfa).

Note: You can replace each call to the function with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).

Perform cell-averaging CFAR detection on a 41-by-41 matrix of cells containing Gaussian noise. Estimate the empirical pfa and compare it to the required pfa. To get a good estimate, perform this simulation on 1000 similar matrices. First, set a threshold using the required pfa. In this case, there are no targets and the pfa can be estimated from the number of cells that exceed the threshold. Assume that the data is processed through a square-law detector and that no pulse integration is performed. Use a training-cell band of 3 cells in width and 4 cells in height. Use a guard band of 3 cells in width and 2 cells in height to separate the cells under test (CUT) from the training cells. Specify a required pfa of 5.0e-4.

p = 5e-4;
rs = RandStream.create('mt19937ar','Seed',5);
N = 41;
ntrials = 1000;
detector = phased.CFARDetector2D('TrainingBandSize',[4,3], ...
    'ThresholdFactor','Auto','GuardBandSize',[2,3], ...
    'ProbabilityFalseAlarm',p,'Method','SOCA','ThresholdOutputPort',true);

Create a 41-by-41 image containing random complex data. Then, square the data to simulate a square-law detector.

x = 2/sqrt(2)*(randn(rs,N,N,ntrials) + 1i*randn(rs,N,N,ntrials));
x2 = abs(x).^2;

Process all the cells in each image. To do this, find the row and column of each CUT cell whose training region falls entirely within each image.

Ngc = detector.GuardBandSize(2);
Ngr = detector.GuardBandSize(1);
Ntc = detector.TrainingBandSize(2);
Ntr = detector.TrainingBandSize(1);
cutidx = [];
colstart = Ntc + Ngc + 1;
colend = N - ( Ntc + Ngc);
rowstart = Ntr + Ngr + 1;
rowend = N - ( Ntr + Ngr);
for m = colstart:colend
    for n = rowstart:rowend
        cutidx = [cutidx,[n;m]];
    end
end
ncutcells = size(cutidx,2);

Display the CUT cells.

cutimage = zeros(N,N);
for k = 1:ncutcells
    cutimage(cutidx(1,k),cutidx(2,k)) = 1;
end
imagesc(cutimage)
axis equal

Perform the detection on all CUT cells. Return the detection classification and the threshold used to classify the cell.

[dets,th] = detector(x2,cutidx);

Find and display an image with a false alarm for illustration.

di = [];
for k = 1:ntrials
    d = dets(:,k);
    if (any(d) > 0)
        di = [di,k];
    end
end
idx = di(1);
detimg = zeros(N,N);
for k = 1:ncutcells
    detimg(cutidx(1,k),cutidx(2,k)) = dets(k,idx);
end
imagesc(detimg)
axis equal

Compute the empirical pfa.

pfa = sum(dets(:))/ntrials/ncutcells

pfa = 4.5898e-04

The empirical and specified pfa agree.

Display the average empirical threshold value over all images.

mean(th(:))

ans = 31.7139

Compute the theoretical threshold factor for the required pfa.

threshfactor = npwgnthresh(p,1,'noncoherent');
threshfactor = 10^(threshfactor/10);
disp(threshfactor)

    7.6009

The theoretical threshold factor multiplied by the noise variance should agree with the measured threshold.

noisevar = mean(x2(:));
disp(threshfactor*noisevar);

   30.4118

The theoretical threshold and empirical threshold agree to within an acceptable difference.

Perform cell-averaging CFAR detection on a 41-by-41 matrix of cells containing five closely-spaced targets in Gaussian noise. Perform this detection on a simulation of 1000 images. Use two detectors with different guard band regions. Set the thresholds manually using the Custom threshold factor. Assume that the data is processed through a square law-detector and that no pulse integration is performed. Use a training cell band of 2 cells in width and 2 cells in height. For the first detector, use a guard band of 1 cell all around to separate the CUT cells from the training cells. For the second detector, use a guard band of 8 cells all around.

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).

p = 5e-4;
rs = RandStream.create('mt19937ar','Seed',5);
N = 41;
ntrials = 1000;

Create 1000 41-by-41 images of complex random noise with standard deviation of 1.

s = 1;
x = s/sqrt(2)*(randn(rs,N,N,ntrials) + 1i*randn(rs,N,N,ntrials));

Set the target cells values to 1.5. Then, square the cell values.

A = 1.5;
x(23,20,:) = A;
x(23,18,:) = A;
x(23,23,:) = A;
x(20,22,:) = A;
x(21,18,:) = A;
x2 = abs(x).^2;

Display the target cells.

xtgt = zeros(N,N);
xtgt(23,20,:) = A;
xtgt(23,18,:) = A;
xtgt(23,23,:) = A;
xtgt(20,22,:) = A;
xtgt(21,18,:) = A;
imagesc(xtgt)
axis equal
axis tight

Set the CUT cells to be the target cells.

cutidx(1,1) = 23;
cutidx(2,1) = 20;
cutidx(1,2) = 23;
cutidx(2,2) = 18;
cutidx(1,3) = 23;
cutidx(2,3) = 23;
cutidx(1,4) = 20;
cutidx(2,4) = 22;
cutidx(1,5) = 21;
cutidx(2,5) = 18;

Perform the detection on all CUT cells using two CFAR 2-D detectors. The first detector has a small guard band region. The training region can include neighboring targets which can affect the computation of the noise power. The second detector has a larger guard band region, which precludes target cells from being used in the noise computation.

Create the two CFAR detectors.

detector1 = phased.CFARDetector2D('TrainingBandSize',[2,2], ...
    'GuardBandSize',[1,1],'ThresholdFactor','Custom','Method','CA', ...
    'CustomThresholdFactor',2,'ThresholdOutputPort',true);
detector2 = phased.CFARDetector2D('TrainingBandSize',[2,2], ...
    'GuardBandSize',[8,8],'ThresholdFactor','Custom','Method','CA', ...
    'CustomThresholdFactor',2,'ThresholdOutputPort',true);

Return the detection classifications and the thresholds used to classify the cells. Then, compute the probabilities of detection.

[dets1,th1] = detector1(x2,cutidx);
ndets = numel(dets1(:));
pd1 = sum(dets1(:))/ndets

pd1 = 0.6416

[dets2,th2] = detector2(x2,cutidx);
pd2 = sum(dets2(:))/ndets

pd2 = 0.9396

The detector with the larger guard-band region has a higher pfa because the noise is more accurately estimated.