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phased.CFARDetector2D
Two-dimensional CFAR detector
Description
The phased.CFARDetector2D System
object™ implements a constant
false-alarm rate detector (CFAR) for selected elements (called cells)
of two-dimensional image data. A detection is declared when an image
cell value exceeds a threshold. To maintain a constant false alarm-rate,
the threshold is set to a multiple of the image noise power. The detector
estimates noise power for a cell-under-test (CUT) from
surrounding cells using one of three cell averaging methods, or an
order statistics method. The cell-averaging methods are cell averaging
(CA), greatest-of cell averaging (GOCA), or smallest-of cell averaging
(SOCA).
For each test cell, the detector:
estimates the noise statistic from the cell values in the training band surrounding the CUT cell.
computes the threshold by multiplying the noise estimate by the threshold factor.
compares the CUT cell value to the threshold to determine whether a target is present or absent. If the value is greater than the threshold, a target is present.
To run the detector
Define and set up your 2-D CFAR detector. You can set the
phased.CFARDetector2DSystem object properties when you create the object, or leave them set to their default values. See Construction. Some properties that you set at construction time can be changed later. These properties are tunable.Find the detections by calling the
stepmethod. The output of this method depends on the properties of thephased.CFARDetector2DSystem object.
Note
Alternatively, instead of using the step method
to perform the operation defined by the System
object, you can
call the object with arguments, as if it were a function. For example, y
= step(obj,x) and y = obj(x) perform
equivalent operations.
Construction
detector = phased.CFARDetector2Ddetector.
detector = phased.CFARDetector2D(Name,Value)detector, with
each specified property Name set to the specified Value.
You can specify additional name-value pair arguments in any order
as (Name1,Value1,...,NameN,ValueN).
Properties
Methods
| reset | Reset states of System object |
| step | Two-dimensional CFAR detection |
| Common to All System Objects | |
|---|---|
release | Allow System object property value changes |
Examples
Set 2-D CFAR Threshold for Noise-Only Data
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.
Detect Targets in Background Noise
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.
More About
Training Cells
CFAR 2-D requires an estimate of the noise power. Noise power is computed from cells that are assumed not to contain any target signal. These cells are the training cells. Training cells form a band around the cell-under-test (CUT) cell but may be separated from the CUT cell by a guard band. The detection threshold is computed by multiplying the noise power by the threshold factor.
For GOCA and SOCA averaging, the noise power is derived from the mean value of one of the left or right halves of the training cell region.
Because the number of columns in the training region is odd, the cells in the middle column are assigned equally to either the left or right half.
When using the order-statistic method, the rank cannot be larger than the number of cells in the training cell region, Ntrain. You can compute Ntrain.
NTC is the number of training band columns.
NTR is the number of training band rows.
NGC is the number of guard band columns.
NGR is the number of guard band rows.
The total number of cells in the combined training region, guard region, and CUT cell is Ntotal = (2NTC + 2NGC + 1)(2NTR+ 2NGR + 1).
The total number of cells in the combined guard region and CUT cell is Nguard = (2NGC + 1)(2NGR + 1).
The number of training cells is Ntrain = Ntotal – Nguard.
By construction, the number of training cells is always even. Therefore, to implement a median filter, you can choose a rank of Ntrain/2 or Ntrain/2 + 1.
Algorithms
References
[1] Mott, H. Antennas for Radar and Communications. New York: John Wiley & Sons, 1992.
[2] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.
[3] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.
