A Robust CFAR Detector Based on

Ordered Statistic

Wenlin Hu" , Yongliang Wang', Shouyong Wang', Qianxue Fang'1.Wuhan Radar institiute, China

2.National University of Defense Technology, China

Abstract-An improved version of VI-CFAR called OSVI-CFAR is presented. It is a combination of the orderedstatistics (OS) CFAR, the smallest-of OS (SOOS) CFAR andthe greatest-of OS (GOOS) CFAR. In homogeneous andclutter edge environments, the detection performance andfalse-alarm regulation properties for the OSVI-CFARdetector are almost consistent with the VI-CFAR based onmean level (called MLVI-CFAR). But in multiple targetsituations which the interfering targets are present in boththe halves of the reference window, the detectionperformance for the OSVI-CFAR detector is improvedgreatly, so it is more robust than the MLVI-CFAR inpractice. Finally, some important properties of the OSVI-CFAR detector are analyzed and discussed.

Key words: CFAR,VI, OSVI, nonhomogeneous environments

I. INTRODUCTION

Radar fast threshold constant false alarm rate (CFAR)detector keeps CFAR by estimating background andadjusting adaptive detect threshold, such as the cell-averaging CFAR (CA-CFAR) detector and orderedstatistic CFAR (OS-CFAR) detector. It is well known thatfor a homogeneous Rayleigh environment, the CA-CFARis optimal. Unfortunately, CA-CFAR suffers performancedegradation in nonhomogeneous environments [1]. Thedetection performance of the OS-CFAR is improved inmultiple target situations and the loss is also acceptable inhomogeneous environments [2]. But the OS-CFAR isunable to prevent excessive false alarm rate at clutteredge[3]. M.E.Smith proposed the VI (variability index)CFAR detector which is a combination of the CA-CFAR,the smallest-of CA (SOCA) CFAR and the greatest-of CA(GOCA) CFAR[3,4], and is called MLVI-CFAR here. TheMLVI-CFAR offers a low-loss in homogeneousenvironments and good false-alarm regulation propertiesin clutter edge environments. Unfortunately, theperformance of the MLVI-CFAR detector may beseriously degraded when the interfering targets are notconfined to a single half of the reference window. In thiswork, the robustness of the MLVI-CFAR detector isimproved in multiple target situations by substituting themean level CFAR for OS-CFAR, and it is called OSVI-CFAR. At the same time, the detection performance andfalse-alarm regulation properties of the OSVI-CFAR arealmost consistent with the MLVI-CFAR in homogeneousand clutter edge environments.

II. OSVI-CFAR DETECTORThe reference window of the OSVI-CFAR detector is

divided into leading (Window A) and lagging (Window B)halves. The VI-CFAR defines two statistics VI and MR,they are written repeatedly below [3,4].

VI=1+± =1± (x x)2 (x)2/1 n i=

MR = XA |XB= Yxi | Exi

(1)

(2)

xi is the samples of the leading or lagging half of thereference window. x is the arithmetic mean of xi in a halfreference window. n =N 2 , N is the size of the wholereference window. &2 is estimated population varianceand ,i is the estimated population mean.

The VI-CFAR estimates the background of theunder test through the decision results of thehypothesis testes below[3,4].

JVI < KV7 > Nonvariable

|VI > KV7 > Variable

K 1 <MR< KMR > Same MeanslMR <K-1 or MR > K > Different Means

celltwo

(3)

(4)

where K, is the threshold of the VI hypothesis testing,and KMR is the threshold of the MR hypothesis testing.

Two crucial environment decided problems areimplemented through VI and MR hypothesis testes, i.e.whether the data in each half of reference window ishomogeneous, and whether the power levels of the leadingand lagging window are identical. The CFAR methods indifferent situations are listed in TABLE.I.

TABLE I. OSVI-CFAR ADAPTIVE THRESHOLD

Leading LaggingWindow WindowVanable? Vanable?

Different Mean? Adaptive Threshold

S=T-Z

Equivalent CFARMethod

No No No Tos (N,ko )OSB (ko ) OS-CFAR

N N NNo No Yes T0( -Os(.TS 2 2 B(y 2'

Yes No

Yes Yes

N-OTos ( ,k) OS (k)

T (N k) OS, (k)02

TO0( 2k)O ()

OSGO-CFAR

OS-CFAR

OS-CFAR

OSSO-CFAR

0-7803-9582-4/06/$20.00 C2006 IEEE

In TABLE.I., T, (n , n) is the threshold multiplierfactor of the OS-CFAR, with a reference window sizen, and order value n . OS _(A,B,(k) and OS.i (A,B,(k) arethe k-th order statistic of the half reference window with abigger and smaller sum respectively. OSA(k) and OS (k)are the k-th order statistic of the half reference window Aand B respectively, k < N12 .

The worst clutter edge situation is that the leadingwindow is filled with clutter add noise, the laggingwindow is filled with noise only, and the cell under test isin clutter region. This situation corresponds to the secondrow of TABLE.I. The OSVI-CFAR uses GOOS-CFAR tocontrol false alarm peak. If the order value of the OS-CFAR is taken on the maximal value., the false-alarmregulation properties for the OS-CFAR are best [5], so theparameters k of the OS-CFAR is set equal to N 2.

In homogeneous environment, the goal of the OSVI-CFAR is to approximate the performance of the CA-CFAR. This requires that the values of KVI and KMR wereselected to ensure low error probability of hypothesis testsexpressed by (3), (4). The error probability of hypothesistests is also called the confidence level. For the VIhypothesis test, it is denoted by ac, and given in (5), for theMR hypothesis test, it is denoted by,8, and given in (6)[4].

a =P[VI > KVI Homogeneous Env.] (5)

= 1-P[KLR < MR <KMR Homogeneous Env.] (6)

3.3 X 10-4, the confidence level of MR hypothesis test 8was set equal to 0.08, and corresponding KVI and KMR areequal to 4.76,1.806 respectively.

A. Performance in Homogeneous EnvironmentFigure. 1 shows the probability of detection (PD) for

the OSVI-CFAR, the optimal detector, the CA, GO andOS-CFAR in homogeneous environment.

The symbol "OSVI(10)" denotes that the order valueof the OSVI-CFAR is equal to 10, the symbol "OS(30)"denotes that the order value of the OS-CFAR is equal to30. It can be seen from Figure.1 that all of the CFARdetector perform similarly and exhibit some CFAR lossrelative to the optimal detector. When PD=0.5, the lossesfor the OSVI-CFAR relative to the CA,MLVI,OS-CFARare about equal to 0.2,0.25, 0.5dB respectively.

0.9

0.8

0.7

0.6

o 0.5

0.4

0.3

0.2

0.1 _

0N

optCAGOMLVIOSVI(1 0)OS(30)

The confidence level a and,8 decrease with increasingKVI and K. . However, the sensitivity for detectingnonhomogeneous environment decreases at the same time.For reducing the false alarm peak that clutter edge locatesin N12 (called the primary false alarm peak), a is takenthe order of nominal PFA(probability of false alarm) [4].In an analogous fashion, , should be set small enough.However, another factor which must be considered insetting , is the probability of switching from GOOS-CFAR mode to OS-CFAR mode when clutter has filledWindow A completely and begins to fill Window B. Inthis case, there will be an increase in PFA (called thesecondary false alarm peak) as the combined Window(AB) is selected more frequently. If , is too small, thesensitivity is decrease in detecting "different mean", thiswill result in the secondary false alarm peak increasing.Hence, f8 should not be too small. In practice, typicalvalues of f8 will not exceed 0.1 [4].

III. OSVI-CFAR PERFORMANCE ANALYSISIn our analysis below, the commonly used Rayleigh

model for the clutter and target statistics and an even valuefor the reference window size N will be assumed. Theoperation of the OSVI-CFAR was simulated for a varietyof homogeneous, interfering targets, and clutter edgeenvironments. All performance results of the OSVI-CFARin this paper were based on 100,000 Monte-Carlosimulation trials. The reference window size N is 36. Theconfidence level of VI hypothesis test a was set equal to

5 10 15SNR /dB

20 25 30

Figure 1. Detection performance of the MLVI,OSVI,CA,GO,OS-CFAR in homogeneous environment.

B. Performance in Multiple Target SituationsIt is assumed that both the interfering target and main

target (target in cell under test) agree with Swerling IIfluctuation, and their powers are equal to each other (i.e.SNR=INR, INR denotes interfering-to-noise ratio). Thereis no interfering target in cell under test. For analyzing thedifferent effect of location of interfering target in thereference window on the detection performance of theMLVI and OSVI-CFAR, two kinds of cases are discussedbelow, i.e. the interfering targets are present in both thehalves of the reference window and the interfering targetsare confined to a single half of the reference window.

Figure.2 and Figure.3 show the PD of the OSVI, CA,GO, SO, OS, and MLVI-CFAR in the case of twointerfering targets in the reference window. Figure.2corresponds to both interfering targets are located inWindow A, and Figure.3 corresponds to one interferingtarget in each half of reference window. It can be seen thatthe MLVI-CFAR exhibits a low-loss relative to the CA-CFAR and outperforms the OSVI-CFAR when bothinterfering targets are located in Window A. Wheninterfering targets are located in both Window A andWindow B at the same time, the thresholds of both the SOand MLVI-CFAR are overestimated, so the detectionperformances degrade quickly while the OS and OSVI-

CFAR perform well. For the OSVI-CFAR, even if theselected reference window contained the interferingtargets, the detection performance would not seriouslydegrade. It can also be seen from Figure.2 and Figure.3that the increase in using a half of reference Window withbigger mean leads to somewhat CFAR loss compared withthe OS-CFAR.

0.9

0.8

0.7

0.6

2 0.5

04

0.3

0.2

0.1

Figure 4. PFA comparison of OSVI, MLVI, CA, GO, OS, SO-CFAR inclutter edge (CNR=1odB).

-4CNR=10dBCNR=20dB

soMLVIOS(30)OSVI(10)CAGO

0 5 10 15 20 25Last Cell Containing Clutter

30 35

Figure 5. PFA comparison of OSVI-CFAR indifferent CNRs (k= 16).

0 5 10 15 20 25 30SNR \ dB

Figure 2. PD comparison of CA,GO,SO,OS, MLVI, OSVI-CFAR whentwo interfering targets in Window A.

0.9 MLVIOS(30)

0D8 E OSVI(1 0)CA

07 GO

0.3 - -

0.4 - ~

0.2 -004~

--------031 --

5 10 15SNR \ dB

20 25 30

Figure 3. PD comparison of CA,GO,SO,OS, MLVI, OSVI-CFAR whenone interfering target in each half Window.

C. Performance in Clutter Edge EnvironmentIt is assumed that clutter edges progressed from left

to right (Window A to Window B), and clutter-to-noiseratio is CNR.

-2 --

-4-68> t -'F- -: , ,

8-6 -8 t \ t * i ~~~~~som-10 <? ' X oCA

0 ~~~~~~~~~~~~~~~OS(30)-12

-14

GOMLVIOSVI

-16 _

Figure.4 shows the PFA for the OSVI, MLVI,CA,GO,OS, SO-CFAR in the clutter edge environments when theCNR=lOdB. The order values of OSVI and OS-CFARequal to 16 and 30 respectively. It can be seen that thefalse-alarm regulation properties of the OSVI-CFAR andMLVI-CFAR are almost consistent, and both outperformthe GO-CFAR. The false-alarm regulation properties ofthe CA-CFAR and OS-CFAR are poor relatively, and SO-CFAR is the worst.

Figure.5 shows the PFA for the OSVI-CFAR withdifferent CNRs. The order value k is 16 in the simulation.It can be seen that the primary false alarm peak for theOSVI-CFAR when CNR is equal to 20dB is higher thanthat CNR is equal to 10dB. However, as the clutter edgeworks its way into more cells of Window B, the biggerCNR results in a more accurate decision fornonhomogeneous environments, so the secondary falsealarm peak for the OSVI-CFAR reduces on the contrary.

IV. CONCLUSIONSIn this paper, we presented an improved version of

VI-CFAR, called OSVI-CFAR detector. The OSVI-CFARis more robust than the MLVI-CFAR in multiple targetsituations where the interfering targets are present in boththe halves of the reference window, while theirperformances in homogeneous and clutter edgeenvironments are almost consistent. So there is a betterapplied potential for the OSVI-CFAR.

In multiple target situations, the OSVI-CFAR offersan additional detection loss compared with OS-CFAR, butthe loss is endurable. In clutter edge environments, thefalse-alarm regulation properties of the OSVI-CFAR iseven better than the GO-CFAR, its primary false alarmpeak is lower than that of the GO-CFAR, and thesecondary false alarm peak is lower than or equal to thatof the GO-CFAR. The primary false alarm peak increaseswith increasing CNR, but the secondary false alarm peakdecreases by contraries.

REFERENCES-18 _ - -

0 5 10 15 20 25 30 35Last Cell Containing Clutter

CL -6_!o0

0k

[1] Mohammad Ali Khalighi, Mohammad Hasan Bastani, "AdaptiveCFAR Processor For Nonhomogeneous Environments,"IEEETrans on AES, 2000,36 (3),pp. 889-897.

[2] Rohling H, "Radar CFAR Thresholding in Clutter and MultipleTarget Situation," IEEE Transaction on AES, 1983, 19(4),pp. 608-621.

[3] M E.Smith, P K.Varshney, "VI-CFAR. A Novel CFAR AlgorithmBased on Data Variability,"IEEE International Radar conference,Edinburgh,UK: IEEE, 1997,pp. 263-268.

[4] M E.Smith,P K.Varshney, "Intelligent CFAR Processor Based onData Variability,"IEEE Trans on AES,2000,36 (3) pp. 837-847.

[5] P. P. Gandhi, S. A.Kassam, "Analysis of CFAR Processors inNonhomogeneous Background," IEEE Trans on AES, 1988,36(3),pp. 427-445.