a new and robust cfar detection algorithm

I. INTRODUCTION

A New and Robust CFAR Detection Algorithm

VASSILIS ANASTASSOPOULOS

GEORGE LAMPROPOULOS, Member, IEEE A.U.G. Signals, Ltd. 'Ibronto, Canada

In this peper a new constant false alarm rate (CFAR) detection method is proposed which is based on a combination of median and morphological filters (MEMO). The MEMO algorithm has robust performance with small CFAR loss, very good behavior at clutter edges and high detection performance in the case of closely spaced narrowband signals (targets). The proposed MEMO method is favorably compared with cell averaging (CA) and

ordered statistics (OS) CFAR detectors. The Monte Carlo method is employed to analyze the MEMO-CFAR detector.

Manuscript received September 27, 1990; revised April 12 and July 15, 1991.

IEEE Log No. 9104940.

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada through the Department of Electrical Engineering, Lava1 University, Quebec City, Quebec, Canada, under the grant NSERC CODE OGPIN 011.

Authors' address: A.U.G. Signals Ud., 'Ibronto Research and Development Laboratories, 560 Lauder Ave., Bronto, Ontario, Canada M6E 3 6 .

0018-9251/WO9IM-0420 $1.00 @ 1992 IEEE

Constant false alarm rate (CFAR) radar employs adaptive threshold techniques for automatic signal detection [l-21. This threshold has to be proportional to the mean power of the local clutter. The knowledge of the statistics of the clutter is important in order to properly design a CFAR receiver. Clutter statistics obey various distributions such as Rayleigh, log-normal, Weibull or kdistribution [l, 31. Rayleigh distribution applies satisfactorily to sea clutter for vertical polarization and low resolution waveforms. It also applies to land clutter which is due to homogeneous terrain such as deserts or some type of farmland [l].

Cell averaging (CA) CFAR receivers perform optimally in uniform Rayleigh clutter [2]. Their performance degrades in multiple targets and nonuniform clutter conditions. Modified versions of the CA-CFAR receiver which overcome some of these problems have been proposed [4, 51. Ordered statistic (OS) techniques [6, 7J have been proven to work satisfactorily in both multiple targets and nonuniform clutter cases, although they present a small increment in detection loss. OS-CFAR methods overcome many difficulties which arise in various situations of multiple targets in clutter, but many detection problems in special clutter cases remain to be solved. Missing a target near the clutter edges due to clutter region expansion and missing small targets in the presence of a multiple target situation are two such cases.

A combination of median and morphological filters (MEMO algorithm) is employed in this work in order to handle some of the previously mentioned detection problems. The median filters display good behavior in dropping outliers and, consequently, the target from the background clutter, but they give biased estimates of the mean [6]. An adaptive algorithm based on median filters overcomes the problems of bias so that an unbiased mean estimate is obtained. The morphological filters, open-close and close-open, which are used next, further improve the estimate of the mean, since they both give root sequences for the corresponding median filter [SI. The proposed MEMO mean estimator performs nearly the same as the CA estimators in the case of uniform Rayleigh clutter. In clutter edges or multiple targets situations it is shown that the MEMO estimator is most preferable. Actually, this was expected because both MEMOS are robust in the presence of outliers. Additionally, they follow the abrupt changes of the mean of the clutter.

This work is organized as follows. In Section I1 the CFAR detection problem for the case of uniform Rayleigh clutter is stated. The basic parameters which are used to evaluate the performance of a CFAR detector, such as the probability of false alarm and the probability of detection, are analyzed. Based on these parameters, the characteristics of the most

420 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 28, NO. 2 APRIL 1992

-~ ~~ ~ ~ __ -~ _ _ _ ~ _ _ _ ~ I l l ~ Tr- ~-

known CFAR detectors are discussed. The proposed MEMO-CFAR algorithm is introduced in Section 111, and its performance is analyzed extensively. The theoretical analysis of the algorithm is based on a statistical simulation method (Monte Carlo) [9, 101 and the results are compared with those obtained by CA and OS algorithms using the same method. Experimental testing of the algorithm is provided using simulated data. The conclusions are presented in Section 1V.

Mean Estimator

Z

II. CFAR DETECTION PROBLEM

In a general CFAR detection problem, the signal under investigation xi(n) is that obtained at the output of a square law detector, and is simply described as

x i (n ) = s(n) + $(n), i = 0,l.

For i = 0, only the noise @(n) is assumed to be present (xo) and this is actually the background clutter. For i = 1, both the narrowband signal s(n) (target) and the clutter are assumed to be present (XI). When the input time sequence to the square law detector is normally distributed, its output xo (noise only) obeys the exponential probability density function (pdf) (Rayleigh-power pdf) [ll]:

(1) 1 p ( x ) = -e-x/P, c1

x 3 o where p is the mean power of the noise.

in Fig. 1. The estimate of the mean power of the clutter Z , is multiplied by a factor T , according to the required probability of false alarm Ph, and the threshold TZ is compared with the variable Y;: in the middle delay unit. This is also called “test cell” and probably contains the signal for detection Y1. If Y;: is found greater than T Z the target is presumed to be present. In some CFAR detectors [4, 7] the test cell and sometimes the two neighbouring cells are excluded from the clutter mean power estimation in order to avoid a positive bias in case of Y1. In other detectors (OS), which seem to be robust in the presence of outliers (targets), all the delay units are used to form the estimate Z [6]. The random variables x ( n ) in the 2M + 1 delay units, in Fig. 1, are assumed to be statistically independent and identically distributed, and to obey (1).

The diagram of a general CFAR detector is shown

A. Evaluation of Pf, and Pd

A constant false alarm detector always gives the same probability of false alarm Ph which can be a priori defined using the proper value for the threshold T . Generally, the mean estimator characterizes the specific detector, and the accuracy of its estimation affects the value of Ph. When a desired Pf, is given

Threshold TZ

Yes no (target) 1 (no target)

Fig. 1. Block diagram of general CFAR detector.

and a specific mean estimator has been selected the probability of detection Pd can be determined as a function of the SNR. The values of the threshold T and the Pf, are related as follows [6]:

Ph = P[yo T Z ]

Equation (2) gives a descriptive explanation of the way the pdf pz (x ) affects the Ph. The output pdf p, (x) depends on the input pdf and the estimator itself. In Fig. 2 it is shown that the Ph is the dashed area formed by the multiplication of the two functions in the integral of (2). This area decreases either by increasing T or by using a better estimator. For an ideal estimator, the pdf pz ( x ) becomes an impulse b(x - p ) and the Ph is given by [2]

ph = e-T. (3)

The probability of detection can now be determined as a function of the signal-to-noise ratio (SNR) S. In this case the test cell (Fig. 1) contains the signal Y1 (target plus noise) and the neighboring delay units contain only noise. For the Swerling case 1 fluctuating target model, the signal Yl is distributed according to (1) with mean (1 + S)p. The probability of detection Pd is then given by

Pd = P[y1 T Z ]

= 1” Ply, 2 Txlp, ( x ) dx

JO

For an ideal estimator, Pd is given by

(4)

ANASTASSOPOULOS & LAMPROPOULOS: A NEW AND ROBUST CFAR DETECTION ALGORITHM 421

_ _ _ _ ~ _. - m I

X

Fig. 2 Descriptive explanation of dependance of PEa on p2(x) .

10

’d

0 5

0 0 0 10

Pfa’ 10-6

A S N R 4 dB

Fig. 3. Probability of detection p d , as function of SNR. Ideal detector (solid line) and real detector (dashed line).

Analytic expressions for P d in case of nonfluctuating and fluctuating (Swerling case 3) targets in Rayleigh clutter can be found in [2] for the CA-CFAR receiver. Comparisons between different CFAR algorithms can be carried out using the curve which expresses the probability of detection P d as a function of the SNR (S) for a specific value of Ph. In Fig. 3, the curve which corresponds to the ideal estimator is depicted for Ph = (solid line). Another curve is also shown (dashed line), which represents a real estimator and is a translated version of the ideal one to the right. The difference in the performance of the two CFAR algorithms can be measured as the distance between the points A and B of the two curves which correspond to the same Pd. This distance is called “additional detection loss” or “CFAR loss” [l, 61. The value of P d for which the CFAR loss can be determined, may be arbitrary but here we use P d = 0.5.

The evaluation of the pdf pz (x ) in the output of the estimator is the first task towards the calculation of the necessary value of T from (2) and after that the corresponding Pd(SNR) curve from (4). For this purpose, we have to consider two different aspects that are strictly related to pdf evaluation. First, the pdf function p z ( x ) may be different in (2) and (4) and this depends on the assumptions which have been made about the structure of the estimator and the presence or absence of the signal. When the test cell does not contribute to the mean estimate, the pz (x ) in the same for both (2) and (4). Such cases have been reported so far for CA [4] and modified ordered statistic [7l CFAR

procedures. Excluding the test cell from the estimation of the mean, a positive bias in the estimate is avoided when the signal is present. In other CFAR procedures, all the cells of the frequency window are used for the estimation of the mean power of the clutter including the test cell. The OS-CFAR algorithm [6] is a typical example. The pdf pz (x ) now changes according to the presence or absence of the signal.

The second serious aspect towards pdf evaluation is that it may lack an analytic expression if the mean estimation process is complicated. This particular problem is faced later on in this work by means of a statistical simulation technique known as the Monte Carlo method [9]. This method is very simple and highly helpful when integrals like those of (2) and (4) are to be evaluated. It is proven that in such an evaluation there is no need to know the analytic expression of the pdf pz(x) . The evaluation of the integral can be based only on the values of the random numbers at the output of the estimator and the frequency of their appearance. On the other hand, a large number of events are needed in order to have reliable statistical results. Monte Carlo method has already been used successfully in an adaptive CA-CFAR technique [12].

B. CA and OS-CFAR Detectors

An extensive analysis and comparisons between CA and OS-CFAR detectors can be found in [6]. It is proven there that the OS-CFAR detector is preferable compared with CA and CAGO-CFAR detectors, especially in the case of clutter edges and/or the presence of multiple targets. However, a significant drawback fo the OS detector is that it causes an extension in the homogenous regions of the clutter. The whole situation is explained here by means of an example. If the required value of Pf, is then an OS filter with length N = 29 bins and the 19th ordered bin selected for the output is an appropriate selection according to [6] with T = 20.2. This filter causes an extension of four bins on each side of a uniform region of the clutter (8 bins totally). Each target lying on these regions is missed. The 19th ordered value of the 29 bins wide window is the only selection that results in an almost unbiased estimation of the mean (1.0327 p), and a smaller CFAR loss [6]. Every other bin with higher ordering gives an overestimation of the mean (positive bias) while the lower ordered bins underestimate the mean (negative bias). The OS-CFAR detector also presents an additional detection loss compared with the corresponding CA detector which in our example (N = 29) is equal to 0.4 dBs. A median filter will not cause extension in the homogenous regions of the clutter but it will give an underestimation of the mean (0.71 p). This results in a higher value of T for the same Ph (T = 32), which gives an additional detection


- _- _ _ _ ~ . _ _ _ . _ -~ n i -T--- ~

loss [6]. In the next section, the median filter is used in such a way that no bias in the estimation of the mean power of the clutter arises. This is actually the first stage in the proposed MEMO-CFAR detector.

Ill. MEMO-CFAR DETECTOR

The proposed MEMO algorithm is actually an ordering method since it combines median and morphological filtering. The median filter has been employed because it does not enlarge the homogeneous regions of the clutter. An unbiased estimation of the mean power of the clutter is also achieved through a proper modification of the exponential distribution of the noise. The morphological filters which follow decrease further the uncertainty in the estimation of this mean (variance).

A. Description of MEMO Detector

A block diagram of the proposed MEMO-CFAR detector is given in Fig. 4. The first stage of the detector includes a median filter and a logic circuit. Both are used to transform the input sequence x(n) into a new x’(n), so that the second median which follows can give an unbiased estimate of the mean of the signal x ( n ) . Accordingly, the exponentially distributed input sequence x(n) is simultaneously inserted into the first median filter and the logic circuit (Fig. 4). The output of the median filter whose length equals N ( N = 2M + l), is a biased (negative bias) estimate m of the mean p given by [6]

N

m = p c (l/i>. (6) j = ( N t 1)/2

For a given length N of the median filter, an initial unbiased estimate p1 of the mean power of the clutter can be found if (6) is solved with respect to p. The logic circuit evaluates p1 from m and N, and modifies the incoming sequence so that every x(n) , which is less than Xp1 (0 < X < 1) is replaced by p1. The value of A was determined experimentally for some values of N, and is given in Bble I. Additionally, in the logic circuit, every value of x(n) greater than 10 m is replaced by pl. The new sequence x’(n) has a pdf which is shown in Fig. 5(a). Actually, the new pdf is the summation of two different pdfs. These are shown separately in Fig. 5(b). The curve (1) represents the transformed values of x ( n ) while the curve (2) represents the values of x ( n ) which were not altered. Thus the operation of the logic is twofold. Firstly, it converts the smallest values of the clutter to the initial estimate of the mean p1. So the pdf of x’(n) has its “center of gravity” (mean) shifted to higher values compared with the mean of the exponential pdf. As a result the sequence x’(n) when passed through the

LOGIC filter

filter (OC + CO) /2

x‘”

1 Target

Fig. 4. Block diagram of proposed MEMO-CFAR detector.

Fig. 5. (a) pdf of new sequence x’(n). (b) nVo parts which constitute new pdf.

TABLE I

0.335 0.333 0.331

29 0.330 33 0.329 31 0.328

second median filter will give an unbiased estimate of the original mean power of the clutter. Secondly, the logic circuit converts values of the clutter greater than 10 m to the initial estimate of the mean p1. This results in the absence of the outliers in the signal x‘(n). Consequently, the estimate U, at the output of the second median filter, has not been affected by the presence of targets.

algorithm to smooth the sequence x’(n). This median Next, a second median filter is used in the MEMO


~- .~ _ _ _ ~ -717 I 7T-- __-

is of the same length N, as the first one, and gives at its output an unbiased estimate ~(n), of the mean of the original signal x(n) . Finally, the output of the second median u(n) is processed by a morphological filter which includes an open-closing parallel with a close-opening [SI procedure and gives their average as the final estimate z(n) of the MEMO detector. The window length for the morphological filters equals M + 1 (M = (N - 1)/2) which is the equivalent length of that used in the median filters. It is proven in [8] that morphological filters, open-close and close-open, give root signals which confine the root of the equivalent median filter from below and above, respectively. Consequently their average gives quite a smoothed (small variance) version z(n) of the input sequence u(n).

~ ~

CA os MEMO

Theoretical 17.69 20.2 Experimental 17.72 20.2 18.8

B. Performance of MEMO Detector

The performance of the MEMO detector is considered here. First, the probability of false alarm Pb and its dependence on the threshold T is determined. According to (2) for the evaluation of Pb, the analytic expression of the pdf p(z ) , at the output of the estimator, is required. This pdf is obviously a simple function of the pdfs at the outputs of the open-closing and close-opening filters. The distribution function F,(u) at the output of the close-opening filter according to [8] is given by:

F,(u) = MF(u)M - ( M - l )F(uy+’ + F ( U y ( 1 - F(u))

( M + 1)MF(u)2y1- F(u))2. 2

+ (7)

A similar equation holds for the distribution function at the output of the open-closing filter. The size of (7) makes the whole task of evaluating p ( z ) very difficult, since the distribution function F(u) at the output of the second median filter is also difficult to be determined. On the other hand, (7) is valid only when the variables U are statistically independent and identically distributed [SI. This is not true for the variables u(n) which are correlated as being the output of a median process. Consequently, any attempt to determine analytically p ( z ) from the original pdf p ( x ) is of no use.

In order to determine Pf, and Pd for the MEMO-CFAR detector, the Monte Carlo method is applied. The Monte Carlo method is a simple statistical simulation technique which can be used for the evaluation of integrals like (2) and (4), when the output of the estimator is analytically nontractable [9]. The necessary condition to have sufficient accuracy using this method is the large number of trials which must be incorporated in the experiment. For the simulation experiments of this paper 50000 random numbers were used which are exponentially distributed with mean p = 1. The random numbers exponentially

TABLE I1 Value of T for Pr, =

distributed were derived using the normal distribution according to [lo]. The probability of false alarm can be evaluated by means of the Monte Carlo method if (2) is changed to the form:

where L = 50000 and z ( i ) is the output sequence of the specific estimator. The proposed MEMO detector was compared with CA and OS-CFAR detectors. Theoretical and experimental results concerning the required value of the threshold T to achieve Pf, = are given in Table 11. The window length for the CA estimator was selected to be 29 bins. For the OS estimator the window length was 29 bins while the 19th ordered bin was taken as output. In the MEMO detector the median had 29 bins length and the equivalent morphological filters a length of 15 bins. This window length was considered so that the Pfa for the three detectors would be of the order for an acceptable value of T. The theoretical value of Pb for the CA-CFAR detector is given by [2]

1 Pb =

(I+$>” (9)

where N = 29. For the case of OS-CFAR detector Pb is as follows [6]:

(10) N (k - 1)!(T + N - k)!

p h ’ k ( k ) ( T + N ) !

where N = 29 and k = 19. It is evident from the results in n b l e I1 that the performance of the MEMO-CFAR detector lies between those of CA and OS detectors, in the case of uniform clutter. The agreement between theoretical and experimental results for CA and OS detectors ensure the validity of the simulation method and the reliability of the data used (exponential random variables).

The performance of the MEMO estimator, when only noise is present, can also be evaluated using the mean, the variance and the first 6 high-order normalized central moments of the variables at its output. The same work was carried out also for CA and OS-CFAR detectors and the results are depicted in Bble 111. In the first column of the Bble are given the theoretical moments for exponentially distributed random variables together with the moments for the 50000 variables used (experimental data). This


exponential pdf CA estimator OS estimator f * * * i. . .*

Mean 1 1 1 1 1.033 1.032 Var 1 1 0.034 0.034 0.061 0.061

3rd mom. 2 2.002 0.373 0.378 0.521 0.509 4th mom. 9 9.019 3.222 3.253 3.437 3.427 5th mom. 44 44.104 3.892 3.869 5.728 5.595 6th mom. 265 264.150 19.770 19.709 25.079 24.592

is to ensure that the used variables were actually exponentially distributed. In the second and third columns are given the theoretical and experimental moments for the CA and OS estimators, respectively. The theoretical moments can be evaluated easily since there exists an analytic expression for the pdf at the output of both CA and OS estimators [6, 91. Theoretical and experimental moments are almost the same, which means that the selected random variables are considered reliable to examine the performance of the MEMO estimator and, furthermore, to comapre it with other estimators. The experimental moments shown in the third column of the nb le I11 correspond to the variables at the output of the MEMO estimator. These moments show the superiority of the proposed detector. A totally unbiased mean, a smaller variance, and smaller high-order of central moments have been obtained.

In Tmble IV, some comparisons are given between the OS and MEMO-CFAR detectors in the case that nonfluctuating targets are lying in the frequency observation window. These comparisons are based on the experimentally evaluated mean and variance in the cases of 1, 3, and 5 nonfluctuating targets. It is obvious that the MEMO-CFAR detector is more robust in the presence of outliers (targets) since it gives a smaller bias in the mean estimate and smaller variance. The higher order moments were also found smaller for MEMO detector. The theoretical values for OS-CFAR detector are given in order for the reliability of the data used to be verified once more. The probability of detection as a function of the SNR is given in Fig. 6 for the ideal, the OS, and the MEMO-CFAR detectors. These curves have been drawn for the case of one nonf luctuating target in the frequency observation window (29 bins) and for probability of false alarm Ph = The detection loss of the MEMO-CFAR detector is 0.3 dBs smaller than the detection loss of the OS detector. In Fig. 7, the same curves for the case of 3 nonfluctuating targets are given. In this case, the CFAR loss for the MEMO detector is 0.7 dBs smaller than that of the OS detector.

considered at the points next to a clutter edge. For the bin at the lower level of the clutter edge, the Pr,

Finally, the probability of false alarm was

MEMO est * * 1 0.0446

0.386 3.114 3.465 17.287

TABLE IV Mean and Variance with Nonfluctuating Brgets in the Frequency

Observation Window (29 Bins)

1 Target 3 Targets 5 Targets

Note: *lheoretical values. *+Experimental values.

f ig. 6. Probability of detection as function of SNR for one

and Pfa = 1. Ideal CFAR detector. 2 MEMO-CFAR nonfluctuating target in frequency observation window (29 bins)

detector. 3. OS-CFAR detector.

0.0

Fig. 7. Probability of detection as function of SNR for 3

and Pfa = 1. Ideal CFAR detector. 2 MEMO-CFAR

0

nonfluctuating targets in frequency observation window (29 bins)

detector. 3. OS-CFAR detector.

was found many orders smaller than the value in the uniform clutter case when the MEMO detector is used. This is also valid for the OS detector, although the value found for Pr, was not as much decreased. Actually, for the example of the 29 bin window which has been used until now, the Pb was found to be approximately and 10-l' for the OS detector. These small values result because the mean power of the clutter is overestimated. This happens because fewer clutter bins participate in this estimation, since the bins in the high level of the clutter are treated as outliers. In the case of the OS detector, the theoretical value of Ph at the

for the MEMO detector,

425 ANASTASSOPOULOS & LAMPROPOULOS: A NEW AND ROBUST CFAR DETECTION ALGORITHM

-_ - -___ 111 1 7-

lower clutter edge can be found if the values N = 19 and k = 19 are substituted in (10). For the MEMO detector, the Ph was evaluated using the Monte Carlo method and half the window for the morphological filters. The median filters were taken as maximum fdters (15-ordered bin in 15 length window).

The probability of false alarm at the high level of the clutter edge becomes much larger than lod6. Consequently, the performance of the MEMO detector degrades. The value which was found using the Monte Carlo method is approximately 5 The median filters were taken in this case as minimum filters (l-ordered bin in 15 length window). For the OS-CFAR detector, Pk equals which can be evaluated from (10) with N = 15 and k = 5. This value of Pfa for the OS was considered for the fifth bin from the clutter edge (the first 4 bins belong to the clutter extension). It is worth mentioning that for the CA detector the value of Pk in the high level of the clutter edge increases only 40 times, as was found in the edge effect analysis in [2].

IV. SIMULATION RESULTS

The performance of the proposed MEMO-CFAR detector is analyzed in this section using simulated data. These data were selected in such a way that the performance of the MEMO and OS-CFAR detectors can be demonstrated in the presence of multiple targets or a target near a clutter edge.

A uniform clutter of 256 independent and identically distributed random numbers obeying exponential pdf were used. The mean power of the clutter is equal to one. All the bins from 80 to 150 were multiplied by loo0 so that a homogenous clutter region was formed (30 dBs clutter edges) with width 71 bins. Six narrowband targets were added to bins 78,81,120, 123, 126, and 152 with corresponding signal to noise ratio (SNR) 23, 20, 30, 14, 30 and 23 dBs. In Figs. 8 and 9 the detection results using the OS and the MEMO-CFAR receivers are given respectively. The window length for all the filters was taken 29 bins (15 for the morphological filters). The value of T used to determine the threshold TZ, for a required Ph = was taken according to n b l e 11. The OS detector (Fig. 8) misses the targets lying near the edges of the clutter and on the lower side of them. This is due to the extension of the clutter region 4 bins on each side. It also misses the target at bin 123 because the two neighbouring targets cause an overestimation of the mean power of the noise at bin 123 and the small target is 'covered' by the threshold level (masking effect). As a result, only three targets are detected. The MEMO-CFAR receiver detects all the six simulated targets. It is worth mentioning that the clutter region between the bins 80 and 150 is not enlarged so that the targets at bins 78 and 152

1 dB

4 0 4 v m A A 4 m ! I I 1 I I 1 1

0 100 2 0 Frequency

Fig. 8. Performance of OS-CFAR detector (29-bin window, 19th

Signal. @) Adaptive threshold (TZ) . (Pfa = D--Detection). ordered bin as output) in case of multiple target in clutter. (a)

/ I

0 100 200 Frequency

Fig. 9. Performance of MEMO-CFAR detector (29-bin window, 15-bin morphological windows) in case of multiple target in clutter.

D+Detection). (a) Signal. @) Adaptive threshold (TZ). (Pfa =

are easily detected. The weak target at bin 123 is also detected, due to the small bias which is caused by the neighbouring targets on the estimation of the mean power of the clutter.

V. CONCLUSION

The MEMO-CFAR detector was introduced and analyzed. It is based on median and morphological filters and uses a simple logic circuit to overcome the problem of bias in the estimation of the mean power of the clutter which is caused by the use of median filters. The MEMO-CFAR detector presents small detection loss, small bias in the presence of multiple targets and preserves the length of the uniform regions of the clutter. It was shown, using simulated data, that the masking of a target by a clutter edge or by stronger targets is successfully faced by the MEMO-CFAR detector. The MEMO detector is time consuming compared with the corresponding (the same window length) OS detector. It requires almost three times as much execution time as the OS detector does in a conventional computer. In spite of this, its circuitry presents high modularity and, consequently, is not


~. ~- - _ -__ ~ 111 -7 rr- _____~ __

complex. It includes two alike median filters, four max and four min filters, (dilation-erosion) which constitute the morphological structure.

REFERENCES

Skolnik, M. I. (1980) Introduction to Radar Systems (2nd ed.). New York: McGraw-Hill, 1980.

Fmn, H. M., and Johnson, R. S . (1968) Adaptive detection mode with threshold control as a function of spatially sampled clutter-level estimates. RC4 Review, 29 (1968).

Radar seaclutter at low grazing angles. IEE Proceedings, 137, Pt. F, 2 (Apr. 1990), 102-117.

Analysis of some modified cell-averaging CFAR processors in multiple-target situation. IEEE Transactwns on Aerospace and Electronic Systems, AES-18, 1 (Jan. 1982), 102114.

Hansen, V. G., and Ward, H. R. (1972) Detection performance of the cell averaging LOG/CFAR receiver. IEEE Transactwns on Aerospace and Electronic Systems, AES-8 (Sept. 1972), 648-652.

Chan, H. C. (1990)

Weiss, M. (1982)

[6] Rohling, H. (1983) Radar CFAR thresholding in clutter and multiple target situation. IEEE Transactwns on Aerospace and Electronic Systems, AES-19, 4 (July 1983), 603421.

[7l Elias-Fuste, A. R., Mercado, M. G., and Davo, E. R. (1990) Analysis of some modified ordered statistic CFAR OSCO and OSSO CFAR. IEEE Transactwns on Aerospace and Electronic Systems, 26,l (Jan. W O ) , 197-202

Morphological filters: Statistics and further syntactic properties. IEEE Transactwns on Circuits mzd Systems, CAS-34, 11 (Nov. 1987), 12921305.

[9] Pugachev, V. S. (1984) Probability Theory and Mathematical Statistics for Engineers. Elmsford, NY Pergamon, 1984.

[lo] Blackman, S . S. (1986) Multiple-Target Tracking with Radar Apptications. Dedham, MA: Artech House, 1986.

Detection of Signals in Noise. New York Academic Press, 1971.

Cell-averaging CFAR for multiple-target situations. IEE Proceedings, 133, Pt. F, 2 (Apr. 1986), 176-186.

[8] Stevenson, R. L., and Arce, G. R. (1987)

[U] Whallen, A. D. (1971)

[12] Barboy, B., Lomes, A., and Perkalski, E. (1986)

Vassilis Anastassopoulos received his B.Sc. and Ph.D. degrees in 1980 and 1986, respectively from the Department of Physics, University of Patras, Greece.

From 1980 to 1985 he was a Research Assistant in the Electronics Laboratory, University of Patras. From 1985 to 1987 he was a research scientist in the Communications and Information Department (CID) of the Hellenic National Defence General Staff (HNDGS). From 1987 to 1989 he was a Lecturer at Electronics Laboratory, Department of Physics, of the University of Patras. From 1989 to 1990 he was a Research Associate of the Department of Electrical Engineering, University of Toronto, Canada, working on nonlinear filters and pattern recognition and classification. Since 1990 he has been working as a Lecturer at the Electronics Laboratory, Department of Physics, University of Patras, Greece. His research interests are digital signal processing, image processing, radar signal processing and pattern recognition, and classification.

Dr. Anastassopoulos is a member of the Greek Physics Society.

George A. Lampropoulos (S’SM’81) received his B.Sc. degree from the University of Patras, Greece, in 1979, and his M.Sc., and Ph.D. degrees from Queen’s University, Kingston, Ontario, Canada, in 1982 and 1985, respectively, all in electrical engineering.

From 1984 to 1989, he was with the Dept. of Electrical Engineering, Royal Military College of Canada. For a short period in 1989, he visited the Communications Group at the University of Toronto. Since 1987, he has been an adjunct professor at Lava1 University, Quebec City, Canada. Since 1986, he has been President of A.U.G. Signals Ltd. His areas of expertise lie in digital signal processing, and network analysis, design and implementation.

section of the IEEE from 1987 to 1989, as Secretary, Tkeasurer, and Vice Chairman. Since 1989, he has been the Educational Activities Chairman of the Central Canada Council of the IEEE, and Chairman of Conferences of the Toronto Section of the IEEE. He has been member of the executive groups of a wide range of professional and social organizations. Among several listings of Who’s Who, he is listed in the 1990 Marquis Who’s Who in the World.

Dr. Lampropoulos was a member of the Executive Committee of the Kingston


-I_- _______ - _ T T - 1 -TTT-- ~ - -

a new and robust cfar detection algorithm

Documents