Average Decision Threshold of CA CFAR and excision CFAR Detectors in the Presence of Strong Pulse Jamming 1

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1 Average Decson hreshold of CA CFAR and excson CFAR Detectors n the Presence of Strong Pulse Jammng Ivan G. Garvanov and Chrsto A. Kabachev Insttute of Informaton echnologes Bulgaran Academy of Scences Acad. G. Bonchev Str., bl., 3 Sofa, Bulgara Phone: 359/ e-mal: cabachev@t.bas.bg, garvanov@t.bas.bg Introducton Cell-Averagng Constant False Alarm Rate (CA CFAR sgnal processng proposed by Fnn and Johnson n [] s often used for radar sgnal detecton. he detecton threshold s determned as a product of the nose level estmate n the reference wndow and a scale factor to acheve the desgn probablty of false alarm. he presence of strong pulse ammng (PJ n both, the test resoluton cell and the reference cells, can cause drastc degradaton n the performance of a CA CFAR processor as shown n []. For eepng of constant false alarm rate n PJ, the CA CFAR processor presented n [8,] s used. For the mnmzaton of CFAR losses n case of pulse ammng, PI or BI s mplemented n CFAR processors as shown n [4,7,9]. he use of excson CFAR detectors, supplemented by a postdetecton ntegrator or a bnary ntegrator as shown n [5,6,9], ncreases the CFAR losses. Mnmum CFAR losses n PJ are obtaned n [4,] wth a CFAR adaptve postdetecton ntegraton (API processor wth adaptve selecton on PJ n reference wndows and approry selecton n test wndows as shown n [4], and adaptve censorng n reference and test wndows as presented n []. In such stuatons, t would be desrable to now the CFAR losses, dependent on the parameters of PJ, for ratng of radar behavor. We use the crteron offered by Rollng and Kassam n [,3], based on the average decson threshold (AD. he AD and the detecton probablty are closely related to each other. he dfference between the two CFAR systems s expressed by the rato between the two ADs measured n db, as shown n [,3]. We assume n ths paper that the nose n the test cell s Ralegh envelope dstrbuted and target returns are fluctuatng accordng to Swerlng II model, as t s n [3,4]. As a dfference from the authors n [4], we assume that the samples of PJ are dstrbuted accordng to the compound exponental law, where weghtng coeffcents are the probabltes of corruptng and non-corruptng of the samples. We have used weghtng coeffcents n the nterval between and. For values of the weghtng coeffcents hgher than.3, the Posson process model s used, but t s rough []. he results n ths case are correct as far as processor behavour s concerned, but the numercal values are not accurate. he bnomal dstrbuton s correct n ths case. In ths paper new analytcal expressons for the average decson threshold (AD of a CA CFAR and excson CFAR detectors n pulse ammng are derved. he results obtaned for the AD of a CA CFAR processor wthout pulse ammng are equal to those presented n [3]. he expermental results show that the nfluence of nterference on the detecton process, when havng CA CFAR and excson CFAR processors n pulse ammng, s smlar to that gven n [6,8,9], obtaned by usng conventonal methods for the calculaton of the CFAR losses. he expermental results show that excson CFAR processors are most sutable for use when the probablty for the appearance of pulse ammng taes values n the nterval ( to.5. In cases when the probablty for the appearance of pulse ammng taes values n the nterval (.5 to, we recommend CA CFAR processors. hs wor s supported by II 44, MPS Ltd. Grant RDR and Bulgaran F SR Grant I 9/99

2 Performance of CA CFAR and excson CFAR detecton n the presence of pulse ammng. Probablty of detecton and false alarm of CA CFAR detectors Consder a radar detector, n whch the receved sgnal s sampled n range by ( resoluton cells resultng n a vector of ( observatons. he samplng rate s such that the samples are statstcally ndependent. After fltraton, the sgnal s appled to a square-law detector and then processed n the CA CFAR decson element. In condtons of pulse ammng the bacground envronment ncludes random nterferng pulses and the recever nose. herefore the samples surroundng the cell under test (a reference wndow may be drawn from two classes. One class represents the nterference-plus-nose stuaton, whch may appear at the output of the recever wth the probablty. hs probablty can be expressed as = t c F, where F s the average repetton frequency of PJ and t c s the length of pulse transmsson. he other class represents the nose only stuaton, whch may appear at the output of the recever wth the probablty (. he probablty densty functon (pdf of the test resoluton cell s assumed to be dstrbuted accordng to Swerlng II case [8, ]: ( ( ( ( ( x x f x = exp exp ( λ s λ s λ r s λ r s where λ s the average power of the recever nose, r s the average nterference-to-nose rato (IR of pulse ammng, s s the per pulse average sgnal-to-nose rato (SR and s the number of observatons n a reference wndow. In ths case the Posson process model s used, and t s vald only for.3. he probablty densty functon (pdf of the reference wndow outputs can be defned accordng to (, settng s =. he probablty of pulse detecton P D s obtaned n [8] as: PD = ( ( s ( r s ( λ λ where M (. s the moment generatng functon (mgf of the nose level estmate. In a conventonal CA CFAR detector the nose level estmate s formed as a sum of all the outputs of the reference wndow: =. In ths case the mgf of the estmate s defned to be x = x ( ( U = Mx ( U, where M U s obtaned n [8]: M ( U = s the mgf of the random varable x. he mgf of the estmate C ( = ( λ U ( λ ( r U he probablty of target detecton n [8] s computed by usng the followng expresson: PD = C ( = ( r ( r r s r s s s he probablty of false alarm s evaluated by (4, settng s =.. Probablty of detecton and false alarm of excson CFAR detectors In an excson CFAR processor the nose level estmate s formed as an average mean of K nonzero samples at the output of the excsor { y }, that s: = y. Accordng to [5] the = operaton of the excsor s defned as follows: (3 (4

3 x : x B y = : othewse (5 where B s the excson threshold. he probablty that a sample x survves at the output of the excsor, s gven as: B ( ( B P = exp exp (6 λ λ r he probablty that out of samples of the reference wndow survve at the output of the v = C P P. he mgf of the random varable y at the output of the excsor s gven as: ( ( excsor can be obtaned n [6] by usng the followng expresson: ( exp( R BU exp R BU M y ( U = exp R ( r exp R where R B B = R =. ( λ ; λ r ( ( ( ( ( ( ( ( ( Snce the random varables x ( are ndependent, the mgf of the estmate can be obtaned as follows: M ( U, = M ( U /. In ths artcle we use the moment generatng functon on the excson CFAR processor from [6] where Y ( U = CP ( P ( U, = ( exp( R BU / ( R r / ( ( exp( R BU / ( exp( R ( M U = (, C = ( exp ( ( / (9 he probablty of target detecton for excson CFAR n [6] s computed by the expresson: PD = C P ( P ( ( s,, ( r s ( = λ λ he probablty of false alarm s evaluated by (, settng s =..3 Average decson threshold of CA CFAR and excson CFAR detectors he average decson threshold AD s defned as a normalzed quantty []: ADCFAR = / λ ( ( where the random varable s the result of the estmaton method used n the CFAR system, s the scalng factor for threshold adustment adapted to the estmaton method and requred P FA, and stands for the expectaton. d ( / λ = ( d M / λ = ( For the mathematcal expressng of the AD, we use the moment generaton functons (mgf (3 and (8, presented n [6, 8] and the method descrbed n [, 3]. We obtan new analytcal results for the AD of CA CFAR and excson CFAR processors n strong PJ, as follows:.3. Determnaton of the AD for a CA CFAR processor n PJ Usng (3 and (, we substtute U = / λ and for = we have the AD expresson: (7 (8 3

4 ( AD d ( ( d M CACFAR = = ( = C r = (4 λ λ where s computed by expresson (4, settng s =. For =, or wthout pulse ammng, AD = / = P fa. CACFAR = as n [3], where (.3. Determnaton of the AD for excson CFAR processor n PJ Usng (8 and (, we substtute U = / λ and for = we have the AD expresson: ( AD = C P ( P C = = ( ( exp( R exp( R B ( exp( R exp( R r ( ( exp R where s computed by expresson (, settng s =. ( exp( R ( exp( R ( exp( R exp( R ( B (5 3 umercal results he new analytcal expressons obtaned n the prevous secton mae possble the estmaton of the qualty of CA CFAR and excson CFAR detectors n the presence of very ntensve pulse ammng. he results are accurate for.3, but not precse for >.3. Fg. CA CFAR processor Fg. XC CFAR processor AD,, are for r = 5 db, AD,, are for r = 5 db, AD,, are for r = 3 db AD,, are for r = 3 db he expermental results are obtaned for the followng parameters: average power of the recever nose λ =; average nterference-to-nose rato (IR r =5 and 3 [db]; probablty for the appearance of pulse ammng wth average length n the range cells from to ; number of reference cells for CA CFAR end excson CFAR processors =6; probablty of false alarm P fa = 6 and excson threshold B =. In a CA CFAR processor, the nose level estmate n the reference wndow ncreases wth the ncreasng of the average nterference-to-nose rato and the probablty for the appearance of pulse ammng wth average length n the range cells (Fg.. In order to eep the false alarm probablty constant, the scale factor must be decreased when the PJ frequency ncreases. he average decson threshold (AD ncreases when the probablty for the appearance of pulse ammng taes values from to.5, and then decreases for value of > 5. (Fg.. 4

5 In the excson CFAR processor, the ammng pulses are censored and the nose level estmate n the reference wndow s ept constant (Fg.. In order to eep the false alarm probablty constant, the scale factor must be ncreased wth the ncreasng of PJ frequency. he average decson threshold (AD s constant when the probablty for the appearance of pulse ammng taes values between and.5, and then ncreases for value > 5. (Fg.. he average decson threshold (AD for an optmal detector s constant when the probablty for the appearance of pulse ammng taes values between and, (Fg. and. 4. Conclusons. ew analytcal expressons for the average decson threshold (AD of CA CFAR and excson CFAR detectors n pulse ammng are derved n ths paper. When CA CFAR and excson CFAR detectors operate wth a fxed scale factor, the detecton probablty s decreased n strong PJ, but the false alarm probablty s not mantaned constant. In our case, the scale factor s adusted to PJ so that the false alarm probablty s mantaned constant. he results obtaned for the AD of a CA CFAR processor wthout pulse ammng are equal to those presented n [3]. he usng of averaged characterstcs for the analyss of dfferent CFAR processors s a very convenent mathematcal apparatus for precse and easy determnaton of detector energy losses. he expermental results show that excson CFAR processors are most sutable for use when the probablty for the appearance of pulse ammng taes values n the nterval ( to.5. In cases when the probablty for the appearance of pulse ammng taes values n the nterval (.5 to, we recommend CA CFAR processors. he results obtaned n ths paper can practcally be used for the desgn of modern radar systems. References [] Fnn, H. M., P. S. Johnson, Adaptve detecton mode wth threshold control as a functon of spatally sampled clutter estmaton, RCA Revew, vol. 9, o 3, 968, pp [] Rohlng H. Radar CFAR hresholdng n Clutter and Multple arget Stuatons, I rans., vol. AS-9, o 4, 983, pp [3] Gandh, P. P., S. A. Kassam, - Analyss of CFAR processors n nonhomogeneous bacground, I rans., vol. AS-4, o 4, 988, pp [4] Hmonas S., CFAR Integraton Processors n Randomly Arrvng Impulse Interference, I rans., vol. AS-3, o 3, 994, pp [5] Goldman H., Analyss and applcaton of the excson CFAR detector, I Proceedngs, vol.35, o 6, 988, pp [6] Behar., C. Kabachev, xcson CFAR Bnary Integraton Processors, Compt. Rend. Acad. Bulg. Sc., vol. 49, o /, 996, pp [7] Kabachev C.,. Behar, - CFAR Radar Image Detecton n Pulse Jammng, I Fourth Int. Symp. ISSSA'96, Manz, Germany, 996, pp [8] Behar., CA CFAR radar sgnal detecton n pulse ammng, Compt. Rend. Acad. Bulg. Sc., vol. 49, o 7/8, 996, pp [9] Kabachev C.,. Behar, echnques for CFAR Radar Image Detecton n Pulse Jammng, I Fourth Int. Symp. UM'96, Praga,Cheh Republc, 996, pp [] Behar., C. Kabachev, L. Duovsa, Adaptve CFAR Processor for Radar arget Detecton n Pulse Jammng, Journal of LSI Sgnal Processong, vol. 6, o /,, pp [] Kabachev C., L. Duovsa, I. Garvanov, Comparatve Analyss of Losses of CA CFAR Processors n Pulse Jammng, CI, o,, pp [] Amov, P., vstratov, F., Zaharov, S.: Rado Sgnal Detecton, Moscow, Rado and Communcaton, 989, pp. 95-3, (n Russan. 5