Constant False Alarm Rate Detectors in Intensive Noise Environment Conditions

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1 BUGARIA ACADEMY OF SCIECES CYBEREICS AD IFORMAIO ECHOOGIES Voum, o 3 Sofa Contant Fa Aam Rat Dtcto n Intnv o Envonmnt Condton yuba Douova Inttut of Infomaton and Communcaton chnoog, 3 Sofa E-ma: douova@t.ba.bg Abtact: A dffnt tchnqu of CFAR dtcto pocdu fo movng tagt dtcton n no nvonmnt condton wth a Poon dtbutd fow and Ragh amptud dtbuton popod n th pap. h xpon of th dtcton and fa aam pobabty a dvd fo a hghy fuctuatng Swng II tagt. A compaatv anay of th pfomanc of dffnt ada dtcto tuctu png contant fa aam at don. h a a CA CFAR (C Avagng Contant Fa Aam Rat), an EXC CFAR (EXCon Contant Fa Aam Rat), a CFAR BI (Contant Fa Aam Rat wth Bnay Intgaton), an EXC CFAR BI (EXCon Contant Fa Aam Rat wth Bnay Intgaton) and an API CFAR (Adaptv cnong Pot dtcton Intgaton Contant Fa Aam Rat). A mthod fo o tmaton, whch aow choong of optma dtcto paamt, dvopd. h tmat a obtand of th ffctvn of CFAR dtcto n no nvonmnt condton and thy a compad to pattn, nvtgatd by oth autho. h ut achvd can b uccfuy appd fo ada tagt dtcton and n th xtng communcaton ntwo cv, that u pu gna. Kywod: Rada dtcto, CFAR dtcto, no nvonmnt, andomy avng mpu ntfnc, pobabty of dtcton, pobabty of fa aam, dtctabty poft (o).. Intoducton Modn ado-ytm functon n compx ctomagntc nvonmnt, und condton of catd atfca and natua ntfnc wth unnown o vaab paamt. hat uuay mutua ntfnc, fom adacnt ado-ctonc 3

2 dvc, a a u powfu and appang cauay,.., havng no nvonmnt chaacttc wth ag ntnty. h concn pcay gna fom ma ada fo a taffc conto. Randomy Avng Impu Intfnc (RAII), n uch ca, cvd not ony at th bac ada antnna chann, but ao at th dob and th bacob dagam of th antnna, and cvng pob not ony at th bac fquncy chann. Sgna dtcton n noy o cutt nvonmnt a vy mpotant pat of tagt dtcton pocdu. In thoy th no and cutt bacgound w b dcbd by a tattca mod wth.g. Raygh, o xponntay dtbutd andom vaab of nown avag no pow. But n pactca appcaton th avag no o cutt pow abouty unnown and om tattca paamt can addtonay vay ov ang, tm and azmuth. In automatc ada dtcton, th gna cvd ampd n ang and fquncy. Each amp pacd n an aay of ang and Dopp outon c. h cutt bacgound n th c und tt tmatd by avagng th output of th naby outon c (ang and/o Dopp). h tagt dtcton dcad, f th gna vau xcd a pmnay dtmnd thhod. Cunt tmatng of th no v n th fnc wndow fom th thhod. h dtcton thhod obtand by cang th no v tmat wth a contant α to achv a dd pobabty of fa aam P FA. A an tmat of th no v, th tmat popod by F n n and Johnon n [] qut oftn ud. Avagng th output of th fnc c uoundng th tt c fom th tmat. hu a contant fa aam at mantand n th poc of dtcton. h th convntona C Avagng Contant Fa Aam Rat (CA CFAR) dtcto, popod by F n n and Johnon n []. h CA CFAR poco a vy ffctv n ca of tatonay and homognou ntfnc and a ffctv amot a th da yman-paon dtcto, whn th numb of fnc c bcom vy ag. h pnc of tong andomy avng mpu ntfnc n both, th tt outon c and th fnc c, can cau datc dgadaton n th pfomanc of CA CFAR poco. Such typ of ntfnc non-tatonay and non-homognou and oftn caud by adacnt ada o oth ado-ctonc dvc. In a non-homognou nvonmnt, th dtcton pfomanc and th fa aam guaton popt of CA CFAR dtcto may b ouy dgadd. Dung th at fw ya a ot of dffnt appoach hav bn popod to mpov th dtctabty of CFAR dtcto opatng n andom mpu no [-9]. On way fo png contant fa aam at und th condton th ung of th xcon CFAR dtcto pntd n pap [, ], but t not ffctv nough. Mo ffctv fo th tabzaton of fa aam th mpmntaton of Pot-dtcton Intgaton (PI), and Bnay Intgaton (BI) n CFAR gna poco, tudd and anayzd n pap [5, 9]. Mot ffctv th Adaptv Pot-dtcton Intgato CFAR (API CFAR) gna poco wth adaptv cton on mpu no n fnc and n tt wndow and a potdtcton ntgaton pocdu [5, 3]. 3

3 h no n tt c a Raygh nvop dtbutd and tagt tun a fuctuatng accodng to Swng II mod n [-4]. Impu no xt ony n th tt wndow n [5], th avag ptton fquncy of pu ammng n th ca dtmnd by th numb of pu n a wndow. In fnc [7-, ] th autho aum that th amp of th tota ntfnc a dtbutd accodng to th compound xponnta aw, wh th wghtng coffcnt a th pobabt of couptng and non-couptng of th amp. h pobabt fo appang of th mpu no wth avag ngth n th c of ang dpnd on th mutpcaton of th avag ptton fquncy of mpu no and th no ngth. In uch tuaton t woud b dab to now th CFAR o dpndng on th paamt of th mpu no, fo atng th bhavo of th ada. h a two appoach fo cacuaton of CFAR o, offd by Rohng and Kaam n [, 4]. h convntona mthod to comput th addtona SR ndd fo CFAR pocng chm byond that fo th optmum poco, to achv a fxd dtcton pobabty (.g.,.5), ud n [5, 7-, ]. Fo a patcua CFAR chm th o obvouy va wth th dtcton pobabty. Atnatvy, th autho n [, 4] u anoth cton, atd to th on bad on th Avag Dcon hhod (AD), nc th thhod and th dtcton pobabty a coy atd to on anoth. hn th dffnc btwn two CFAR ytm n a homognou cutt tuaton xpd by th ato btwn th two AD maud n db n [, 4]. Such tmaton and o anay a not dcbd n [4, 5, 7]. On th oth hand, n [8, 9, ] th o a tmatd, but fo a dffnt vau fo th pobabty of dtcton.9755 and th ut a compad wth th am CFAR chm n th tuaton wthout mpu no. Sma nvtgaton pntd n [] and th ut, whch a achvd fo CFAR poco, a qua to tho pntd n [] fo th ca wthout mpu no. Ung th AD appoach and th Momnt Gnatng Functon (MGF) fo modng of th mpu no pntd n []. h o of CFAR dtcto a cacuatd fo dffnt vau of fa aam pobabty, fo a dffnt numb of obvaton n th fnc wndow, an avag Intfnc-to-o Rato (IR) and pobabt fo appaanc of mpu no wth avag ngth n th c n ang. h dtcton pfomanc of CFAR poco popod by H o u n [] fo th ca of homognou nvonmnt and ch-qua famy of fuctuatng tagt mod (Swng I, II, III, and IV). In th pap th tudy pntd of th tuaton fo a hghy fuctuatng tagt Swng II typ tagt mod dtcton und ntnv no nvonmnt condton. A compaatv anay of th pfomanc of dffnt typ of CFAR dtcto cad out. h tuctu gv th pobty fo png a contant fa aam at n th pnc of andom avng mpu ntfnc. In th tudy on vy nttng ca condd th mt, whn ncang th pobabty of th appaanc chang th dtbuton aw fom Poon to bnomna. h bnomna mod mo gna than Poon dtbuton mod 33

4 [3]. h chang of th dtbuton aw and th paamt of RAII ad to wond dtcton poc. h ach wo pfomd n MAAB computatona nvonmnt.. Sgna mod Ung th appoach popod n [], nw ut a obtand fo Swng II typ tagt dtcton mod of pfomanc n no nvonmnt (Randomy Avng Impu Intfnc RAII). h gna n th fnc wndow aumd to b wth Poon dtbuton and ha th foowng Pobabty Dnty Functon (PDF) [4]: () f ( x) P ( ) λ xp x xp ( ) ( ) ( ) λ λ λ wh th p pu avag Sgna-to-o Rato (SR), λ th avag pow of th cv no, th avag IR, th pobabty of appaanc of RAII. Und condton of bnoma dtbuton of pu ntfnc, th pobabty of ntfnc-pu-no occunc n th bacgound nvonmnt ( ). h pobabty of appaanc of two ntfnc n a ng c and havng ony no pobabty ( ), wh t F, F th avag ptton fquncy of pu ntfnc and t c th ngth of pu tanmon [4]. h dtbuton bnoma whn th pobabty of pu ntfnc abov. [4]. In th tuaton th output of th fnc wndow a obvaton fom tattcay ndpndnt xponnta andom vaab. Conqunty, th PDF of th fnc wndow output may b dfnd by: c x () λ ( ) f xp B ( x) ( ) x xp λ λ ( ) x xp ( ) ( ) λ λ λ x wh λ th avag pow of th cv no and /λ th p pu avag IR. In th nxt two fgu, accodng to pap [5], compaatv muaton xamp a hown fo Poon and fo bnoma dtbuton of pu ntfnc, wth gna and no paamt vau 7 db, λ, 3 db,.. 34

5 Fg.. Examp of Poon dtbuton of pu ntfnc Fg.. Examp of bnomna dtbuton of pu ntfnc 3. CFAR poco tattca anay In th modn ada ytm, png contant fa aam at, th tagt dtctd accodng to th foowng agothm []: (3) H H : Φ : Φ ( q ) ( q ), q, q > αv, < V α 35

6 wh H th hypoth that th tt outon c contan th cho fom th tagt and H th hypoth that th tt outon c contan th andomy avng mpu ntfnc ony, V th no v tmaton. h contant α a ca coffcnt, whch dtmnd n od to mantan a gvn contant fa aam at. h dffnt CFAR tuctu ma u of dffnt agothm fo no v tmaton V [5-4]. In th pap va typ of gna poco a anayzd a CA (C Avagng), an EXC (EXCon), a BI (Bnay Intgaton), an EXC BI (EXCon wth Bnay Intgaton) and an API (Adaptv cnong Pot dtcton Intgaton). On Fg. 3 on xamp pntd of th adaptv thhod pocdu fo on-dmnona CFAR poco n condton of andomy avng mpu ntfnc [5]. h gna tuctu of an adaptv CFAR poco hown on Fg. 4. Fg. 3. Adaptv thhod pocdu fo on-dmnona CFAR poco Input gna Squa ow Dtcto CFAR agothm hhod pocdu C o m p a a t o Output of th CFAR Fg. 4. Gna tuctu of an adaptv CFAR poco 36

7 37 t u aum that pu ht th tagt, whch modd accodng to Swng II ca. h gna cvd ampd n ang by ung outon c utng n a matx wth ow and coumn. Each coumn of th data matx cont of th vau of th gna obtand fo pu ntva n on ang outon c. t u ao aum that th ft / and th at / ow of th data matx a ud a a fnc wndow n od to tmat th no-puntfnc v n th ada tt outon c. In th ca th amp of th fnc c ut n a matx X of z Ν Λ. h tt c o th ada tagt mag ncud th mnt of th / ow of th data matx and a vcto Z of ngth. h pobabty of dtcton fo a CA CFAR poco fo tagt of ca Swng II, accodng to [8] (4) M M C P CA CA CA CA D CA wh CA th thhod contant fo CA CFAR poco. h pobabty of dtcton fo CFAR BI gna poco n th no tuaton [9] (5) { } 3 D BI R R R C C P wh:, BI BI BI R, BI BI BI R R BI BI BI 3, wh BI th thhod contant fo CFAR BI poco.

8 Fo compaon on th nxt two fgu, th output of CA CFAR and CFAR BI dtcto a pntd. Fg. 5. Examp of a CA CFAR output dtcto h pobabty of dtcton fo an EXC CFAR poco fo tagt mod Swng II, accodng to [6] (6) EXC EXC P D EXC C PE PE е MV, еm V, λ λ wh M V(). th Momnt Gnatng Functon (MGF) and EXC a pdtmnd ca facto fo EXC CFAR poco. 38 Fg. 6. Examp of a CFAR BI output dtcto

9 h MGF of th no v tmat V, may b obtand a (7) MV ( U ) PE ( PE ) MV ( U, ) wh U f (,,, λ ) EXC and th pobabty that a amp x uvv at th xcon output cacuatd a B E E (8) E xp xp. ( ) B P λ λ M V, th condtona MGF of th tmat V wh th numb of amp uvvd at th xcon output. h pobabty of pu tan dtcton fo EXC CFAR BI poco vauatd n uch no tuaton a n [7, ] by h functon ( U ) * * (9) PD CP D EXC ( P D EXC ) EXC BI M wh M bnay dcon u, P D EXC th pobabty of pu dtcton, whch may b found ung th xpon fo EXC CFAR poco wth Poon mpu no. In th on vy ffctv CFAR dtcto ca pap condd, whn both th two-dmnona fnc wndow and th tt c a couptd by andomy avng mpu ntfnc, who avag ptton fquncy and magntud a unnown, [3]. h cnong pocdu gvn n [4, 5], n od to mov th unwantd amp fom both th fnc wndow and th tt c bfo fomng th adaptv thhod and th tt tattc, ud. In th ca th numb of th ntgatd amp n th tt c and ao n th fnc wndow a andom vaab wth bnoma dtbuton. Accodng to th cnong agothm a th mnt wth hgh ntnty of gna a movd fom th fnc wndow and th tt outon c. h cnong agothm cont of th foowng tag: Stag. h mnt of th fnc wndow x ( x, x,..., x ) outon c z ( z z,..., ) magntud, (), z and th tt a an-odd accodng to ncang x x... x... x and z z... z... z. Stag. Each of th o and mnt compad wth th adaptv thhod, accodng to th foowng u: x x z z () x,,...,, and z,,...,, wh x x and z z. 39

10 4 Aft th top of th cuv pocdu, t aumd that mot o a of th andomy avng mpu ntfnc a n th cond pat of th fnc wndow and th tt outon c. In th pap popod th mo gna xpon fo th pobabty of tagt dtcton n th pnc of Poon dtbuton no nvonmnt condton may b cacuatd a n [3]: () API API API API API API API API D API P wh API a pdtmnd ca facto fo API CFAR poco that povd a contant fa aam at (P FA ). h pobabty of fa aam fo th CFAR poco wth tagt mod ca Swng II n andomy avng mpu ntfnc obtand fo vau of gna-to-no ato. Fo compaon and cacuaton of CFAR dtcto o th ato a ud btwn two vau of SR fo dffnt CFAR poco, maud n db. h appoach condd n [4]: (3) CFAR CFAR SR SR og Δ, by 5. cont, CFAR D CFAR D D FA P P P P. 4. umca ut It povd n th pap that dffnt CFAR poco ud fo gna dtcton on th homognou bacgound of unnown ntnty and n th pnc of andomy avng mpu ntfnc wth nown paamt, mpov th dtcton pfomanc. In uch CFAR poco t uuay aumd that th no amptud a Raygh dtbutd vaab and th pow, thfo, an xponntay dtbutd vaab. h numca ut pntd a obtand aft dtad muatona anay of CFAR dtcto pfomanc und no nvonmnt condton. h anay of th pfomanc of dffnt tuctu of on-dmnona and two-dmnona CFAR gna poco CA CFAR (c avag), EXC CFAR (xcon), CFAR BI (bnay ntgaton), EXC CFAR BI (xcon and bnay ntgaton) and API CFAR (adaptv pot ntgaton) don.

11 h achvd ut fo CA CFAR dtcto thhod anay wth th vau of th pobabty of fa aam (P FA ), fo two vau of numb of obvaton n th fnc wndow (), fo two vau of avag ntfnc-tono ato (IR) and fo fv dffnt vau fo a pobabty of appaanc of mpu ntfnc wth avag ngth n th c n ang a pntd n ab. ab P FA 6 3 IR, db IR3, db IR, db IR3, db h pobabty of dtcton fo CA CFAR dtcto hown on Fg. 7 fo contant dtcton thhod achvd fo non homognou ntfnc wth paamt avag pow of th cv no λ, avag IR 3 db, pobabty of appaanc of mpu ntfnc wth avag ngth n th ang c.. h ut fo EXC CFAR dtcto thhod anay wth pobabty of 4 fa aam ( P FA ), xcon contant B E, fo two vau of numb of obvaton n th fnc wndow (), an avag ntfnc-to-no ato (IR 3 db) and nn dffnt vau fo pobabty of appaanc of mpu ntfnc wth avag ngth n th c n ang a pntd n ab. h pobabty of dtcton fo EXC CFAR dtcto hown on Fg. 8. h tudy anayzd fo contant dtcton thhod achvd fo non homognou ntfnc wth paamt avag pow of th cv no λ, avag IR 3 db, pobabty of appaanc of mpu ntfnc wth avag ngth n th ang c..9. 4

12 Fg. 7. Pobabty of dtcton fo CA CFAR dtcto ab Fg. 8. Pobabty of dtcton fo EXC CFAR dtcto 4

13 ab 3 pnt th obtand thhod contant und qua xpmnta condton fo th dffnt CFAR dtcton tuctu wth two-dmnona bnay ntgaton pocdu. h ut a achvd fo a vau of pobabty of fa 4 aam ( P FA ), fo two vau of bnay u /6 and 6/6, fo nn vau of pobabty of appaanc of mpu ntfnc and an avag ntfnc-tono ato (IR3 db). ab 3 M//6 M/6/ h pobabt of dtcton fo CFAR BI dtcto wth two dffnt vau of bnay u on nxt two fgu Fg. 9 ( M / / 6) and Fg. ( M / 6/ 6) a pntd. h ut a achvd fo th foowng paamt - pobabty of fa aam P FA 4, avag pow of th cv no λ, avag IR 3 db, pobabty of appaanc of mpu ntfnc wth avag ngth n th ang c..9. Fg. 9. Pobabty of dtcton fo CFAR BI dtcto 43

14 Fg.. Pobabty of dtcton fo CFAR BI dtcto ab 4 pnt th obtand thhod contant vau und qua xpmnta condton fo th two-dmnona EXC CFAR BI dtcto. h 4 ut a achvd fo vau of pobabty of fa aam ( P FA ), fo two vau of bnay u /6 and 6/6, fo nn vau of pobabty of appaanc of mpu ntfnc and an avag ntfnc-to-no ato (IR3 db). 44 ab 4 M//6 M/6/ h pobabt of dtcton fo EXC CFAR BI dtcto wth two dffnt vau of bnay u on nxt two fgu Fg. ( M / / 6) and Fg. ( M / 6/ 6) a pntd. h ut a achvd fo th foowng paamt pobabty of fa aam P FA 4, xcon contant B E, avag pow of th cv no λ, avag IR 3 db, pobabty of appaanc of mpu ntfnc wth avag ngth n th ang c..9. h numca ut fo th obtand thhod contant vau n qua xpmnta condton fo th two-dmnona API CFAR dtcto a ncudd

15 n ab 5. h ut a achvd fo th vau of pobabty of fa aam (P FA ), fo two vau of numb of obvaton n th fnc wndow (, ), fo two vau of avag IR and fo fv dffnt vau fo a pobabty of appaanc of mpu ntfnc wth avag ngth n th c n ang. Fg.. Pobabty of dtcton fo EXC CFAR BI dtcto Fg.. Pobabty of dtcton fo EXC CFAR BI dtcto 45

16 ab 5 P FA 6 and 6 6 and 3 IR db and IR db and IR 3 db IR 3 db h pobabt chaacttc of dtcton fo API CFAR dtcto a hown on Fg. 3 fo contant dtcton thhod achvd fo non homognou ntfnc wth paamt pobabty of fa aam ( P FA 4 ), fo vau of numb of obvaton n th fnc wndow ( 6, 6), an avag ntfnc-to-no ato (IR3 db) and fv dffnt vau fo pobabty of appaanc of mpu ntfnc wth avag ngth n th c n th ang.. 46 Fg. 3. Pobabty of dtcton fo API CFAR dtcto

17 5. Concuon h xpmnta ut va th nfunc of th ntfnc on th dtcton poc, whn havng contant fa aam at n no nvonmnt condton. h pap pntdcond th ut obtand by th popod adaptv thhod dtmnaton pocdu and th anay of dffnt CFAR dtcto tuctu n ntnv andomy avng mpu ntfnc nvonmnt. h nd fo an adquat thhod anay pocdu, nabng btt dtcton ut fo ow vau of SR, condd. h vau of th tt outon c and th pobabty of fa aam ov th avag dtcton thhod a tudd. h appcaton of cnong tchnqu n th dtcton agothm mpov th CFAR dtcto ffctvn. h ut obtand may hav gnfcant pactca appcaton fo CFAR dtcto wong und no nvonmnt condton. h obtand ut how, that th API CFAR (Adaptv cnong Pot dtcton Intgaton CFAR) poco th mot ffctv n th condton. A a fna concuon th ut achvd n th pntd pap confm onc agan th ncty fo ynth of nw agothm fo movng tagt dtcton, aung obutn and hgh ffcncy of th ada ytm. h ut obtand n th pap coud pactcay b ud n ada and communcaton ntwo. R f n c. F n n, H., R. J o h n o n. Adaptv Dtcton Mod wth hhod Conto a a Functon of Spatay Sampd Cutt Etmaton. RCA Rvw, Vo. 9, 968, o 3, H o u, X.,. M o n a g a,. a m a w a, Dct Evauaton of Rada Dtcton Pobabt. IEEE an., Vo. AES-3, 987, o 4, G o d m a n, H., I. B a -D a v d. Anay and Appcaton of th Excon CFAR Dtcto. In: IEE Poc., Vo. 35, Pt.F, 988, o 6, K a b a c h v, C.,. D o u o v a, I. G a v a n o v. Hough Rada Dtcto n Condton of Intnv Pu Jammng. Sno & anduc Magazn, Spca Iu Mutno Data and Infomaton Pocng, 5, Kabachv, C., I. Gavanov,. Douova. Adaptv Cnong CFAR PI Dtcto wth Hough anfom n Randomy Avng Impu Intfnc. Cybntc and Infomaton chnoog, Vo. 5, 5, o, Kabachv, C., I. Gavanov,. Douova. Excon CFAR BI Dtcto wth Hough anfom n Pnc of Randomy Avng Impu Intfnc. In: Poc. of th Intnatona Rada Sympoum IRS 5, Bn, Gmany, 5, D o u o v a,., C. K a b a c h v. Pfomanc of Hough Dtcto n Pnc of Randomy Avng Impu Intfnc. In: Poc. of th Intnatona Rada Sympoum IRS 6, Kaow, Poand, 6, Kabachv, C.,. Douova, I. Gavanov. C Avagng Contant Fa Aam Rat Dtcto wth Hough anfom n Randomy Avng Impu Intfnc. Cybntc and Infomaton chnoog, Vo. 6, 6, o, D o u o v a,. Hough Dtcto wth Bnay Intgaton Sgna Poco. Compt. Rnd. Acad. Bug. Sc., Vo. 6, 7, o 5, D o u o v a,., V. B h a, C. K a b a c h v. Hough Dtcto Anay by man of Mont Cao Smuaton Appoach. In: Poc. of th Intnatona Rada Sympoum IRS 8, Wocaw, Poand, 8,

18 . D o u o v a,. Movng agt Hough Dtcto n Pu Jammng. Cybntc and Infomaton chnoog, Vo. 7, 7, o, D o u o v a,. Hough Dtcto wth On-dmnona CFAR Poco n Randomy Avng Impu Intfnc. In: Poc. of Dtbutd Comput and Communcaton two, Intnatona Wohop, Sofa, Bugaa, 6, Bha, V., C. Kabachv,. Douova. Adaptv CA CFAR Poco fo Rada agt Dtcton n Pu Jammng. Jouna of VSI Sgna Pocng, Vo. 6,, R o h n g, H. Rada CFAR hhodng n Cutt and Mutp agt Stuaton. IEEE anacton, Vo. AES-9, 983, o 4, D o u o v a,., I. G a v a n o v. Hough Dtcto hhod Anay n Pnc of Randomy Avng Impu Intfnc. Cybntc and Infomaton chnoog, Vo.,, o,