Distributed Adaptive CCAWCA CFAR Detector

Transcription

1 Dstrbuted Adaptve CCAWCA CFAR Detector Panzh Lu School of Electronc and Informaton Engneerng X an Jaotong Unversty X an 749 panzhlu98@63com Chongzhao Han School of Electronc and Informaton Engneerng X an Jaotong Unversty X an 749 czhan@malxjtueducn Y Yang School of Electronc and Informaton Engneerng X An Jaotong Unversty X An 749 jafeyy@63com Mng Le School of Electronc and Informaton Engneerng X an Jaotong Unversty X an 749 lemngxjtu@63com Abstract - In the sense of lelhood rato test (LRT, a new type of dstrbuted constant lse alarm rate (CFAR scheme-ccawca(censored cell-averagng R-weghted cell averagng CFAR detector s presented Its characterstc s that censored cell-averagng (CCA CFAR algorthms are used n local processors to form the estmaton of SR of local observatons, and then the estmaton transmtted to the data fuson center (DFC Fnally, the fuson center maes the fnal decson based on the weghted cell averagng (WCA Snce the weghts are adjusted accordng to dfferent SR adaptvely, the proposed detector can be avalable n the case that the target echo and nose/clutter have dfferent level for every sensor In addton, t does not need a pror nowledge about the nterference n order to perform well Furthermore, unle the OS-CFAF the tolerance of nterferng targets s restrcted n apponted value's Under Swerlng assumpton, the analytc expresson of detecton probablty and lse alarm probablty are derved Keywords: Radar, Automatc Censorng Technque, CFAR, Detecton Probablty, False Alarm Probablty, Dstrbuted Detecton Introducton In the past several years, a consderable amount of wor on sngle sensor constant lse alarm rate (CFAR sgnal detecton has been done The detecton of sgnals becomes complex when radar returns from nonstatonary bacground nose (or nose plus clutter The use of multple sensors s wdely ncreasng n survellance systems One of the man goals of usng multple sensors s to mprove performance such as relablty and speed Also, we can acheve a larger area of coverage In multple sensor systems, one possblty s to mae the sensors transmt complete observatons to a central processor Ths opton requres a large number of communcaton channels; thus dstrbuted sgnal processng s preferred n many stuatons In such dstrbuted detecton systems, some of the processngs of the sgnal s done at each sensor and the locally avalable partal results can be processed further to obtan global results Some wor on dstrbuted detecton has been reported n the lterature [-] In lterature [-5], dstrbuted Bayesan detecton has been consdered The eyman-pearson approach to dstrbuted detecton has been consdered n lterature [6-8] Decson problems for varous networ topologes have been treated n lterature [9-] Recently, some wor on CFAR detecton usng decentralzed processng has been reported n the lterature [-8] Barat and Varshney[] develop the theory of cell-averagng CFAR(CA-CFAR detecton usng multple sensors and data fuson, where detecton decsons are transmtted from each CA-CFAR detector to the data fuson center The overall decson s obtaned at the data fuson center based on some nown / fuson rule Elas-Fuste et al[3]have extended [] and analyzed the performance of CFAR detecton systems wth dstrbuted sensors and data fuson n a homogeneous Gaussan bacground nose In ther confguraton, the system conssts of CFAR detectors employng dfferent algorthms, namely cell-averagng (CA CFAR and ordered statstcs (OSCFAR detectors They maxmze the global probablty of detecton for a gven fxed global probablty of lse alarm by optmzng both the threshold levels of the local detectors and the / decson rule at the data fuson center But for the local OS-CFAR detectors, they use some predetermned order numbers rather than fndng the optmum settngs In [4], Hmons and Baret propose a dstrbuted CFAR processor wth data fuson for correlated targets n nonhomogeneous clutter Uner and Varshney[5] analyze the case that employs OS-CFAR detectors However, t s necessary to fnd more effectve local processng measures to mprove the dstrbuted detectons The reference [6] propose a scheme called S+OS based on the local test statstcs (LTS, whch nvolves more nformaton of local observatons than that of bnary decson Dstrbuted OS-CFAR detectors wth the AD or the OR fuson rule s consdered by Wner and Varshney [7] The problem of dstrbuted CA-CFAR detecton of dependent sgnal returns s studed by Blum and Kassam[8] The common ground amoung all of these dstrbuted CFAR detecton

2 schemes s that the fnal decson based on ndvdual decsons of each sensor emerges from a countng rule such as AD or OR In addton, compared wth dstrbuted detecton based bnary local decson, the dstrbuted detecton based on LTS (local test statstc s always better It can be explaned n two ways Frstly, the LTS usually nvolves much more nformaton of orgnal observaton than bnary local decson does Secondly, LTS can be regarded as the results of multlevel-quantzaton when the number of quantzaton level approaches to nfnty Generally speang, multlevel-quantzaton s better than bnary quantzaton Therefore, t can be thought ntutvely that the dstrbuted detecton based on LTS s always better than that based on bnary local decson Fnally, optmal fuson can be used to obtan further mprovement of dstrbuted detecton based on LTS, such as fuson based on lelhood rato test by the use of eyman Pearson or Bayesan crteron Adaptve CCA CFAR The CFAR detecton methods mentoned above mply a pror nowledge of the number of the nterferng targets present n the wndow; otherwse the procedure s not closed (a statstcal crteron for termnaton of the censorng s absent So we utlze the adaptve censored cell-averagng CFAR To obtan the average bacground level (threshold, t s natural to attempt to remove the nterference from the reference sequence And therefore, a censorng scheme s proposed whereby samples exceedng an adaptve threshold are excluded from the reference set The threshold s then recomputed based on the censored sample set The teratve procedure s repeated untl no reference cell sample exceeds the computed threshold, whch then forms the detecton threshold for the prmary target, we thereby detect not only the prmary target, but also the nterferences whch themselves may be targets nput square-law detector cell-sum cell buffer cell reset cell sum cell under test spe averager spe sum threshold threshold table spe counter comparator P R cells- j spes Fg Bloc dagram of multstep CFAR procedure Fg shows the bloc dagram of the adaptve CFAR procedure ntroduced above Let x, x,, x be the powers n cells n a reference wndow and α a threshold coeffcent provdng a specfed lse alarm rate ( P n the wndow of length Ths ran ordered sequence s denoted as: x( x( x( The subscrpts wthn parentheses mean the varables x,,,, The procedure n some of the cells can be represented n the followng form: ( The sum of the x s formed: S x( ( Outputs n each cell are then compared wth a threshold b αs ( Outputs, whch exceed ths threshold, are dscarded from the sum and a new sum:, S x j (3 s formed Here j s the total number of the dscarded outputs and,,, s a sequence of the cell ndces,,, such that the last j cells correspond to the dscarded outputs ( Smlarly, we ntroduce a threshold coeffcentα, whch provdes a lse rate P n the wndow formed by ( the cells counted n (3 Then the outputs of these remanng cells are compared wth a threshold b αs (4 And some more cells are dscarded so that the remanng j j cell outputs form a sum: S x (5 l The procedure s contnued untl no spes (exceedng threshold are detected Obvously, ths algorthm s always convergent, and therefore the absence of spes after several steps s the crteron for termnaton of the procedure ( m The probabltes P are the sngle-bn lse-alarm rates at each teraton state The total average number of ( m lse alarms s and thus the overall lse P m m l alarm probablty per bn s gven by P P ( m m m m m The smplest way to eep the rate of lse alarms ( m constant s to mae all P be equal to the updated value of P Square-law detectors enter a buffer, whch stores the cell powers that are smultaneously summed by the cell averager The result s multpled by the threshold coeffcent, whch s obtaned from the threshold table for specfed and P The threshold thus obtaned s then compared wth each power stored n the buffer If the

3 power n the cell under test does not exceed the threshold, the comparator proceeds to the next cell; otherwse, a spe s declared and the detecton procedure s ntalzed The detecton procedure conssts of three stages: ( summaton of the spe powers, ( spe countng and (3 zero nserton (nto the buffer nstead of the spe power When all the cell powers n the buffer have passed the comparator the frst cycle of the CFAR procedure s completed If the output of the spe counter s not zero, the next cycle starts by subtractng the sum of the spe powers from the total sum Then the detecton proceeds n the same shon as that on the frst cycle The only dfference s that the number of cells remanng after the spes rejecton determnes the threshold coeffcent The procedure s termnated when no spe s detected at the current cycle As the result of the procedure all targets that are present n the reference wndow may be detected Under the condton of Gaussan nose bacground, the output of square-law detector follows the exponental dstrbuton As shown n Fg, the outputs of the test cell under test, whch s the one n the mddle of the tapped delay lne, s denoted by x The outputs of the cells surroundng the test cell, { x },,,, are combned to yeld an estmate z of the nose level n the test cell, that s, z f( x, x,, x (6 Where the operator f denotes the processng of the receved observatons The outputs of the cell under test x s then compared wth the adaptve threshold Tz accordng to: X > Tz < (7 Where the scalng constant T s selected so that the preassgned probablty of lse alarm s acheved Hypothess H denotes the presence of a target n the test cell, whle hypothess H s the null hypothess The probablty of lse alarm may be wrtten as a contour ntegral P F ω φ ( ( T c X H ω φ X ω (8 π Where φx ( ω E exp( ωx s defned to be the moment-generatng functon (MGF of the random varable X The ntegraton contour c s crossng the real ωaxs atω cand s closed n an nfnte semcrcle n the left halfω -plane c s chosen so that the ntegraton contour encloses all the poles ofφx H( ω that le n the left halfω -plane We assume that the cell outputs are observatons from statstcally ndependent random varables That s, the probablty densty functon (PDF of output of the th cell s gven by f ( x λ exp x λ (9 ( ( X Where λ denotes the parameters of the dstrbuton from whch the observaton x s generated otce that we use uppercase letters to denote the correspondng observatons The value of λ depends on the contents of the th cell If the th cell contans thermal nose only, λ s normalzed to λ If t s mmersed n the clutter, λ ( λ + C where C denotes the rato of average clutter power to thermal nose power at the recever nput If t s a cell n the homogenous regon and t contans a target return then λ ( λ + S ; S denotes the rato of target return average sgnal power to thermal nose power at the recever nput However, f t s a cell n the clutter and t contans a target return then λ ( λ + C+ S Therefore, the MGF of the output of the test cell under hypothess H s gven by: φx ( [ ( ] H ω + ω + C ( ote that f the test cell s n the homogenous bacground C Consequently, the pont at whch the ntegraton contour c n (8 s crossng the realω -axs s such that ( + c < c < Solvng the ntegral n (8, we obtan that PF φz [ T ( + C] ( When the censorng procedure decdes that the test cell s n the clear, we censor the hgher ordered samples, that s x,, ( + x( The lower ordered samples are added together to form the estmated of the nose level n the test cell, that s: z x ( ( The MGF of the estmated Z of the nose level n the test cell s obtaned [9] j+ φ Z ( ω ω + (3 j j+ Thus, the probablty of lse alarm and detecton probablty s obtaned from ( and (3 to be: j+ T + (3 j + P F j T j+ P d + j µ j j+ 3 Dstrbuted CFAR Detector (3 In ths secton, the dstrbuted adaptve censored cell-averagng (CCAWCA-CFAR CFAR detector for a networ s defned and approprate parameters are developed For a two-sensor networ, the equatons for the detector n homogeneous bacground are derved

4 Consder the -sensor dstrbuted networ as shown n Fg Here, Y { Y } s observaton (excludng the test j sample, where,,, ndcates the number of the sensors, and j,,,, represents the sample number n the range cells avalable to the th sensor In general, needs not be equal to It s assumed that all the sensors scan the same search envronment The sample n the test cell for the th sensor s denoted by X, In each local CCA-CFAR detector, a few of the largest reference cells are censored and the remanng ones are averaged to estmate the total nose power m Z x, j j l m m l Sens or CCA- CFAR Phenomenon H Y,X Y,X Y,X Fus on Cent er U Sensor CCA- CFAR G(S, S,, S Z Comparator Sensor CCA- CFAR S (Z,X S (Z,X S (Z,X H H Fg Dstrbuted CCAWCA CFAR Detector Then the rato statstc S X Z from the th sensor s sent to the fuson center At the fuson center, the global test statstc Z can be computed by WCA, e Z GS (, S,, S WX / Z Fuson center decdes the presence or the absence of a target n the test cell by comparng Z wtht, wheret s an approprate scalng ctor It s assumed that Y, Y,, YM and Y,, M + Y are IID random varables that follow an exponental dstrbuton In the case of homogeneous nose, EY [ j ] λ, where λ s the nose power of the th sensor We denote the correspondng densty and cumulatve dstrbuton functon as f ( y and F ( y, respectvely, and let CR represents the clutter-to-nose power rato In the case of nonhomogenrous bacground, the expected value Y s λ + CR, dependng on whether the of j λ or ( sample Y j s from nose-only regon or from clutter Assumng a Swerlng II fluctuatng target, the test sample T x, also has an exponental dstrbuton wth mean λ The mean λ s unnown and depends on the target presence/absence, the clutter level, and the target strength: λorλ( + CR under H λ (6 λ λ( + SR under H Where hypothess H represents the presence of a target and hypothess H means no target, and λ λ( + CR represents the sgnal-plus-nose power, where SR s the rato of sgnal power to nose Under H, n clutter bacground, λ + CR λ equals to ( For convenence and wthout loss generalty, we study performance of the CCAWCA detector n the case of two sensors At the fuson center, applyng a lelhood rato test (LRT to the case descrbed by (6 yelds f X ( x H LR > < f X ( x H H H T L (7 Where T L s an approprate threshold Smplfyng (6 gets H ' X X > + T (8 λ λ λ λ < H Further smplfyng (8 yelds H X X + w > T λ λ < (9 H r + r λ λ Where w, L,and r r + L r λ Usng S denotes S X Z ( Where Z Rm x ( From (8 and 9, we get Z S + WS, Snce the MGF of the Z can be represented as [9] M Z j ( s + s + j+ j ( Then the probablty densty functon (PDF of Z can be denoted as + (! z + Z( z e! (!(!( + f z, Z> (3 And the PDF of the test statstc S at the fuson center s

5 fs ( s zf ( x, z dz zfx ( sz fz ( z dz (4 Substtutng ( and (3 nto (4 yelds: a t s fs ( s + ct, Z> (5 ( + r ( + r (! + Where at, c t (!(!( + Assumng S and S are ndependent each other, the jont PDF between S and S can be represented as: f ( s, s f ( s f ( s (6 S, S S S Thus, we can evaluate the detecton probablty of the CCAWCA detector by (6 through (5: Pd Pr( S > T fs, s ( s, s dsds (7 S + WS > T Substtutng (4 and (5 nto (7 yelds: at s Pd ( + ct S+ WS> T ( + r ( + r at s ( + ct dsds ( + r ( + r at at s ( + ct ( + r ( + r S + WS > T ( + r s ( + ct dsds ( + r at at ( A A µ ( + λ µ ( + λ µµ ( + λ( + λ Where: A A A + A ctct + T + A ( ( + dy + Wµ ( + λ + µµ ( + λ( + λ A3 {( c ( c F ( c + a TW t t t t ( ct att attw at( ct + att + attw ct + attw F at( ct + att atwct + + ( ( } F HypergeometrcF awc t (, + ; ; ( c + a T + a Wc t t t t (8 F HypergeometrcF awc t ( t + atw T (, + ; ; ( ct + att at + atwct We can drectly obtan the lse alarm probablty P by settng d, d, W e: P at at ( s + ct ( s + ct dsds S+ WS> T Where: aa ( B B t t µµ B, B B + B 3 c c t t + T + B ( ( + + µ + B µµ 3 {( c t ( c t F ( c ( t + a t T c t + a t T + a t T a ( c + a T + a T t t t t ( ( ct+ att F} at( ct+ att at ct F HypergeometrcF atc (, + ; ; ( ct + att + atct F HypergeometrcF at( ct + att (, + ; ; ( c + a T a + a c t t t t t 4 umercal Analyss results (9 In ths secton, we dscuss the performance of the adaptve censored cell-averagng CFAR detector And we compare ts performance wth typcal detectors such as the central order statstc detector (COS, the OSAD, OSOR, MOS (maxmum order statstc and mos(mnmum order statstc detector The specfc values of parameters used n our analyss are lsted n Table Table parameters and calculaton values for constant T for P Detector RC (l P T CCAWCA S 5 63 S 5 COS S 5 44 S 5 MOS S 5 58 S 5 mos S

6 S 5 OSOR S S 5 OSAD S S 5 In Table, S and S represent sensor and sensor, and RC denotes reference cell number And we analyze below varous ranges of parameters over whch the comparsons are made ncludng detector comparsons under homogeneous bacground clutter and under the nterferng target (mult-target or clutter edge stuaton Also we dscuss two nds of stuatons, n whch two sensors have the same SR/CR/IR or not Moreover, snce the closed-form expressons for P d of CCAWCA n nonhomogeneous bacground s not avalable, we analyze t usng Monte Carlo smulaton Under homogeneous bacground, the CCAWCA -CFAR outperforms the mos, OSAD and OSOR detectors, but not as good as the COS detector does The detecton performance of all the CFAR detectors, n the case of homogeneous bacground and two sensors havng the same SR (e L, are shown n Fg3 When the two sensors have the dfferent SR, here, we choose the rato of SR of sensor to that of sensor s, and ts detecton performance are shown Fg4 In the case of mult-target bacground, the detecton performance are shown n Fg5- (L, t analyss the stuaton s that Pd as a functon of SR when the number of nterferng targets at sensor has and sensor vares from to When two sensors have the same SR (SR, e L, the detecton performances of all the CFAR detectors are shown n Fg When two sensors have dfferent SR (e L, the detecton performance s shown Fg From Fg and Fg we can see that all detectors performance depend on the selected ran For number of nterferng targets from to 4, the detectors has nearly good performance as the COS detector does But once the number of nterferng targets exceeds ts tolerable range, we observed that the mos, CCAOR, and OSOR perform better than the others, and the other detector have a sharp drop n P d Fg4 Pd versus SR n dfferent weghts (L Fg5 IRIL Fg6 IRIL Fg7 IRIL Fg3 Pd versus SR n dfferent weghts L Fg8 IRIL3

7 Fg9 IRIL4 Fg Probablty of detecton versus number of nterferng targets at sensor (L Fg Probablty of detecton versus number of nterferng targets at sensor (L The numercal analyss results ndcate that, n the case of homogeneous bacground, the performance of the CCAWCA-CFAR detector s not better than that of COS CFAR detectors; but n nonhomogeneous bacground t performs better than OSAD, OSOR, and COS, whle t has a tolerable drop n P d And the CCAWCA-CFAR detector requres only half communcaton band wdth of the MOS detector s and the mos detector s The most mportant advantage of the CCAWCA detector s that t can be avalable n the csase of dfferent SR among sensors In addton, another advantage of the method proposed here becomes obvous when dealng wth a dense target envronment, because t does not need pror nowledge of the target stuaton 5 Summares and Conclusons In ths paper, we have developed a novel adaptve CCAWCA-CFAR detector used n dstrbuted sensors For a Swerlng II fluctuatng target n Gaussan nose of unnown level, we obtan ts closed-form expressons of lse alarm probablty and detecton probablty In summary, the attractve feature of the proposed detector over other CFAR detectors s that t does not need a pror nowledge about the nterference n order to perform well Other CFAR detectors perform well only when the pror nformaton about the nterferng envronment are approprately selected ot enough a pror nformaton wll result n severe degradaton n lse alarm regulaton propertes or detecton performance, especally n acute nterferng envronments Wthout the pror nformaton about the nterferng envronment or the nterference targets not trmmng completely, so ths algorthm has more CFAR loss The advantage of the method proposed becomes obvous when dealng wth a dense target envronment; the algorthm s robust even n the stuaton where the targets wth leaages comprse up to 3% of the reference wndow More mportantly, the CCAWCA detector holds CFAR characterstc n dfferent SR case for every sensor Acnowledgements Ths research wor was supported by the atonal atural Scence Foundaton of Chna, o and the 4th atonal Postdoctoral Scence Foundaton of Chna, o 64 References [] Tenney, Robert R, and Sandell, ls R Jr Detecton wth dstrbuted sensors IEEE Transactons on Aerospace and Electronc Systems, Vol 7, pp 5-5, July 98 [] Sadjad,E Hypothess n a dstrbuted envronment IEEE Transactons on Aerospace and Electronc Systems, Vol, pp 34-37, 986 [3] Rebman, Amy R and olte, L W Optmal detecton and performance of dstrbuted sensor systems IEEE Transactons on Aerospace and Electronc Systems, Vol 3, o, pp 4-3, 987 [4] Char, Z, Varshney, P K Optma data fuson n multple sensor detecton systems IEEE Transactons on Aerospace and Electronc Systems, Vol, o, pp 98-, 986 [5] Hoballah, Imad Y, Varshney, Pramod KDstrbuted Bayesan sgnal detecton IEEE Transactons on Informaton Theory, Vol 35, o5, pp 995-, 989 [6] Hoballah, IY, and Varshney, P K eyman-pearson detecton usng multple radars In Proceedngs of the 5th IEEE Control and Decson Conference, 986, pp 37-4 [7] Srnvasan, R, Dstrbuted radar detecton theory IEE Proceedngs, Part F: Communcatons, Radar and Sgnal Processng, Vol 33, o, 986, pp 55-6

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