A New Model of CFAR Detector

DOI 10.1515/freq-2013-0087 Frequenz 2014; 68(3–4): 125 – 136 Dejan Ivković*, Milenko Andrić and Bojan Zrnić A New Model of CFAR Detector Abstract: This paper presents a new model of the CFAR (Constant False Alarm Rate) detector. Mentioned CFAR detector is named cell-averaging-trimmed-mean CFAR (CATMCFAR), which is a combination of cell-averaging CFAR and trimmed mean CFAR. It is implemented in the receiver of the software defined radar. Expressions for the probability of detection, the probability of false alarm and the average decision threshold are derived. The article presents detection of simulated radar targets in Weibull clutter and real radar targets in real clutter and compares characteristics of new CATM-CFAR with some realized well known CFAR detectors. Keywords: CFAR detection, radar target, clutter, software radar receiver PACS® (2010). 84.40.Xb, 07.50.Qx *Corresponding author: Dejan Ivković: Military Technical Institute, Ratka Resanovića 1, 11030 Belgrade, Serbia. E-mail: divkovic555@gmail.com Milenko Andrić: University of Defence, Generala Pavla Jurišića Šturma 33, 11000 Belgrade, Serbia Bojan Zrnić: Defence Technologies Department, Nemanjina 15, 11000 Belgrade, Serbia 1 Introduction Radars work always in an environment where there are different sources of noise. It must use the adaptive threshold detector, which has a feature that adjusts automatically its sensitivity according to variety of the interference power. Thus it maintains a constant probability of false alarm. Detector in radar receivers with this feature is the constant false alarm rate (CFAR) processor. The basic model of adaptive threshold detector is cell-averaging CFAR (CA-CFAR) [1]. A test cell is in the middle of reference window. Surrounding cells of test cell are termed reference cells. CFAR calculates interference power in the test cell on the basis of the average amplitude in the reference cells (Z). Then the variable Z is multiplied by a constant called the scaling factor of the detection threshold (T) and thus it forms a detection threshold (S) which is compared to the signal level within the test cell. Constant T is determined by the required probability of false alarm (Pfa). The increasing of the number of reference cells induces to an increase of the probability of detection (Pd ). However, there are two basic detection problems associated with the CA-CFAR algorithm. The first problem is the clutter edge and the second problem is the appearance of multiple target situation. The energy of interference changes in the case of the clutter edge rapidly. For example, this occurs at the border between land and sea. Multiple target situation can cause the masking of weaker targets in neighborhood of stronger targets. To reduce the negative effects of the two above problems many modifications of the conventional CA-CFAR have been made. In general, these modifications can be classified into several groups. The first group consists of CFAR algorithms that use the averaging technique. The smallest-of CFAR (SO-CFAR) [2] is designed to improve target detection in case of multiple target situations. SO-CFAR selects the part with a smaller sample sum for threshold computation. The greatest-of CFAR (GO-CFAR) [1] is designed to improve target detection in case of the clutter edge. It minimizes the Pfa at a clutter edge by selecting the part with a greater sample sum. The second group consists of algorithms that use ordering technique, in which sorting of reference cells by the amplitude in ascending order is made. The censored cell-averaging CFAR (CCA-CFAR) is used for case of multiple target situations and it is the first trimmed mean CFAR (TM-CFAR) [3] where the ordered range samples are trimmed only from the upper end. Here the interference power is estimated as a linear combination of sorted cell contents of the observed reference window. Different analysis of the TM-CFAR is given in [4] where T1 smallest ranked cells and T2 greatest ranked cells are discarded. Ordered-statistic CFAR (OS-CFAR) [5] forms detection threshold on the basis of the k-th ordered reference cell. The censored mean level CFAR detector (CMLD-CFAR) [6] is used for two correlated targets in N size reference window. The optimal censored mean level CFAR detector (Opt-CMLD-CFAR) [7] is proposed for multiple target situations. The third group consists of some algorithms which are combination of above mentioned techniques, also in order to reduce problems of clutter edge and interfering targets. In [8, 9] is proposed combination of smallest-of and greatest-of concepts with OS-CFAR, but here there is a Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM 126 D. Ivković et al., A New Model of CFAR Detector decrease of the probability of detection in homogenous clutter. The weighted order statistic and fuzzy rules CFAR (WOSF-CFAR) [10] detector uses some soft rules based on fuzzy logic to cure the mentioned problems by OSSO and OSGO-CFAR detectors. The fourth group consists of algorithms that in theirs procedures have some kind of a fusion center. This group can be divided into two subgroups on the basis of the implementation method of a data fusion. The first subgroup consists of models which practice a data fusion from several distributed CFAR detectors in space. Distributed fuzzy CA-CFAR and OS-CFAR detectors [11] give good results for homogenous environment and in multiple target or clutter edge situations also. The fuzzy cellaveraging CFAR (FCA-CFAR) and the fuzzy greatest-of CFAR (FGO-CFAR) [12] detectors are applied in a decentralized fuzzy fusion data center. The second subgroup consists of models which practice a data fusion by using a parallel operation of several CFAR detectors centralized in one sensor. The linear combination of order statistics CFAR (LCOS-CFAR) [13] detector has M channeled reference window with several types of CFAR The And-CFAR and Or-CFAR [14] use binary AND and binary OR to make data fusion from CA-CFAR and OS-CFAR detectors which work in parallel. An algorithm of parallel operation of CA, GO and SO-CFAR detectors with one fusion center based on neural network is proposed in [15]. Also, an algorithm of parallel operation of CA, TM and OS-CFAR detectors with some data fusion rules in multiple target situations is proposed in [16]. In this paper we propose a new CFAR detector named cell-averaging-trimmed-mean CFAR (CATM-CFAR), which is a combination of CA-CFAR and TM-CFAR. The new CFAR has some advantages over other types of CFAR detectors. The paper is organized as follows. The model description that has been used to analyze the performance of the CATM-CFAR detector is discussed in Section 2. In Section 3, a description of CATM-CFAR is given, and exact expressions for parameters of new CFAR detector are derived. Also, a comparison CATM-CFAR with several other models of CFAR detector is done. Simulation results of multiple target detection in Weibull and real clutter are showed in Section 4. Finally in Section 5, we gave some conclusions. 2 Model description Block diagram of typical CFAR detector is shown in Fig. 1. The reference window consists of N + 1 = 2n + 1 reference cells. The cell Y in the middle of the reference window Fig. 1: Typical CFAR detector. Fig. 2: CA-CFAR algorithm. Fig. 3: TM-CFAR algorithm. is cell under test. CA-CFAR and TM-CFAR algorithms are interesting for this paper. Fig. 2 shows the CA-CFAR algorithm which consists of two summers for the leading and lagging windows. Fig. 3 shows the TM-CFAR algorithm. First cells in reference window are sorted per amplitude. Then it trims T1 smallest cells and T2 cells with the highest amplitudes. In this paper we assume that in homogenous clutter envelope detector output samples are all exponentially distributed with probability density function (pdf): f ( x) = 1 − x/2 λ e , 2λ Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM (1) D. Ivković et al., A New Model of CFAR Detector where λ is the reflected radar signal power. Therefore, we assumed Swerling I model for reflected radar signals from a target. Also, it is assumed that values in all reference cells and cell under test are statistically independent. Under the hypothesis H0 when target is not present in the cell under test, λ is background clutter power µ. Under the hypothesis H1 when target is present in the cell under test, λ is µ(1 + SNR), where SNR is signal-tonoise ratio of a target. Value λ for cell under test can be expressed: µ , under H 0 λ= . µ (1 + SNR), under H 1 For optimal detector with fixed optimal threshold SO, Pfa is given by: Pfa = P Y > SO | H 0  = e − SO /2 µ . (3) Similarly, probability of detection for optimal detector PdO is: PdO = P Y > SO | H 1  = e − SO /2 µ (1+SNR ). (4) Combining Eqs. (3) and (4) we can get another form for PdO: − ( SO /2 µ )⋅(1/(1+ SNR )) = PdO e= (e − SO /2 µ ) 1/(1+ SNR ) PdO = Pfa (1+SNR )−1 also. According to [4, 17] it follows from Eq. (9) that for CFAR detectors Pfa is: T  Pfa = M Z   ,  2µ  (10) where MZ is operator for moment generating function of the random variable Z. Similarly, the probability of detection for CFAR detectors can be expressed as: ( = Pd E Z P Y > S | H 1  (2) (5) (6) ( ) ) ( ) = Pfa E Z P Y > S | H 0  , (7) where EZ is operator for expectation of the random variable Z. Pfa can also be written as: ∞ 1  Pfa E= e − y/2 µ dy  , S TZ = Z ∫  2µ   TZ  ( ) Pfa = E Z e −TZ /2 µ . (8) (9) In probability theory and statistics [17], the momentgenerating function (mgf) of a random variable is an alternative specification of its probability distribution and it can be used to find all the moments of the distribution (11) Pd = E Z P Y > TZ | H 1  , S = TZ . (12) We can determine finite form for Pd by replacing µ with µ(1 + SNR) in Eq. (10):   T Pd = M Z  .  2 µ (1 + SNR)  (13) For comparing different CFAR algorithms we can use average decision threshold (ADT). According to [5] ADT can be calculated as: ( )= E TZ ADT= T⋅ 2µ ( ). (14) . (15) E Z 2µ By CFAR it can be written that [4]: T  dM Z    2µ  =− dT 2µ ( ) E Z In the CFAR detector the threshold S changes its amount according to random variable Z. Distribution of the Z depends from the chosen CFAR algorithm and the instantaneous content of all cells in reference window. Generally, by CFAR detectors Pfa is: 127 T =0 By replacing Eq. (10) in Eq. (15) we get: ( ) = − dP E Z 2µ fa dT . (16) T =0 Finite form of the average decision threshold for some CFAR algorithm we can write as: ADT =−T ⋅ dPfa dT . (17) T =0 For required Pfa value we can compare two different CFAR detector by the ratio of theirs average decision threshold measured in dB as [5]: ∆ =10 log ADT1 . ADT2 Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM (18) 128 D. Ivković et al., A New Model of CFAR Detector Also, we may calculate an approximate signal-to-noise ratio loss ΔO for some CFAR detector for a required probability of detection Pd. By replacing SO /2µ in Eq. (4) with ADT of a CFAR detector we get needed value of the SNR of used CFAR detector (SNRn) for required probability of false alarm and probability of detection as:  ADT  SNRn = −1 + .  ln Pd  (19) Needed value of the SNR of optimal detector (SNRO) for required probability of false alarm and probability of detection is calculated from Eq. (6) as: = SNR O ln Pfa ln Pd − 1. (20) Fig. 4: Block diagram of CATM-CFAR detector. According to [4], and expressions Eqs. (19) and (20) we can write that approximate signal-to-noise ratio loss measured in dB is:  ADT  1+  SNRn  Pd ln  = ∆ O 10 = log   10 log  ln Pfa  SNRO   1 − ln P d   ln Pd + ADT  10 log  ∆O = .  ln P − ln P  d fa     ,    (21) under test Y, they decide about target presence independently. The finite decision about target presence is made in fusion center which is composed of one “and” logic circuit. If the both input single decision in the fusion center are positive, the finite decision of the fusion center is presence of the target in cell under test. In each other cases finite decision is negative and target is not at the location which corresponds with cell under test. (22) Eq. (22) is universal and it can be used for all available CFAR models. The smallest signal-to-noise ratio loss has CFAR detector with the smallest average decision threshold. 3 The CATM-CFAR detector The novel cell-averaging-trimmed-mean CFAR (CATMCFAR) optimizes good features of some mentioned CFAR detectors from different groups depending on the characteristics of clutter and present targets with the goal of increasing the probability of detection at constant probability of false alarm rate. It is realized by parallel operation of two types of CFAR detector: CA-CFAR and TM-CFAR. Its structure is showed on Fig. 4. CA-CFAR detector and TM-CFAR detector work simultaneously and independently but with the same scaling factor of the detection threshold T. They produce own mean clutter power level Z using the appropriate CFAR algorithm. Next, they calculate own detection thresholds SCA and STM. After comparison with the content in cell 3.1 Probability of false alarm and probability of detection In each CFAR algorithm the probability of false alarm should be constant value. This fact is considered by CATMCFAR also. Since single decision about target presence of CA and TM parts of the CATM-detector are independent events, according to [17] probability of false alarm PfaCATM and probability of detection PdCATM for CATM-CFAR can be written both as: PfaCATM = PfaCA ⋅ PfaTM , (23) PdCATM = PdCA ⋅ PdTM , (24) where PfaCA and PfaTM are the probability of false alarm of CA and TM parts respectively, PdCA and PdTM are the probability of detection of CA and TM parts respectively. The random variable which represents the mean clutter power level ZCA is: N Z CA = ∑X Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM i =1 N i , (25) D. Ivković et al., A New Model of CFAR Detector where Xi is signal amplitude in i-th cell of reference window. Probability of false alarm PfaCA can be expressed as [1]: PfaCA= (1 + T ) −N . 129 Random variable V is used directly to estimate random variable Z as: Z= (26) N −T1 −T2 ∑ Vi . (34) i =1 By replacing T in Eq. (26) with T/(1 + SNR) we get probability of detection PdCA as: Probability of false alarm PfaTM can be calculated as [4]: −N  T  PdCA=  1 +  . 1 + SNR   (27) PfaTM = N −T1 −T2 ∏ i =1 ( ) MVi T , (35) According to Eq. (17) we get average decision threshold for  T1  T1 − j   −1 CA-CFAR algorithm ADTCA. We have: T1   j N! = ⋅∑   MV1 (T ) , (36) T1 !( N − T1 − 1)!( N − T1 − T2 ) j =0 N − j dPfaCA +T N . =− (28) N − T1 − T2 dT (1 + T ) N +1 ai M= = , i 2,3,..., N − T1 − T2 , (37) Vi T Assuming that T = 0 we get: ai + T ( ) ( ) dPfaCA dT = −N . (29) where ai is defined as: T =0 ai = By replacing Eq. (29) into Eq. (17) ADTCA is: ADTCA = TN . By replacing T in Eqs. (35), (36) and (37) with T/(1 + SNR) we get probability of detection PdTM as: N −T2 ∑ Xj. PdTM = (31) To obtain finite value for ZTM, a new random variable W is introduced which is defined as follows: ∏  T  MVi  .  1 + SNR  (39) According to Eq. (17) we get average decision threshold for TM-CFAR algorithm ADTTM. Assuming that T = 0, we have according to [4] that: dPfaTM dT =− T =0 (32) T1 N! ( −1)T1 − j ∑ ( N − T1 − 1)! j =0 ( N − j ) j !(T1 − j )!  N − T1 − T2 N −T1 −T2 1  ⋅ + ∑ . ai  i =2  N − j (40) By replacing Eq. (40) into Eq. (17) ADTTM is: Random variable W is multiplied with determined coefficient and result is new random variable V which is defined as: Vi = ( N − T1 − T2 − i + 1)Wi , i = 1,2,..., N − T1 − T2 . N −T1 −T2 i =1 =j T1 +1   W1 = XT1 +1   W2 XT1 +2 − XT1 +1  =    .   W = . .     .     X N −T2 − X N −T2 −1  T1 −T2 WN −= (38) (30) The random variable which represents the mean power level ZTM is [4]: ZTM = N − T1 − i + 1 . N − T1 − T2 − i + 1 (33) ADTTM = T1 TN ! ( −1)T1 − j ∑ ( N − T1 − 1)! j =0 ( N − j ) j !(T1 − j )!  N − T1 − T2 N −T1 −T2 1  ⋅ + ∑  ai  i =2  N − j Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM (41) 130 D. Ivković et al., A New Model of CFAR Detector Now we can write a formula for probability of false alarm of a CATM-CFAR by replacing Eqs. (26) and (35) into Eq. (23) as: N −T1 −T2 (1 + T ) ∏ −N PfaCATM= i =1 ( ) MVi T . (42) Similarly, by replacing Eqs. (27) and (39) into Eq. (24) we get expression for probability of detection of a CATM-CFAR detector as:  T  PdCATM=  1 +   1 + SNR  − N N −T −T 1 2 ∏ i =1  T  MVi  .  1 + SNR  (43) To get a formula for average decision threshold of the CATM-CFAR detector ADTCATM we differentiate Eq. (42) and get following expression: ( ) dPfaCATM d (1 + T ) − N N −T1 −T2 = ⋅ ∏ MVi T dT dT i =1  N −T1 −T2  d  ∏ MVi T   i=1   ⋅ 1 +T +  dT ( ) ( ) ( ) −N . (44) Assuming that T = 0 we have that: dPfaCATM dT = −N − T =0 T1 ( −1)T1 − j N! ∑ ( N − T1 − 1)! j =0 ( N − j ) j !(T1 − j )!  N − T1 − T2 N −T1 −T2 1  ⋅ + ∑ . ai  i =2  N − j (45) some other CFAR detector. For the reason of comparison with showed results in [4], Pfa has value 10−6 and size of reference window N has value 24. Parameter k of OS-CFAR has value 18. Parameters for trimming T1 and T2 have value 3 both. Calculations of approximate signal-to-noise ratio loss ΔO and needed value of the SNR of theoretically optimal detector with fixed optimal threshold (SNRO) were made for Pd = 0.5 and Pfa = 10−6 via Eqs. (22) and (6) respectively. For this case, calculated values of scaling factor of the detection threshold T, average decision threshold ADT and approximate signal-to-noise ratio loss ΔO for mentioned CFAR detectors are listed in Table 1. Signal-tonoise ratio loss of the CATM-CFAR has the smallest value of 0.745 dB. Probabilities of detection of optimal detector and CATM, CAOS (And-CFAR from [14]), CA, TM and OS CFAR detectors as a function of the signal-to-noise ratio for parameter values from Table 1 are showed in Fig. 5. It can be seen that detection curve of the CATM-CFAR is the nearest to detection curve of theoretically optimal detector. Table 1: Approximate signal-to-noise ratio loss ∆O. CFAR T ADT ∆O (dB) CATM CAOS CA TM OS 0.418 0.712 0.779 1.327 16.293 16.2702 18.0235 18.6960 19.7933 21.6041 0.745 1.208 1.373 1.630 2.024 Note: Pd = 0.5, Pfa = 10−6, N = 24, k = 18, T1 = 3, T2 = 3, SNRO = 12.772 dB. By replacing Eq. (45) into Eq. (17) ADTCATM is: T1 TN ! ( −1)T1 − j ∑ ( N − T1 − 1)! j =0 ( N − j ) j !(T1 − j )!  N − T1 − T2 N −T1 −T2 1  ⋅ + ∑ . ai  i =2  N − j ADTCATM = TN + (46) Following Eqs. (30), (41) and (46) we can derive that ADTCATM is: ADT = ADTCA + ADTTM . CATM (47) 3.2 Analysis of CATM-CFAR detector In this section we analysed performances of CATM-CFAR detector. Also we compared its features with features of Fig. 5: Detection curves for proposed CFAR detectors (Pfa = 10−6, N = 24). Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM D. Ivković et al., A New Model of CFAR Detector Table 2: Scaling factor T and average decision threshold ADT of CATM-CFAR detector. Symmetric trimming Asymmetric trimming T1 T2 T ADTCATM T1 T2 T ADTCATM 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 0.333 0.364 0.391 0.418 0.445 0.473 0.502 0.534 0.569 0.608 0.653 0.708 16.0090 16.0833 16.1727 16.2702 16.3770 16.4956 16.6312 16.7900 16.9822 17.2246 17.5453 17.9952 2 2 2 2 2 2 4 7 10 14 17 20 4 7 10 15 17 20 2 2 2 2 2 2 0.441 0.513 0.582 0.687 0.721 0.761 0.394 0.403 0.418 0.455 0.506 0.609 16.3708 16.7155 17.1159 17.8563 18.1440 18.5099 16.1757 16.1890 16.2241 16.3449 16.5728 17.2001 Note: PfaCATM = 10−6 and N = 24. Table 2 lists the scaling factor of the detection threshold T and average decision threshold ADTCATM of the CATM-CFAR detector for symmetric and asymmetric trimming for PfaCATM = 10−6 and N = 24. Values of T are calculated iteratively from Eq. (42) for given values of T1 and T2. Values of ADTCATM are computed from Eq. (47). As the trimming increases, both T and ADTCATM increase. But this increase is smaller then appropriate T and ADT increases of TM-CFAR from Table 4 in [4]. This is shown in Fig. 6 for symmetric trimming (T1 = T2). For each value of symmetric trimming points, T and ADT of CATM-CFAR are smaller than appropriate T and ADT of TM-CFAR. Also, changes of T and ADT for asymmetric 131 trimming by CATM-CFAR are minor in comparing with similar changes by TM-CFAR. This is demonstrated in Fig. 7 and Fig. 8 also. Notations CATM(T1, T2) and TM(T1, T2) stand for CATMCFAR and TM-CFAR respectively with lower trimming T1 and upper trimming T2. The notation OS(k) stands for the OS-CFAR where k [5] is well known parameter of OS-CFAR which corresponds to up mentioned trimming value. In general, for each trimming value k, CATM-CFAR detector has ADT values that are better than those for the TM, OS and CA-CFAR detectors. 4 Simulation results In this section we carried out a simulation to prove practically good features of new CATM-CFAR detectors. We considered first simulated targets in Weibull clutter and than real targets in real clutter. Detection results of CA, TM, OS and CATM-CFAR are compared. Main parameters of realized CFAR detectors are listed in Table 3. One model of software radar receiver (SRR) is used for signal processing and target detection. 4.1 Used model of the SRR The main advantage of the software implementation of a radar receiver relative to the hardware implementation are its adaptability in terms of changes in signal processing algorithms in existing functional blocks, possibility of easy implementation of new blocks with new features and less expensive maintenance. Therefore, we can use model Fig. 6: Scaling factor of the detection threshold T and average decision threshold ADT of TM-CFAR and CATM-CFAR for symmetric trimming (Pfa = 10−6, N = 24). Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM 132 D. Ivković et al., A New Model of CFAR Detector Fig. 7: Scaling factor of the detection threshold T of CA, OS, TM, CAOS and CATM-CFAR (Pfa = 10−6, N = 24). Fig. 8: Average decision threshold ADT of CA, OS, TM, CAOS and CATM-CFAR (Pfa = 10−6, N = 24). Table 3: Main parameters of realized CFAR detectors. Model Pfa N T k T1 T2 CA-CFAR TM-CFAR OS-CFAR CATM-CFAR 10−6 10−6 10−6 10−6 16 16 16 16 1.371 2.377 20.954 0.679 – – 12 – – 2 – 2 – 2 – 2 Fig. 9: Block diagram of the used software radar receiver. of software radar receiver (SRR) presented in detail in [16], [18] and [19] and simply replace one CFAR block with another type of CFAR block to get new detection results. Block diagram of the used SRR is shown in Fig. 9. SRR consists only 64 reference cells per each azimuth. For this reason, reference window in CFAR block has maximum of 16 reference cells. 4.2 Simulated targets in Weibull clutter First we simulated a group of three neighborhood targets per azimuth and range. The distance between two adjacent targets is only one radar resolution cell per range. Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM D. Ivković et al., A New Model of CFAR Detector Table 4: Parameters of simulated radar targets in Weibull clutter. Target SNR (dB) fd (Hz) R (km) θ (deg) 1 2 3 12.5 17.5 7.2 2500 3000 3500 8.9 10.8 12.6 198.9 200.7 199.5 So, it is quite difficult to detect all of them by many CFAR algorithms since they interfere strongly for each other. Target parameters are listed in Table 4. Targets have different SNR and different speeds which are determined by appropriated Doppler frequency fd. Targets have similar range R for this model of SRR and approximately same azimuth ϴ. Also, Weibull clutter power is increased to the maximum value in order to identify the benefits of the CATM-CFAR detector. Raw video signal for one antenna revolution is shown in Fig. 10a. Three neighborhood targets can be observed more clearly in Fig. 10b which is selected per azimuth. Result of the signal processing in CA-CFAR detector is shown in Fig. 11. It detects all three targets but there are many false targets in displayed area. Result of signal processing in TM-CFAR detector is shown in Fig. 12. TM-CFAR detects only first and second target from Table 4. However, OS-CFAR detector gives good results. It detects all three neighbourhood targets with somewhat smaller amplitudes (Fig. 13). Amplitude of target 2 is the least. We can see that TM and OS-CFAR detectors do not produce false targets. Result of the new CATM-CFAR detector is shown in Fig. 14. Three neighbourhood targets are easily visible and have the largest amplitudes compared to the previous three CFAR models. Also, there are no false targets. Fig. 11: Result of CA-CFAR processing. Fig. 12: Result of TM-CFAR processing. Fig. 10: Raw video signal with simulated targets in Weibull clutter. Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM 133 134 D. Ivković et al., A New Model of CFAR Detector Fig. 13: Result of OS-CFAR processing. Fig. 15: Raw video signal with real targets in real clutter. Fig. 14: Result of CATM-CFAR processing. Fig. 16: Result of CA-CFAR processing for real targets in real clutter. 4.3 Real targets in real clutter Table 5: Coordinates of real radar targets in real clutter. We made check of the CATM-CFAR by detection of three real targets in real clutter also. We use the card PCI-9812/10 (Fig. 9) for analog-to-digital (A/D) conversion of signals from I and Q branches of one real radar device. Sampling frequency was 2 MHz. Transmitted pulse power of the radar device was 15 KW, frequency was 5.4 GHz, pulse length was 6 μs, pulse repetition frequency was 2350 Hz, intermitted frequency was 30 MHz, antenna scan rate was 1 Hz and horizontal antenna beamwidth was 2.1°. After A/D conversion follows the creation of range bin memory. Then signals are processed in Doppler filter. The output signal from the envelope detector is shown in Fig. 15. This is raw video signal for one antenna revolution in real clutter. Target R (km) θ (deg) 1 2 3 7.3 12.4 6.1 54 71 229 Present real targets can not be seen in the raw video signal. After signal processing in CA-CFAR detector we can see in Fig. 16 three real targets but and some false targets. Extractor of used SRR model determined their coordinates. The coordinates of detected real targets are shown in Table 5. Result of signal processing in TM-CFAR detector is shown in Fig. 17. TM-CFAR detects only second and Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM D. Ivković et al., A New Model of CFAR Detector Fig. 17: Result of TM-CFAR processing for real targets in real clutter. 135 Fig. 19: Result of CATM-CFAR processing for real targets in real clutter. 5 Conclusion Fig. 18: Result of OS-CFAR processing for real targets in real clutter. third target from Table 5. But detection of target 2 is very weak. OS-CFAR detector gives better results than TM-CFAR detector. It detects all three real targets (Fig. 18). But amplitude of target 1 is the smallest and in the detection limit. But we have to emphasize here that the detection of target 1 would be unsuccessful that its signal-to-noise ratio was slightly lower. This statement is true for target 2 detection using TM-CFAR algorithm. Also, we can see that TM and OS-CFAR detectors do not produce false targets again. Results of the detection of real targets in real clutter of the proposed CATM-CFAR detector is shown in Fig. 19. Three real targets are easily visible and have the largest amplitudes compared to the previous three CFAR models. However, in this situation we have some false targets because real clutter fluctuation. In this paper is presented improvement of neighborhood targets detection in clutter environment. It is obtained by the CATM-CFAR detector. Fusion of particularly decisions of internal CA-CFAR and TM-CFAR algorithms within CATM-CFAR detector provides better finale decision and detection. The advantage of using the CATMCFAR detector is shown in the situation of detection of real targets in real clutter also. Others realized detectors were then on the limit of a successful detection, or had a lot of false targets. All analyzed models of CFAR detectors in the article are supported using MATLAB® software. We derived expressions for the probability of detection, the probability of false alarm and the average decision threshold of CATM-CFAR and compared its performances with performances of several other well known CFAR detectors. Also, we derived a new expression for approximate signal-to-noise ratio loss measured in dB which can be used for all CFAR models. Direction of further research would be moving toward an examination of characteristics of the realized CATM-CFAR detector under conditions of jamming signal presence and its effect on detection of radar targets. This work was partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grants III-47029. Received: July 4, 2013. Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/14/15 5:17 PM 136 D. Ivković et al., A New Model of CFAR Detector References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] G.V. Hansen and J.H. 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