CFAR processor for ESM systems applications

M.A.Khalighi and M.M.Nayebi

Abstract: The authors crilisirlcr the design o f a CFAR processor tor the ad;iplivc llirc~liol~liiig syskin or an ISM rcccivcr. For this purposc, thc important specifications of ESM syslelus arc thc rcccption of pulscs with various widtlis iiiid raks , and vulucrahility to iioisc jmi i ic rs . Tlic major dilliculty i n dctcl-nliniiig the statistics i ) T tlic background nnisc is thc proklcin 01' ititcrferiiig sigrinls. In situations ol'tolerable vari;itions in bnckgrountl noisc power, ai1 MEx-CFAR processor is proposcd, which exhibits gord rol~~isliicss against iritcrkririg p l s c s . Whcii Iiirgc vwiatiuns in iioi,sc powcr arc possible, mn AM ICx-CFAR proccssor is prriposccrl. The lkedbaclc lor)p usctt ill thc structitrc ol'the AMIlx proccssnr pcrniits it to i1ti;ipt ilscli'q~iickly to new backgrouiid ctmiliiions. P c r h " c e of the ~"npnscd CFAR processr~s is invesligalctl in viirioiis c i i scs by incans of Monte Carla siiiiulatioii and inctbotls Tor the dctcriniiintioii o f their dcsigtj paraiiictcrs nrc rlisclrsscil.

1 Introduction

CFAR (constant fiilsc alarm rate) rlctectioii is onc of tlic dcsirablc fcaturcs hi, radar nud I<SM (cicclronic support measures) rcccivcrs. Due to tlic variations in the ciwiriiii- iricnl characteristics such as thc background mist powcr, LISC ol' R fixed dctcctioii Uireshold rcwlts in a severe dcgradation in thc clclcction perforinancc, 01' an iiicrease i n FA'AR (falsc alarin tate). This is A critical and sensitive ~problcni, cspcciially in a combiit cnvironmcnt whcrc noisc jutnincrs arc prcsent. Note thal adilitive Irroatltxind noisc jamming can he rnodcllcd i is gaussian noisc [ I ] .

ESM systems iirc il class of elcctrrmic wnrrnre systciiis that. hy dclibcralir~g tlic cnvironincn1 aiid extracting thc spcciiicntioas of cxisting traiisinittcrs, try to obtain a pictnrc of undcl'lyillg scciiario, to cviiluiiIc IIIC thrcat SOII~CBS, and to comiiiaiid a suitable ECM (electronic comtcr mcasurc) in sitwttions o T dangcr [ 2 ] . Ilcrc iiii

adaptivc thrcsliold willi CFAR is nccdcd h r [lie dctcctioii of Iadar p~ilses. Numerous nictliods Iiavc been pmscr i tcd for the design nf CFAR processnIs ror radar receivers, but i i o particular processor has bccii cotisidercd i t i tlic litcm- turc Tor passivc receiving systcins.

DcsiglI of a CYAK proccssor for an IJSM syslcin should be perforincd with attentioii to its special clinracteristics [ a ] . First, ESM systeins do not liavc thc problcin dc lu t t c r aiid thus thorc i s no need to dctcriiiinc the tliresliold in leal timc. l'liis siinplilies the design or B CFAR processor. On thc ntlicr Iiaiirl, most tcctmiqiics iiscd in atlvanccrl ~ i d n r systcms to confront noisc jaintncrs arc riot ;ipplicnblc Tor ESM syslcins beciiuw thc aim of an F,SM systcm is IO

rcccive signals in iill possible directions aiid r~'cqt~cncy bands and to cxlraci their cliartictcristics. ThereFore ESM

systcins arc iiiuch niorc vuliierablc to thc prcscncc 01' noisc jammew than ctmvcnlioi~al rmlnr rccciwrs and slioiild iicccssiirily linvc s t i ffic ieiit rol)ustiicss agai 11 SI vnriatious in iioise pimw

Ilowcvcr, tlic iii;tjar diTliculty in dcicmiiiiing thc b x k - ground noiw stiitislics i s ihc problem o f intdcring ~ ~ d s c s . Various cinittcrs wiih dil'l'ercut ~puisc rates may exist in tlic cnvironmcnl. So, considering ii sct of rcfcacncc seiiiples iitkcn limn llic inpiit to detcrtiiinc ihc noisc Icvcl, most of tliciii m a y bcloiig to tlicsc iiitcrfcring pt~lscs, Therefore thc ~i ia i i i restriction in dcicrminiiy nn ailnptivc tlctcction ihrcnhold for a n ESM syslciii i s possihlc scvcrc iiitcrfcr- encc. Ti) bc used R S II CFAK processor tiiiilcr such conditioiis, CA (cell avcrriging) o r M L D (iiicaii Icvcl detector) iIIItl i ts nindilicd versions siicli ns GoCA (gi'cakcr o f C A ) and SOCA (soiallcr of CIA) tiiivc nhvious wcnk- iicsscs [3]. l r CCA (ccusorcd CA) or CMLD (censored MLD) [4, 51 is used, it should hc dcsigncil lo censor imi iy largcr sninplcs. An OS (ortlcrcd statistics) processor 15-71 should bc based on ii h v r i i i i k , rcl'crrcrl io the nunibcr 01. w h e n c e sainplcs, to hnciicm suirably. hi both C~ISCH, .in adtlitiori to suffcring frcim high CFAR loss, tlicrc worild not be B gumntcct l p c r k " m c e bccnuse of tlic possibility of iiiot'c s w c r c inIcrfcrericc than w a s assuincd. Similarly, gcoiiichic incan aiid geonictric syin~nciry processors 18, 91 would not liiivc suitiiblc pcrl'or~~iaircc if tlnc intcrlcrcrs constirutcd R high percctitagc 41 r thc rcfcrciice sainplcs. Morc suiiablc W A R proccssiws arc thosc that B I ' ~

proposeti to hiiiction in thc prcsciice o f several intcrfcrcrs in tlic refcrcncc window [ I , IO-141. l-lowevcr, m s i nl' ilicse prvccssors nccd inuch coiripiitiition tiinc. Ainoiig thein, the Ex (cxcision) processor [ I ] SCCIIIS to h ~ ' most sui ta lde duc io its siinple structurc. 'I'his CFAR processor acts i1S ii ciinvcntional CA, cxccpt tlirit :it first thc rc~crcre~~cc sil11il>lcs n1.c coinparctl with a primary tlircsholtl and discartled il excectlc(l.

I n this work, the Ex processor is first niotlifcd lo MEx (motlificd Ux), lo account for tlic liSM sysiciii cmdil.ioiis. Ncxt, 011 AMI!x (itthptivc MEx) processor is p r c r c ~ ~ t c d lo work i i i iticr coiitlititrns rif SCYCI'C variation in background iioise pnwct'. I:ccdback is iiscd hi the stniclurc nf tlw AMEx pruccssor ciinbie it to quickly adapt iisclf to a ncw lxickgrurind noisc level. This is a miiqtic l'ealm iii the prcseizted siructure.

JtW / ' v o . - R d w Sonor rVri pig.. Ihl, 117. Ah 2, A p ' i l ZflflO

2 Assumptions and description of models

It is assumcd that thc ESM system iiscs a squ~irc-Ii~w cnvclopc dctcctor in the vidco scctiori nnd tias a cli;iiinci- liscd typc rcceivcr in thc RI: section. With thc assuniptiun that thc vidco bandwidth IIW,, i s niucli sinallcr than thc Itl: bandwidth OW,, it can bc shown that thc saniplcs in tlic input oll thc detector can hc considered to havc n gnussiaii dislributinn. Unilcr the coliditinn of A FV,t/..12RW1, >> I , a n cffcctivc betidwidth can be dcfitictl for tlic systcm as 1151

For an ESM syslcm, i?W,,, and ,!!I$’” arc usually ol‘hc rircicr of sevcrd ~ t - 1 ~ RIUI scvcral ICIIS o r M ~ I X , rcspccrively. Therefore the above-mcritioncd coiiditioii is well satisfied, and so cqn. I liolds for IItV,,; So that the rcccivctl sarnplcs be indcpcnrlciit, tlic sarnpliiig r;ifc miist hc si iwl lcr than BWcfl which is usually valid in praccfical systeins. Tlitis, with the assiiinphii o r gaussian rlistributcd IID (intlcpcn- dent identically disiributcdj seinplcs in ihc dctcdor input, ttie I’UF of iioisc samples et tlic tletc.ctor output is cxprcsscd as i i i crp . 2, wlicrc IT i s thc slandard dcviatinn a i the sainplcs

I n this paper we aliveys assuiiic cmstaiit ninpliindc Tor tlic rcccivccl pulses (e i t lw RS signal or R S intcrferciicc), wliicli i s cquiviilcnt to coiisitlcr nonfluctu;ititig (Swcrling ciixc 0 ) t i~igct~ in radar applic;~tions. l’hcrcrbrc if thc i1~i11)lit~idc o f

rcccivcd pulse cqii;ils A, tlic 1’111; of sigliill pliw iiuisc sainplcs a i tlic rlckctor output will bc

where I,)(.) is thc rnodilicd Bcsscl fimctinn nl’lirsl kind and of order zero.

3 Ex-CFAR processor

Fig. 1 dcpicts the block diagram or the l%CFAK proccs- SOL AI thc lirsc slcp a priniary Ihrcsholtl B,( is uscd to remove prdxhlc iriwrf‘crer samplcs. Thc rcinainirig samplcs are averagccl (as in CA), axid nflcr the i i i i i l t i - plication of the averagc by n ttiresliolcl coefficient the f i n d threshold [I,, is obtttiiietl. When 13,: + rxi, the proces- sor rcduccs to a convcntirwl CA. As staktl in Scction 1, the remarkable katurc of‘ ~ l i i s proccssor is its s i q ) l e structiure.

Importaut dcsigti pnrniiietcrs oftlie processor arc N (total iiutiihcr ol‘ Ic~crcncc satnplcs), 11, ;ind yn. Anolhcr impor- tant parameter called the ‘excisioti coelTicicnt’ is ilcfiired as

Coiisidcritig tlic assurnpiinns of noisc arid sigiinls statistics, the following cqiintioiis CAH bc rlcrivccl fnr falsc al~rii i and detcchii probabilities [I]:

Merc p =A’/2u2 is tlic S N R (signal to l ioisc Tiit iO). It ciiii hc sl1cnvt1 t ha t {I]

111 gciiernl, hy tlccrciising U. iiiirl h i i s ill<, thc inoisc lovcl cstitnntc woiild hc h;~sctl on fcwcr iioisc samples atid tlicrefore n larger Pill will rcsull. With Ihc assumptiot~ o f cnnst;uit (corrcktion of y,)), by any rlccrcnsc in B f i , C1:AK Iriss is iiicrcascd. Approxiiiiatcly, lor 3 > I , !tic CFAR loss rcmains rclaliwly constatit [ I 1.

4 Adaptive thresholding in situations of small variations in noise power

4.7 MEx-CFAR processor In thc Ex-CI;AK algorithm N snmplcs arc lakcii li-oin llic iiiput, md i t is pnssiblc that most of tlicrn ciirrespoiid 10 signal saiuplcs. In swli i~ caw, hy thc cliiniriatioti of interferer stimplcs as A result oC llic cxcisor fiinction, cithcr ii I;ugc CFAK lciss results (if R caiislanl f,” i s cnnsidcrcd), or tlic ITAR wii I incrcase excessivcly (assuin- iiig a cotistant 11,)). The case is highly prohuhlc in ;in IiSM system tlint is typically coriccmcd with various tratisrnis- siois. To OV~’CI%OIIIC this problem, wc apply a inodifcation to tlic 1-x algorithm. Wc iiiiposc ihe conslrairit that llic pIoccssor continues taking s:unples froiri the itipti1 iriitil llic nutnhcr nT iion-cxciscti s m p l c s rcwl ies R constaiit aiid prc- specified vnluc K. In h i s way, i t is s w n tlial. tlic pcrfor- iiiance will bc prcscrvcd iii siiiintioiis or scvorc inicrkr- CIICC. ‘l’lie iicw processor is iiatizccl MGx (tnodiiicd Ex) CFAR.

87

Tlzc false iilann arid detection probabilities for MIix proccssor iirc

( 1 3 )

where if, ;rnd C, atc the V B ~ U C Y of'An (eqn. 7) at id C',? (cqn. 8) For n - K , and an'l P::, arc according to cqiis. G and I O , rcspcctively. 'To facrlitak tlic tiunicricd ccimpu~ation of F'!?, a series o f rccursivc equations arc givctl iii [I] which can bc casily modified and uscd Ibr ihe computation or

,WfiL - ,/;x pi - ' ~ < I , l ,

~ I = K

V"'.

4.2 Performance comparison between M€x and Ex processors To pcrforni a coinparisoil betwecii thc pcrl'onnaiicc o f M I<x aiid l i x pnrccssors: first consider thc conditions of thc benign cnvimnment, i.c. additive gaussinn nnisc plus possibly additive broadband jamining. Table 1 comparcs tlic CFAR loss o f two processors for two valucs or cx 7 3.0 and c l = O . S . P,il = 1W4 is aswiincd. As cxpectcd, for large valuus of 0 , the differciicc hclwccu the requircd SNR ol' two algorilhms for a givcn $, is ncgligiblc, but for sinall CI V ~ ~ L I C N , tlic Ex processor sun'ci~s rrnin greater CFAR loss. Coinputation rcsuits show ihat the aigorithins have similar CFAR perfortnanccs for a > 1 ; however, thc MBx proces- sor exhibits :I (slightly) better Ct'AII prrqicrly [ 161.

Thc perbrmancc of the J.(x prrtccssm in the presence of interferers i s cxlcnsively rliscuascd in [ i7J. To briefly coinptirc it. with the Mtlx proccssor, Fig. 2 shows tlic cn'ccl or interfering signals with the relativc pnwcr of ri = INR (intcrt'crence lo rioisc ratio) on thc delcction of a signal with SNR=r,,. Hcrc i q i k Y = - 6 d R and art: assumcd. It is assuriicd h a t the density of llic inter- fcrcoce is such that among each o f six rcl'crcncc snmples, there Lirc iivc noisc sarnplcs and ono interferer nud it is dciiolcd AS dcmi!y(i/n) l/5. Obviously, the MKx algo- rilliin is inorc robust. Ilnwcvcr, in both CRSCS, for large CL

values, n,; is too 1ai.g~ io cxcise tlic intcrfcrcr s;iinplcs. Thcse comparisons show the neccasity of modification

to thc I?x proccssor it1 tlic form ofMEx Tor use in the ESM q>plicalioii, The effect of ititcrkrcnce can, o f CDUI'SC, ha much iiiurc severc tlian in the observed cases.

= IO

4.3 Determination of design parameters of MEx processor Three importatit paramctcrs o l lhe processor are K, U,, and 7,). Since in situations ol'alinost constant noise power the

Table 1: Comparison of cletectlon performance of Ex and MEx processors, Pm = I O - 4, K= N=24 0: Processor yo SNR(dB) Pd ShrR(dB) P d

-. _I

Ex 12.8 10.0 12.0 3.0 0.48 0.85

MEx 12.7 9.96 11.97

Ex 56.7 10.0 12.0

0-5 0.31 0.73 MEx 43.7 8.68 10.95

88

l,=14 d6 1 .o

a .4

0.2

0 I O

detcnniualion n['flk- is equivalcnt tcr thc dcicrmintltion of 2, thc latter case is ciiscusscd in tlic roliowitig.

4.3.1 Determining number of remained samples after excisor {K): By iticreasiiig K, thc CFAR loss of the proccssor will diminish a s thc cast Tor CA processor. As prcviously pointed m t , in PSM applications llierc is iin

iiccd Lo determine t hc tlircsliold in real h e . Thus, K can bc chosen large ctiougli s o that the maximum dctcctability could result. f-lowcvcr. ii lradc-oBslioiild be rnadc hctwccn this aspect ;md thc sampling h e , especially in h c situa- tion nf scvcrc intcrl'ercnce. In this papcr, by sampling h e , wc nicaii tlic timc requircd to gct K non-cxcised samplcs froni the input. Assuming K = 3.0 titid PJq = 10 ', Fig. 3 sliows y n against K , as well as P, against K roar n signal wiLh S N R = I O d H . K > 60 sccins to be n suitable choicc. We assunic K = IO0 in ~ h c roilowiiig anaIyscs.

4.3.2 Determining excision coefficient a : To deter- iniiic a, three criteria shuiild bc takcn iritn account. 'I'hc first criterion is tlic sanipliiig lime ill noise-only situations. Ai1 exccssive dccrcasc in 01 res~rlts in the cxcision of most input samplcs and h i s R large increiisc in saiiipliiig time. 'I'hc raildoin variable N (total tiiiinbcr o F tnkcn samples for extracting .K non-cxciscd samples) has R negativc binomial

0.7

r,=14 dB 1.0,

distribution, and its Dcqucncy iliiictioii and cxl)cctctl viiluc itre 1181

where P, is the probability tliilt ii s;irnplc survives the excisor 1 1 I

r, = 1 ~ Fa (1 6) Regarding the behaviour o f F,{iV} w.r.t. U, thc suitablc r a n g lor U can be derliiced to bc ils CI ';. 1.7. Tlic ricxt critcrion is the ciitlurctl CFAR loss in h e noise-only ctiviroiiniciit. In hct cvcii h r too w" values of U, with tlic assuinptioii ot' constant P,,, the degrntiiiiion i n P,, o f MEx processor is iiegligible. 'lliiis, this critcrion docs not impose any restriction on the choicc o r a . In othcr words, even if CI reaches to vcry sinall valuc as a restill o r an incrcasc in noise power, keeping PJ, constant by i ic l j~s t i~~g y D w.i.,L. U, llic dclcctioii performance can bc prcscrvcd. l l i c last crilcrion iri rhe dctermination of SI is thc ilctcction loss in h e presence of thc intcrfcrcncc. As an cxalnplc, Pig. 4 shows the cfl'ect o f intcrfcring signals on the P , of the processor under thc m i i c conditions in Fig. 2 (except that K = 100). Valucs i 3.0 secin to be suitable. 011 thc wliolc, 1.7 < CI < 3.0 is aii nppropriatc fiiiigc.

4.3.3 Determining threshold coefficient: y n is choscri wilh respect to the values o f s1 and [j, (design Pfn), according to cqn. 12.

5 Adaptive thresholding in situations of large variations in noise power

5. I Disadvantages of MEx processor Due to tlic possible prcscncc of noisc jamiiiers in a coinbat cnvironment, the varimcc of ttic background noise 0' c m h w c considerable variatinri. hi S U C ~ cases, one may LISC thc MEx plrocessor with fixed /it: ant i yiJ, and thrrs cudure R

dcgradation in CFAR arid detcctioii pcrlbrinance as a prim of the simplicity of the ~ ~ O C C S S O I ' S Function.

If r~ varic.; bctwccn rrlJlj,, aid U,,, , 01 will clxingc bclwccn = OR/2~i,n:r and x,,, -U,/2fi!,i,J: If a iuiddlc valiic is

choscri Tor 8, (corresponding to a iiiitldlc valuc Kor m), for values o f .x closc tn a,,,,, FAR will bc much more than thc

W!' Pinc.-l?odni; Sonni Niwirl.ib,, h l . 147, ,No. 2. Arid 21Mi

prc-dcsigncd valuc; and ror valucs nr CI closc tn a,,,,,, n ratlw wide I2 (iiicl'feclivciicss zone) rcsults. (Thc range bclow B,, iii wl~icli llic iirterl'ercrs are riot excised and t h u s iniliiencc tlic sctting cif tlic clctcction thrcshoki is callcd ;IS

1% [ I 1.j With ii lixctl D,, a latgc iiicrcasc in thc variniicc of iiuisc n r i t only a f k c ~ s tlic FAR bill also lcatls in n long sampling timc; and h i s in ~ u n i WD~SCHS llic dynamicnl beli;tviour ul' thc syslcm.

' r h U s, propcl a L1.i LIS ttll CII I n ll,: W. I,. 1. hac I( g 140u lid no i s c lcvcl is unavnidahlc. Notc l l ia l in our applicalinii, counting cxciscrl sampler; ca i i i i f l l bc a propcr crircrioti for h a change of B,< ns suggestcd in [ l ] bccaiisc of the possibility o f scvcrc irdcrr'crcncc.

5.2 AMEx-CFAR processor Regtirditig Fig, I , any iricrcasc i n thc noisc pnww rcsults io :in iiicrcasc in tlic sainp1c.s' avcrngc C: and Iliiis in R,, . So if this increase i n R,, cnii be soiiiclmw traiisfcrrccl to / I , , it couid be acijustcd w.r.t. thc noisc Icvcl. y,, worild be fixcd, and would bc dctetniiiicd with regard t o f,;,l-Ip Thc itlca of atlaptntion is taken from thc f i ic t tliiit iicc(>rtling to cqn. 11, X(U,,j is proporticwe1 to RE. Sincc wc LISO ii largc iiuinbcr of refercncc sarnplcs for thc cstiiniitioii of noisc l~owcr, Var(H,J is a vcry sniiill viiliic. 'lliis can hc vcrificd using tlic clisractcristic iiinclion 01' O,] given i n [I] . Thus, feetl- back caii he taken from /In tn I] , , via a crjcriicicnl, iintiicd CO, Thc block dingrani 01' the rcsulting nlgoritlun, tiamed AMEx (adaptive MEx) C:FAl<, is showii in Fig. 5 .

Siinulalioiz rcsulis sliow that iii thc steady statc, thc performaiicc of tlic AM1.x procc~sr)r hiis dinost n o ~ C ~ C I I - dencc nii m (tiic stiindartl dcviatioii of llic iioisc samples). Tliercforc aRcr cliorniiig iiti :ippropriiitc CO, thcrc will be 110 anxjcty in thc vnriiitioii rangc of cr. tn tlic scqucl, unless otherwise mentioned, results for AMf+,x proccsstir arc obtained in the stcndy state o f the nlgnrithni, arid art: prescutcd without iiicritiniiing thc valuc o f m.

5.3 Determination of design parameters of AMEx processor '['tic important rlcsigii p;irainctcrs arc K, 'f,) and CIO. Due to the sainc coiisidcrations iii tlic caw of' MEx 1iroccsso~; K = I00 is choscn, n i i d kcm iiow011, all nnalyscs are based on this ;Issutnption.

5.3.1 Determination of threshold coefficient: jj,,

is detcrinined according to thc vduc of CO mid P,{, (,. Fni this piirposc wc iisc sitnulotion rcsults. For jiiskjiico, CIIL'VCS or'y,l agirinsr CO a x prcscrilcd i i i Fig. 6 Tor roour difl'ercnt valucs of P,h.

5.3.2 Defermination of feedback coefficient CO: Since CO and 7,) both appetir a s it cocfficiciit in the fccdback loop, tticii imutual cffcc~ on t l ic I~ctiaviotir of h e processor should Ire taken into ;iccount. rlcrc, our objcctivc is to find an appmpriatc inicrval hr. CO, assum- ing n prc-dcicrniincrl PJfl l , , o ~ (mnx dcsign

89

r

First, CO should be choscn largc cnough so that the algorithtn does not divcrgc. [I CO is chose11 too small tlic dgorithm will iiot convwgc as ;i rcsull of consequent decreasc in Bn and B,. For instance, for y,)= 9.8 vducs n l CO < D. I 7 result in the divcrgcncc o f thc algoriilim. Notc that COl,lj,, (ctlgc or the cotvergencc rcgion) dcpcntls o n thc valiic of y,,. So for greater P,+,, CO,,,,, will bc greater. Bearing in iniiid tlic conrlirion of convergence, another aspect i i i tlic dctcrininatinn of CC1 is the satnplity time. Assuming a constan1 Pfa, by rlecreasiiig CO and thus D, thc rcquircd sampling tinie will iiicrc.casc. I-lowcvcr, the lime does not only depend 011 CO; a id thc vnliic of yo is also importsot. For instillice, siinulatirrn rcsiilts show that fnr fJ,-,,,d,.Ks I O p 2 , vnlucs ofCU > 0.275 are suitable froin this p i i i t or vicw [ IC lJ . Siinulatioti results show that tlic CFAR loss cif thc processor has ~ l inos t no tlcpciidcncc on the value of CO a n d thcrcforc docs not iniposc any Iiniitaliaii on its choice 1161. Fig. 7 shows thc clTcct of interfering signals on tlic Ptf of thc processor with the samc assimplions in Fig. 4. Values of CO < 0.33 sccm to hc suitablc. Thus, 0.275 <CO <0.33 sccnis to bc a n appropriate i titerval, assuniing P,h-,,,(,x 1 O-'. However, f i n d selectioii of CO slioulrl be pcrl'ormed with regard to thc triinsicnt behaviour of the dgorithm, in the c a w s of variation in the m i s e pmwr. II%, shaiild bc chosen so that tlic system has an ;tppropristc timsiciit belinviour (with adequate spcctl) to rcsch iis new slcady state. This subject is discusscd in tlctail in thc I'ollowiiig Section.

5.4 Transient hehaviour of AMEx pmcessor in response to variations in background noise power A fast transient rcsponsc is csscntial For nil appropriate opcraiion in n cornbat environment. Weak. and p w c r r d (or l'ar and nearby) noise jammers can alter thc iinisc lcvcl by switching the jatnrniiig signals 011 and off. Now, if the system does not adapt itsclf promptly to thc iicw condi- tions, its CYAR or dctcctioii pcrlbrinancc will be severely degraded.

5.4.1 lncrease in noise power: Assumc that thc syslcin has reached a steady statc in an alinosl constant noise lcvcl and thoo thc noisc power increases suddenly (this is a critical CIISC, ofcoursc). As rl rcsull, CT R,, and thus h',;-, will iiicrcasc gradunlly and this continues until thc systcm rcncl~cs R new steady state. The grentcr is CO or yo, thc fiwtcr will hc Ilic transietil rcsponse becausc thc cliaiigc in Y would a r k c l BE inore significantly. Vig. 8 shows C U ~ V C S 01' Pfi, against the niiinber o f cyclcs of algoriihin cxcculioii Tor PJii ~ r l = I O - ' and four values of' Ca. Also, thc ciTccl of?,, on the transient response is shown in Fig. 9, I n both cases, it is assunicd that at the bcginriitig (cycle 0),

-. - . '.

'-_______-----

I

4 8 12 16 20 24 . + Y , - , L

l o 0 4 8 12 16 20 24

fi = 20 iiiV. 'I'lie systciii I i i is ~~cachctl a steady statc, wlicii n siidilcrily jumps to 100 mV. As cxpccictl, with an iticrciisc in CO thc transicnt rcspotisc bcctuncs fastcr. SIiiallcr /),;$-~,, t i ~ i d t hus grcatcr IIWC t h Siitiie cffcct. I [OWCVW, a11 cxccssivc incrc;isc in CO will tlcgratlc ttic robustricss o f tlic ;ilgciritlini tigainst iritcrfccring siguals. (Note that thc rcrluc- tion of K will also rcsiilt i i i a l i istcr transient rcsponse ant1 this may t,c aiinrhcr critcrioti for tlic choice or K). 111 tlic ciisc! of' a scvcrc incrcasc in iioisc power thc tnriisicni rcsponsc ol' thc dgorittiin w i l l hc too slow, wid during this time tiic CFAR system will be out of ordcr. Coiisicler- iiig ;in i i ss i i i i i c t l iixix i i i i i m probttble I lite rfcrcncc (Iciisity, if llic systcm is significantly dctainctl l i ~ extracting k' rcfcr- c i m sainplcs, w e may LISC h i s soliition: in SOIIIC cxtcitl), and rcsiart laking saniplcs lioin input. Mowcvcr, h i s case i ~ ~ r c l y hnplwiis and is ratlicr an cxag- yerxtion. Untlet such bad conditions tlic iiicreasc in ihc tletectiou ~tiuesliolrl o f t l ie ESM systciii can prcvcnl i t s iixiiii processor saturating.

5.5 Performance comparison between A M f x and MEx processors Considcriny iipprqwiatc Ixiranictcrs fur Mlh iilitl AMF.x processors: c1 ~ 3 . 0 ancl CO= 0.30, n ctiinparisnn is made bctwccri their IZ in Fig. 10 whcrc ciwcs d P ( / agaiiisl INR ilri: slic>wi~, iissiiniiiig P,iI pr, = IO-" . As cxpcctcd, l l ie AMEu proccssor Iim i i Iiitlc wider I%. 113 fact, regarding the striictiirc of the ~ w " n r , ally incrcnse in R,, as ~ l i c cffcct of noncxcisetl weak interferer sniiiples is transferred to aiid this crcsdts in ii wit lcr 1%. Note that msiiiiiing ii P+(,, t iccrcwiiig CO bclow ii limit will not iriiprovc tlic I% ;illy i~ iorc, hccallsc of the cffcct OT yn. For esample, Iicrc, dccrcasing U 0 to 0.275 docs not restilt iii a noticc;thlc iinprovenicat aE IZ.

SNR=14dB ............................ 1 .a r---''="'

................................................................ .............. ......... ....... ...... ............... 0.4

..........................................................

6 Conclusion

'Thc design or two W A R pi-wcssors liir IiSM syslciii applications l it is t x c i i tliscussctl. Special spccilicaiions o.f BSM syslciiis such as h i n g suljcct to various tnuismis- siotls, vulticmbility 10 noisc jammcrs, anti tlic alwciicc of cluttcr wcrc coiisidcrctl, For situations nl' ~olccrddc varia- lion i n lhc noise porvcr, ai. Mtix-Cl~AR ~"occssor w a s ii7trodticcd and its good Iobiisti ics~: tignirist interfering pulscs t o g c h x w i h ihc mclliod i l l ' dctcrniinnticin o f i t s design priraiiieters was cxplniticd. For siiuations wilh largc variritioii i n backgrouiitl iinisc powcr, an AMRx-CTAR proccastrr was prcscilted wliicli is designcrl via applying n I'cctlback Iutrp in thc structiirc o f the MEx processor. Dctclminaticin ol' thc ptiranictcrs of tlie AMEx proccssor and its trnnsiciii b c l ~ ~ i o u r was carcfiilly iiivcstigatcd u i d i t s cxccllcnt IiAlt regulation capttbiliiy WRS stiowii.

7 I

2 3

4

5

h

7

x

9

92