A CFAR algorithm for radar detection under severe interference

A CFAR Algorithm for Radar Detection Under

Severe Interference

Tri-Tan Van Cao

Defence Science&Technology Organisation

PO Box1500,Edinburgh,SA5111,Australia.E-mail:tan.cao@https://www.360docs.net/doc/e7462529.html,.au

Abstract

A new radar Constant False Alarm Rate(CFAR)detection algorithm operating under severe interference is developed in this paper.The new CF AR algorithm,designated as Switching CF AR(S-CFAR),is presented and analysed in closed-form based on Swerling I nonhomogeneous clutter and target model. Mathematical analysis demonstrates that the S-CFAR is robust when up to half of the search region is occupied by interfering samples.The S-CFAR algorithm is useful in applications where a radar performs detection in a clear region of its range and/or Doppler pro?le with an unknown number of interfering target (and possibly jamming)samples.S-CFAR implementation is also simple since no sample ordering is required.

1.I NTRODUCTION

The radar detection problem can be formulated as a binary decision,i.e.,a target is declared:(i)to be present if the test sample is larger than a prede?ned threshold,or(ii)to be absent otherwise.An automatic detection scheme with an adaptive threshold is often employed to provide a Constant False Alarm Rate(CFAR)performance in order to maintain the rate of false alarm reported at a manageable level[1].

The most basic form of the adaptive threshold processor is the well-known cell-averaging CFAR(CA-CFAR)[2].The input to the processor is the output of the envelope detector, which is sampled in range(and Doppler if possible).Each sample in the range/Doppler dimensions is called a cell.The test cell is the cell at which a detection decision has to be made.The interference power in each test cell is estimated using its surrounding cells which are termed reference cells. In the range-Doppler map,the reference cells form a reference window.The interference estimation is simply the sample mean of the power available in the cells within a reference window.The adaptive threshold is then formed by multiplying the interference estimate with a constant,the value of which is determined by the required false alarm rate.A few immediate neighbours(known as guard cells)on each side of the test cell are excluded from the estimation to prevent possible power spill-over from the test cell.

Under the condition that the sample in each reference cell is independent and identically distributed(iid)and is governed by the exponential distribution,performance of the CA-CFAR processor is optimal(in the sense that the detection probability is maximised for a given false alarm rate)when the number of reference cells is large.However,in general it is not possible to select an appropriate reference sample set satisfying this condition due to the presence of interfering samples,e.g.,other interfering targets and/or jamming signals. If the reference sample set contains a number of interfering signals,the threshold will be raised unnecessarily,leading to target masking.

In order to adapt to the presence of interfering signals, many modi?cations of the conventional CA-CFAR have been proposed in the literature[3].These include:the smaller-of CFAR(SO-CFAR)which is designed to improve target detection in the presence of multiple targets,by splitting the reference window into a leading part and a lagging part and then selecting the part with a smaller sample sum for threshold computation[4];the greater-of CFAR(GO-CFAR)which is designed to minimise the false alarm rate at clutter edge(by selecting the part with a greater sample sum)[5];the excision CFAR in which those samples with amplitudes greater than an excision threshold will not be used for detection threshold computation[6],[7],[8];the order statistic CFAR(OS-CFAR),where the interference estimate is given by the amplitude of the ordered reference sample [9];the censored mean level detector CFAR(CMLD-CFAR), where the largest ranked samples are discarded and the remaining samples are used for interference estimation via the cell averaging method[10];the trimmed mean CFAR (TM-CFAR)where the smallest ranked samples are also discarded in addition to the largest ranked samples[11],

etc.A variety of combinations of different CFAR algorithms are also proposed,e.g.,[12],[13],[14],etc.

However,if the actual number of interfering samples ex-ceeds the assumed value,robustness of these modi?ed CFAR algorithms is no longer guaranteed.In addition,none of the above mentioned CFAR algorithms exploits the statistical properties of the sample in the test cell during reference sample selection.

Recently,a CFAR detection algorithm known as Switching CFAR(S-CFAR),that takes into account the amplitude of the test cell for reference sample selection,has been proposed in[15].The unique structure of the S-CFAR is its switching action,which allows the processor to select:(i)either only the small thermal noise samples for interference estimation when interferers are present,or(ii)the whole CFAR window to minimise the false alarm rate when there are no interferers. Continuing this research theme,closed-form analysis of the

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S-CFAR algorithm in a nonhomogeneous environment based on Swerling I target/background model is?rst given in this paper.Application of the S-CFAR for target detection in the presence of an unknown number of interfering samples is then presented.

2.T HE S-CFAR A LGORITHM.

A generic CFAR processor receives input from the square law detected video range samples(i.e.,range cells).Assume that the amplitude in each cell is an iid random variable with an exponential pdf described by:

(1) where if the cell contains thermal noise only(is the thermal noise power);if the cell contains a target return with an average signal-to-noise ratio(SNR)of, and if the cell contains a clutter return or an interfering target with an average interference-to-noise ratio (INR)of.This means that Swerling I targets in Rayleigh background are assumed[11].The S-CFAR processor consists of the following two detection stages.

Stage1.Samples in a CFAR window with reference cells are partitioned into two sets and as follows:

(2)

i.e.,a reference sample,,either belongs to the set if it is less than the threshold,or belongs to the set,otherwise,where is the amplitude of the sample in the test cell,and is a scaling factor.

Stage2.Let be the number of samples contained in.A target is declared in the test cell if:

(i)

(3)

(ii)

(4)

where and are constants,and is a threshold integer.

Inequalities(3)and(4)mean that the S-CFAR switches between the sample set and the whole reference window, depending on the value of,hence the name switching CFAR.In the following section,the probability of detection of the S-CFAR algorithm is computed.

3.M ATHEMATICAL A NALYSIS.

From(3)and(4),the detection probability of the S-CFAR is:

(5)where(with)and(with)

are the probabilities of detection when there are exactly samples in.is the statistical average performed over the probability density function(pdf)of the sample in the

test cell,and a subscript denotes a probability conditioned on.

https://www.360docs.net/doc/e7462529.html,putation of.

Let be the number of interfering samples contained in a CFAR window.One has:

(6) where the sum starts from:

(7) which is the possibly smallest number of interfering samples sorted to;is the probability of detection when there are interfering samples sorted to.Note that can be expressed as:

(8) where is the probability that there are exactly interfering samples and thermal noise samples in ,and is the probability that the test cell survives the Stage2threshold formed by those samples in.In the following section,and are computed.

The probability that a sample,the pdf of which is described by(1),is sorted to is:

(9)

By setting in(9),the probability that a thermal noise sample is sorted to is:

(10) By setting in(9),the probability that an interfering sample is sorted to is:

(11) For interfering samples that appear in the CFAR window, the probability that there are exactly of them sorted to

is then:

(12)

For thermal noise samples that appear in the CFAR window,the probability that there are exactly of them sorted to is:

(13)

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From(12)and(13),is then:

(14) Let:

(15) where and are the thermal noise and interfering samples sorted to,respectively.The pdf of is:

(16) where satis?es,and,,

https://www.360docs.net/doc/e7462529.html,ing(16),one has:

(17) where:

(18) From(8),(14),(17),and with,one has:

(19) where:

(20)Combining(19)with(6),and then averaging over the pdf of ,one has:

(21) where:

(22) in which and are de?ned in(18)and(20),respec-tively.

https://www.360docs.net/doc/e7462529.html,putation of.

One has:

(23) where is de?ned in(7);and is the probability of detection when there are samples sorted to(), of which are interfering samples.One has:

(24) where is given in(14),i.e.,the probability that there are samples in,of which are interfering samples; and is the probability that the test cell survives the conventional CA-CFAR thresholding test performed over the whole reference samples,of which are in.Let:

(25)

where and are the thermal noise samples sorted to and,respectively;and and are the interfering samples sorted to and,respectively.The pdf of is:

(26)

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where satis?https://www.360docs.net/doc/e7462529.html,ing(26)one has:

(27) where:

(28) Substituting(14)and(27)into(24),then:

(29) where is as de?ned in(20).Combining(29)with(23) where,and then performing the average over the pdf of,one has:

(30) where:

(31)in which and are de?ned in(20)and(28),respec-tively.Finally,substituting(21)and(30)into(5),one has:

(32) where and are de?ned in(22)and(31),

respectively;and is given in(7).

4.S-CFAR D ESIGN U NDER S EVERE I NTERFERENCE. Application of the S-CFAR algorithm for target detection under severe interference is addressed in this section.Suppose

that the detector is expected to operate in the clear region

of a range and/or Doppler pro?le(e.g.,of an airborne radar operating low PRF or high PRF modes[16],or in the en-

tire search region of an electronic support system which is

designed to detect signals from all possible directions[17]). The interference consists of an unknown number of interfering

targets and possibly jamming signals.Suppose that the number

of interfering samples occupied up to half of the clear region. Of course,if there are too many interfering samples(e.g.,

occupying more than half of the clear region),not much can be done from a CFAR perspective.

Supposed that the largest CFAR window that covers the whole clear region consists of cells.In an ho-

mogeneous thermal noise only environment,assume that a conventional CFAR window with cells is employed.

Theoretically,the larger a CFAR window is,the better its

detection performance is(i.e.,closer to the performance of the optimum detector),provided that the more distant cells

still have the same statistics as that of the noise in the test

cell.Since the number of interfering samples is unknown and the S-CFAR detector can be tuned to tolerate a large number

of interfering samples(as demonstrated later in this paper), the largest CFAR window with cells is considered. With the nominal value(half window size),Fig. 1shows versus the false alarm

probability of the CA-CFAR and the S-CFAR at different

values of.The curves are computed using(32)by setting .Assume that a is required.At this value,as decreases from to,the S-CFAR curves move further away from the CA-CFAR curve.This

means that in order to achieve the same,a larger CFAR

constant is required,and consequently there will be more CFAR loss in an homogeneous environment as decreases. Note that larger leads to poorer detection performance in a

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l o g (P f a )

β

Fig.1:Selection of

for window size

.

Fig.2:Selection of

for window size

and

.multiple target situation.A reasonable choice is ,i.e.,corresponding to an S-CFAR curve that does not deviate too far from the CA-CFAR curve.

After selecting the CFAR window size and the sorting threshold multiplier ,the S-CFAR false alarm probability

is again plotted for different values of as shown in Fig.2.As decreases,the curves move away from the

curve with

.This means that larger (and hence more CFAR loss in an homogeneous environment)is

required in order to achieve the same

.However,a smaller gives better detection performance in a non-homogeneous

environment.Therefore,a reasonable choice is

,i.e.,corresponding to an S-CFAR curve that does not deviate

too far from the curve with

.At ,the curve gives .

In summary,parameters of the S-CFAR processor are:,,,and .

5.P ERFORMANCE A NALYSIS .

From an interference estimation point-of-view,as a reference sample is located further from the test cell,it is less repre-sentative of the noise level in the test cell.For this reason,to be realistic in the following performance comparisons,a quarter of the designed S-CFAR window is expected to contain interfering samples.Fig.3shows the detection performance at

of the designed S-CFAR processor ()

in the presence of interference samples (at the

Fig.3:S-CFAR and CA-CFAR detection performances.

Fig.4:Detection performances in worst case.

same SNR),and of the CA-CFAR processor with the nominal

window size

in a thermal noise only environment.It is evident that the detection performance of the large window S-CFAR processor at SNR above 10dB is still better than that of the CA-CFAR processor in terms of CFAR loss.

Fig.4shows the detection probabilities at

of the designed S-CFAR,CA-CFAR (

),and OS-CFAR (

,)in the presence of interference with the same SNR as that of the target.Parameters of the OS-CFAR are selected such that it has the same CFAR loss as that of the designed S-CFAR in a homogeneous thermal noise only environment.The CA-CFAR fails with only contaminated cells.S-CFAR detection,however,is very robust with up to 32interfering samples in its CFAR window.Provided that an SNR of 20dB can be maintained,S-CFAR detection has very small CFAR loss (less than 0.5dB).Although OS-CFAR does have some degree of robustness against interference,its detection performance suffers from severe CFAR loss (e.g.,6dB in worst case even with the target SNR of 20dB).These results show that the problem of target masking due to severe interference can not be solved by simply extending the CFAR window of the CA-CFAR or OS-CFAR detectors.

Fig.5shows the detection thresholds at

of the large window S-CFAR (

,,)and OS-CFAR (,)in worst

case.There are three groups of targets:ranges [17-23],[25-36],and [40-51].Nearly half of the range pro?le is ?lled with

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Range

S i g n a l L e v e l (d B )

Fig.5:CFAR detection thresholds in worst case.

Fig.6:CFAR detection thresholds.

interfering targets/jamming samples of the same SNR=15dB.The large window OS-CFAR detects nothing due to the large CFAR loss as analysed above.The large window S-CFAR detects one (largest)sample in the ?rst group,two samples in the second group,and one sample in the third group.Fig.6shows the detection thresholds at

of the designed large window S-CFAR,the normal window OS-CFAR (

,),and SO-CFAR ().There are three groups of targets:ranges [16-20],[27-40],and [46-50],all of the same SNR=18dB.The OS-CFAR detects only two samples in the ?rst group,whereas it misses all samples in other groups.The missing of the second group is due to the fact that the actual number of interfering samples (i.e.,14)is greater than the nominal number (i.e.,8)the OS-CFAR is designed to tolerate.The missing of the third group is due to the low SNR of the target/interfering samples.In general,as analysed in [11],an SO-CFAR can detect the ?rst and the last samples in a group of targets.However,in this case SO-CFAR can only detect three largest samples in the ?rst group.The missing of the second group is due to the presence of the nearby ?rst and third groups,while the missing of all the third group is due to the low SNR of the samples at the right edge of the group.The designed S-CFAR detects four samples in the ?rst group,nearly most of the samples in the second group,and up to three samples in the third group.

6.C ONCLUSIONS

A new CFAR detection algorithm,designated as S-CFAR,has been analysed in closed form in a nonhomogeneous environment based on Swerling I target/background model.Application of the S-CFAR algorithm for detection with severe interference is demonstrated using a large CFAR window that covers the whole range of the search region.Simulation based on synthetic data shows that the S-CFAR algorithm has a much better performance than that of the CA-CFAR,SO-CFAR,and OS-CFAR,in terms of detecting groups of targets or targets masked by interfering signals.The S-CFAR algorithm is useful in applications where detection of targets and/or the presence of jamming signals is performed in the clear region of the range and/or Doppler pro?le.

A CKNOWLEDGEMENTS

The author would like to thank Dr.Thomas A.Winchester and Dr.John L.Whitrow for their valuable inputs to this paper.

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