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 846 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. 848 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) 850 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) 851 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 852 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. 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