1. science
2. mathematics
3. statistics

Journal of Information & Computational Science 12:2 (2015) 845–853
Available at http://www.joics.com
January 20, 2015
A New Adaptive CFAR Detection Algorithm ⋆
Panzhi Liu a,b,∗, Penglang Shui b , Meng Hui a , He Huang a
a School
of Electronic and Control Engineering, Chang’an University, Xi’an 710064, China
b National
Key Lab. of Radar Signal Processing, Xidian University, Xi’an 710071, China
Abstract
Aim to solve the problem of lower detection probability and the false alarm probability exceeding the
design value, a new method is proposed for the randomness interference number in CFAR (Constant
False Alarm Rate) detection. This method estimates the background noise power levels based on the
reference variance statistics. Therefore it can automatically adjust the detection threshold, varying with
the background noise level change. The computer simulation results show that it needn’t sort the samples
like order statistics OS (k), and be subject to the specified K value restrictions. And the method can not
only adaptively adjust the threshold according to the interference number, but also retain the optimal
detection performance of the ML method in a homogeneous detection environment. It has good usability
and is easy to implement.
Keywords: Signal Detection; CFAR Detection; Computer Simulation; Radar Adaptive Threshold
1
Introduction
CFAR detection (CFAR, Constant False Alarm Rate) involves target detection using adaptive threshold estimation techniques. The threshold is the product of the local background
noise/clutter power and a scaling constant based on the desired Probability of False Alarm (PFA).
So, in order to design a good CFAR detector, statistical information of background noise/clutter
is particularly important. Usually, they obey a certain distribution, such as the Rayleigh, lognormal, Weibull distribution or K distribution [1, 2]. The chaff, sea clutter of incident angle greater
than 5 degrees, and that incident angle greater than 5 degree angle ground clutter in undeveloped
zone can be described by Rayleigh distribution.
Cell average CFAR algorithm is the optimal detector [3], under a condition that the samples
in the CFAR window are independent and identically distributed (IID) and obey exponential
distribution. In practice, its performance loss is serious in both cases. This is because of the
nonhomogeneity of clutter within a CFAR window which makes above assumption invalid: (i)
⋆
This work is supported by the National Nature Science Foundation of China (Nos. 41101357, 51407012,
61102163), Important National Science & Technology Specific Project (No. 2010ZX03006-002-03), and the Special
Fund for Basic Scientific Research of Central Colleges, Chang’an University (Nos. 2013G1321046, 2013G1321037).
∗
Corresponding author.
Email address: [email protected] (Panzhi Liu).
1548–7741 / Copyright © 2015 Binary Information Press
DOI: 10.12733/jics20105587
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P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
there is a clutter edge, e.g., at the border of land and sea, and (ii) there is an outlier, e.g., a
clutter spike, an impulsive interference, or another interfering target [4].
In order to improve the CFAR detector performance under certain situations, such as multitarget and inhomogeneous clutter, many scholars have put forward various improved CFAR algorithm. They can be summarized two kinds methods in the CFAR literature.
Some scholars aim to modify the conventional CA-CFAR. Such as, some scholars put forward
the GO-CFAR algorithm and SO-CFAR algorithm, as the revised CA-CFAR detectors. However,
they can only solve one kind of problems above mentioned, and also cause the performance loss
relative to the optimal detector. GO-CFAR algorithm in clutter edge environment can maintain
good false alarm control performance, but in the multi-targets environment this method will cause
a “shelter” phenomenon. When interference targets are only located in the front or after sliding
window, SO-CFAR algorithm has good resolution in multiple target. But its false alarm control
ability is not ideal.
Rohling proposed OS-CFAR [5] detector, the method processes the ordered samples in the
slip window. In addition, Order Statistics (OS) method has good detection performance in the
multi-targets situation, but at the same time this method has a certain loss. So, it is still to be
solved under the condition of certain clutter edge. In multi-targets environment, compared with
ML-CFAR detector, OS-CFAR detector has a certain advantage. Because the method removed
some possible interference target signal of reference samples, to a certain extent, this can reduce
probability of the interference echo into clutter power estimate. The clutter power estimate tends
to be more reasonable. However, when the interference number exceeds the limits of tolerance,
OS-CFAR performance declines seriously. On this basis, the scholars put forward many new
CFAR methods, such as He You proposed GOS-CFAR method based on automatic censoring
technique [6, 7].
Another group of scholars put forward combine the advantages of different methods [8]-[10], to
get better detection performance. They used some methods to determine the nonhomogeneity
of the detection background, and then carried out properly CFAR processing. In literature [11],
firstly, calculates the second order statistic and the ratio of the means of leading and lagging
window sample, then select appropriate CFAR methods from CA, GO, SO algorithm according
to above two data. Similar to the above method, MMR method [12], also based on the ratio of
the means of leading and lagging window sample. An improved method was proposed [13] based
on literature [11]. It introduced the fuzzy function to confirm the nonhomogeneity of background.
At the same time, the author KIM [14] used goodness-of-fit test to determine the characteristics
of non-uniform background. It combined multi-resolution and OS, called CI-CFAR.
As shown in previous analysis, when the number of interference randomly changes, it makes
the background noise power level deviate from the actual value, which makes the false-alarm
probability and detection probability change. So the constant false alarm rate detection cannot
be realized and even affect the reliability of test results. So it requires appropriate detection
scheme to make the appropriate treatment for the specific circumstances.
2
Basic Hypothesis of Constant False Alarm Detector and
Model Description
Radar detection is often in interference background, intentionally or unintentionally, so detection
P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
847
background power often changes. As we all know, in target detection, target is often under the
background of noise and other disturbance, but we always hope the false alarm probability of
detection system can remain near the designed value, whatever interference power level changes.
Even if false alarm probability changes, also hope the change is small. So this needs the Constant
False Alarm Rate (CFAR) technology. A typical processor with constant false alarm rate block
diagram is shown in Fig. 1.
In put signals
Match filter
Envelope detector
Xn+1
X2n
X0
Xn
…
… X2 X1
…
Comparator
CFAR processing
Stop shift register
Test cell
Z
Decision
D=1
D=0
S=TZ
T
Fig. 1: CFAR processor block diagram
The proposed CEAR processor block diagram is provided in Fig. 1. Signals corresponding to
samples of radar time/range returns from a matched filter receiver are processed firstly squarelaw/linear-law envelope, and then a sequential set of N+1 outputs is stored in a tapped delay
line. The N+1 samples correspond to a test cell centered in an N cell reference window.
A reference window can be divided into two parts. They are leading (Window A) and lagging
(Window B) halves. Usually, for a homogeneous noise environment, there is an assumption, input
signals are independent, identically distributed (IID), zero mean, Gaussian random processes.
Consequently, the envelope amplitude at the output of a square-law detector is an exponentially
distributed random variable (the linear-law detector has an output which is Rayleigh distributed)
[3]. The samples in the reference window are independent of each other and of the sample in the
test cell. According to the different CFAR algorithm, clutter power level can be gotten:
Z = f (x1 , x2 , . . . , x2n )
(1)
where f (.) stands for the pretreatment of the received reference samples. Their common Probability Density Function (pdf) is described by:
( x)
1
fd (x) = ′ exp − ′ ,
λ
λ
x≥0
(2)
where, λ′ =1+A if a reference cell contains a target with an average Signal to Noise Ratio (SNR)
equal to A and λ′ = 1 if a reference cell has no target.
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P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
The adaptive threshold is equal to the product of a scaling constant and a background noise/
clutter power estimate.
The decision criterion for this algorithm is
H1
X0 >
< TZ
H0
(3)
in which H1 , represents target present and H0 , represents no target. This process is repeated
when the next sample is received from the envelope detector.
Most CFAR detection method is focused on the use of the first-order statistics of samples.
We know that the second order statistics of the samples, can display the degree of each sample
deviates from the sample mean. At the same time, the goal of CFAR detection is to select the
appropriate subset of reference cells used for background noise/clutter estimation in nonhomogeneous environment. So this paper proposed a new CFAR detection algorithm utilizing the first
and second order statistics, which can dynamically adjust the threshold.
3
The Average Adaptive Detection Method Based on
Statistics
Adaptive CFAR detectors based on the statistics block diagram is shown in Fig. 2. To get the
clutter power level, the adaptive CFAR detector in Fig. 2 doesn’t depend on a priori information
about the interference, such as interference target number. Where X0 is a test cell, the reference
window is divided into leading (Window A) and lagging (Window B) halves. This method first
2n
∑
calculates the statistics of the sample in the reference window: mean x¯ and variance σ 2 = (xi −
i=1
x¯)2 /2n. And calculate variance of each sample σi2 = (xi − x¯)2 , i = 1, . . . , 2n. Then, σi2 and σ 2 is
Input signal
Square law
detector
Match filter
…
Xn+1
Xn
X0
X2 X1
…
σ2 of 2n samples, and σi2 of each sample
Remove the samples not
satisfied some condition
Mean of samples retained
Comparator
X2n
Stop shift register
Test cell
Decision
D=1
D=0
S=TZ
T
Z
Fig. 2: CFAR block diagram based on statistics information
P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
849
compared. If σi2 > Kδ σ 2 (where Kδ is determined by Eq. (4)), xi is removed, and replaced by the
mean of the remaining valid samples; Otherwise, xi is reserved. According to new samples kept,
we can calculate the mean of the new samples.
¯ < Kδ } = α
1 − P {|δi − δ|
(4)
where the parameter α is the probability of the δi falling out of the limit of δ in a Rayleigh
background. The typical value of α should not exceed 0.1 [3].
Assume that k sampling values are kept finally, then
1∑
1∑
1 ∑ ′
xi =
xi + (2n − k)
xi
x¯ =
2n i=1
k i=1
k i=1
2n
k
k
′
(5)
The 2n samples no longer conforms with the requirements of independent, Identically Distributed (IID), the PDF of x¯′ cannot simply get by convoluting a PDF of x′i . We can implement
equivalent computing for Eq. (5):
k
k
k
k (
(1
)∑
)
∑
1
1∑
1∑
′
x¯ =
xi + (2n − k)
xi =
+ 2n/k − 1
xi =
+ 2n/k − 1 xi
(6)
k i=1
k i=1
k
k
i=1
i=1
Therefore, new variables can be introduced.
)
(1
+ 2n/k − 1 xi
yi =
k
(7)
So the average estimates of clutter power level:
z=
k
∑
βxi
(8)
i=1
where β = k1 + 2n/k − 1. Input signals are assumed to be independent, Identically Distributed
(IID). Their common Probability Density Function (pdf) is described by:
(
1
1 )
f (yi ) =
exp −
yi
(9)
βλ
βλ
Therefore, Moment Generating Function (MGF) of y can be obtained based on Eq. (9):
Mx (u) = (1 + β ′ u)−α (α = 1) = (1 + β ′ u)−1
(10)
The MGF of the sum of IID random variable is the product of the MGF of each variable.
Therefore Moment Generating function of Z can be gotten:
That is:
Z : G(k, µ′ )
(11)
MZ (u) = (1 + β ′ u)k
(12)
Then the detection probability
(
T )k
Pd = MZ (u) u= ′ T = 1 +
µ (1+λ)
(1 + λ)
(13)
The false alarm probability:
Pf == (1 + T )k
(14)
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P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
4
Performance Analysis
This paper proposes a new adaptive cell average CFAR method, and gives the detection probability and false alarm probability analytical form of the detector. For testing performance of
the new detector, the proposed detector-modified cell average CFAR detector (MCA-CFAR) will
be compared with the traditional CA-CFAR detectors, OS-CFAR detector, in Gauss noise background and multiple targets situation. Related parameters and threshold T for a given false alarm
probability each detector are shown in Table 1.
Table 1: Detector parameters
Detector
RCN
k(l)
Pf a
T
CA
28
/
10-6
0.6379
OS
28
19
10-6
20.2
MCA
28
/
10-6
/
Homogeneous environment: Three detector performance curves for gauss noise environment are
shown in Fig. 3. The detection performance of MCA-CFAR this paper proposed is in accord with
CA-CFAR in Fig. 3. It also can be proved from the analytic expression of detection probability.
That is there is no interference, namely k = 2n in Eq. (1). At the same time, because this method
retains more sampling, the effect is obviously better than OS detector.
Multi-targets situation: Fig. 4, Fig. 5 and Fig. 6 show three detectors detection performance
respectively, for different interference number(r). From Fig. 4 to Fig. 6, the detection loss of CA
detector is serious, and the detection performance of OS and MCA detector demonstrates their
obvious advantages. Especially in the low signal-to-noise ratio (< 15 db), the proposed algorithm
(MCA) detector is superior to the OS detector. But at a high signal-to-noise ratio (> 15 db), OS
detector performance is with obvious advantages.
From Fig. 4 to Fig. 6, it shows that with the increase of interference target number, CA detector
performance deteriorates seriously; and OS and MCA detection performance will decline to some
degree, but with good anti-interference performance.
0.9
1.0
0.9
0.8
0.8
Probability of detection
Probability of detection
1.0
0.7
0.6
0.5
0.4
0.3
MCA
CA
OS
0.2
0.1
0
0
5
10
15
SNR (dB)
20
25
0.7
0.6
0.5
0.4
0.3
0.2
0.1
30
Fig. 3: The detector performance in Homogeneous environment
MCA
CAr
OSr
0
0
Fig. 4:
5
10
15
20
SNR (dB)
25
30
The detector performance in multitargets environment (r = 4)
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P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
1.0
0.8
1.0
MCA
CAr
OSr
0.9
Probability of detection
Probability of detection
0.9
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.8
MCA
CAr
OSr
0.7
0.6
0.5
0.4
0.3
0.2
0.1
5
10
15
20
SNR (dB)
25
0
0
30
Fig. 5:
The detector performance in multitargets environment (r = 8)
5
10
15
20
SNR (dB)
25
30
Fig. 6:
The detector performance in multitargets environment (r = 9)
Fig. 7 shows simulation results of three methods, when interference number is 10. It can be
seen that, when the number of interference is beyond OS tolerance, OS detection performance
declines obviously compared with MCA method.
Conclusions [5] have shown that when the number of interference is random, the loss of false
alarm sharply will increase with the increasing of uncertainty of interference number. It is greater
than false-alarm loss of a fixed interference number model. From Fig. 7, in multi-target detection
environment, the MCA method can adaptively adjust detection threshold as the number of interference random change. Therefore it can avoid the restriction of fixed number of interference
of the OS detector.
Fig. 8 shows the detection performance of MCA, when the number of interference is varying. It
shows that with the increase of interference number, MCA detector performance decline linearly.
This adaptive algorithm is aimed at improving performance of CFAR detector against multiple
interference targets. In multiple interference background, especially low Signal Noise Ratio (S0.9
0.7
0.6
Probability of detection
Probability of detection
0.8
0.7
MCA
CAr
OSr
0.6
0.5
0.4
0.3
0.2
Fig. 7:
0.4
0.3
0.2
0.1
0.1
0
0
SNR=15 dB
0.5
5
10
15
20
SNR (dB)
25
0
0
30
The detector performance in multitargets environment (r = 10)
5
10
15
20
Number of interference
25
30
Fig. 8: The detector performance of MCA detector
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P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
NR) or uncertainty of interference number, MCA shows better performance than other methods.
Compared with the OS (k), the proposed algorithm is slightly inferior under strong interference
signal environment. The algorithm is preferable for multi-target situation. In multi-target environment, the proposed algorithm has better detection performance, and the interference target
number it can accommodate won’t be restricted.
5
Conclusions
For the problem of uncertain interference number, this paper proposes a new method based on
the statistics of reference sample, to estimate background noise power level. According to the
statistics of the reference sample– mean and variance, the sampling values will be deleted if its
variance is greater than a certain value. The average of remaining valid samples will instead of
it, to calculate the average sampling values. The simulation result shows that this method can
adaptively adjust threshold with the change of the inference number, and keep better detection
performance in homogeneous background like CA-CFAR method. It offers good applicability,
operability. And it does not need to sort reference samples like OS-CFAR, also not be restricted
by k value specified.
Acknowledgments
We are grateful to our reviewers who dedicated their time in reviewing the submitted papers and
provided valuable suggestions to the authors.
References
[1]
M. I. Skolnik, Introduction to Radar Systems (2nd Ed.) [M], New York: McGraw-Hili, 1980
[2]
H. C. Chan, Radar sea-clutter at low grazing angles [C], lEE Proceedings, 137(2), 1990, 102-117
[3]
Mohamed Baadeche, Faouzi Soltani, Performance comparison of some CFAR detectors in homogenous and non-homogenous clutter, ICSIPA, 2013, 101-105
[4]
Hermann Rohling, Ordered statistic CFAR technique - An overview [J], Radar Science and Technology, 10(2), 2012, 117-123
[5]
H. Rohling, Radar CFAR thresholding in clutter and multiple target situations [J], IEEE Trans.
on AES, 19(3), 1983, 608-621
[6]
He You, Hermann Rohling, Performance of two generalized order statistics cfar detectors with
automatic censoring technique in multiple target situations [J], Journal of Electronics, 16(6), 1994,
582-590 (in Chinese)
[7]
He You, Guan Jian, Two new CFAR detector based on greatest of and smallest of selection [J],
Journal of Systems Engineering and Electronics, 17(7), 1995, 6-16 (in Chinese)
[8]
Xiangwei Meng, Dongcai Qu, You He, CFAR detection for range-extended target in Gaussian
background [J], System Engineering and Electronics, 27(6), 2005, 1012-1015 (in Chinese)
[9]
Xiangwei Meng, Jian Guan, You He, Performance avalysis of generalized smallest option of CFAR
algorithm [J], Journal of Electronics Information Technology, 25(1), 2003, 17-23 (in Chinese)
P. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 845–853
853
[10] You He, Xiangwei Meng, A new greatest of selection CFAR detector based on trimmed mean [J],
Journal of Electronics Information Technology, 21(6), 1999, 779-785 (in Chinese)
[11] M. E. Smith, P. K. Varshney, Intelligent CFAR processor based on data variability, IEEE Transactions on Aerospace Electronic Systems, 36(3), 2000, 837-847
[12] T. V. Cao, D. Sinnott, A rare event approach to the detection of target-like signals in CFAR
training data [C], Proc. the IET International Conference on Radar Systems, Edinburgh, UK,
October 2007
[13] K. Cheikh, F. Soltani, Performance of the fuzzy VI-CFAR detector in non-homogeneous environments [C], 2011 IEEE International Conference on Signal and Image Processing Applications
(ICSIPA), 2011, 100-103
[14] Jeong Hun Kim, M. R. Bell, A computationally efficient CFAR algorithm based on a goodness-of-fit
test for piecewise homogeneous environments [J], IEEE Transactions on Aerospace and Electronic
Systems, 49(3), 2013, 1519-1535