Detection of Pulsed Radar in a Time Division Duplexed System

Transcription

1 Deecio of Pulsed Radar i a Time Divisio Duplexed Sysem Brad W. Zarikoff Hamilo Isiue Naioal Uiversiy of Irelad Mayooh Brad.Zarikoff@uim.ie David Weldo Wireless R&D, Vecima Neworks, Ic. Vicoria, BC, Caada V8Z 3B8 David.Weldo@Vecima.com Absrac Dyamic Frequecy Selecio (DFS) is he echology chose by ETSI, FCC, ad Idusry Caada o provide ulicesed access for broadbad radios i licesed bads. I is implemeed by he basesaio or basesaio/subscriber combiaio. I a ime-divisio duplexed (TDD) sysem wih DFS implemeed solely a he basesaio, a periodic quie ime is eforced. This work deermies he likelihood ha a radar pulse rai ca be deeced i a TDD sysem wih radar deecio resriced o he basesaio. The resuls are ailored for TDD sysems such as WiMAX, ad ca be used by desigers o deermie uder wha sysem cosrais DFS ca be implemeed i heir sysems. I. INTRODUCTION Recely, he Federal Commuicaios Commissio (FCC) has opeed he 525 o 535 MHz ad 547 o 5725 MHz bads o ulicesed broadbad wireless use; i Europe, he 547 o 5725 MHz Europea Telecommuicaios Sadards Isiue (ETSI) bad is similarly used. As hese bads are radiioally used for radar purposes (primarily for weaher ad miliary uses), he FCC ad ETSI has imposed cerai resricios for ulicesed broadbad wireless use [], [2], ad refer o hese resricios as dyamic frequecy selecio (DFS). Esseially, hese resricios require he ulicesed commuicaios equipme o sped ime sesig he acive chael for radar presece, before a sessio is esablished ad durig he sessio; his period is referred o as he Chael Availabiliy Check Time ad is 6 secods i duraio (FCC ad ETSI). Durig he commuicaios sessio, he BS mus coiuously look for radar pulses. I he case ha a radar burs is deeced, he basesaio (BS) mus orgaize he commuicaios sessio o be relocaed o aoher chael. The Chael Closig Trasmissio Time is he period allocaed durig which all rasmissios mus cease (2 millisecods for FCC ad secod for ETSI). The Chael Move Time is he period allocaed durig which he commuicaios sessio mus be re-esablished i aoher chael, ad is secods i duraio (FCC ad ETSI). Afer he BS has vacaed he chael, he chael mus be lef vaca for a specific ime period; his period is referred o as he No-Occupacy Period, ad is 3 miues i duraio. This work was doe a Vecima Neworks ad is suppored by Sciece Foudaio Irelad uder Gra No. 8/SRC/I43. Submied o he 2 IEEE 73 rd Vehicular Techology Coferece (VTC-2 Sprig). I a ime-divisio duplexed (TDD) sysem, radar deecio is ypically doe wih sampled daa from he RF receive chai. However, oe of he mai caveas i formulaig a DFS sysem for a TDM/TDMA scheme such as WiMAX is ha he receive chai mus be mued durig rasmissio. This cao be avoided by usig a secodary receive chai, sice he rasmier will sill drow ou ay sigal io he secodary receiver. Hece, he DFS sysem mus accou for his ihere quie ime. A he mome, his ca oly be doe by judicious selecio of he raio bewee he uplik ad dowlik (receive ad rasmi a he BS). Sice he receive mue duraio is deermiisic, bu he radar pulse rai (referred o as a radar burs) arrival ime is radom, i is possible o deermie he saisical overlap of a specific radar burs ad he receive frame of he WiMAX sysem. This provides he focus of his paper: deermiig he probabiliy of a radar pulse ladig wihi he receive porio of a WiMAX frame. We chose he sample radar ypes give i he FCC es procedure [3] o provide examples. Surprisigly, he curre lieraure is sile o aalysis of radar deecio probabiliies. Calculaio of radar deecio probabiliies used i he FCC ad ETSI sadards would have required simulaios a he miimum. Lieraure o DFS for radar appears resriced o deecio algorihms [4] ad policy review [5]. Sice he es radar waveforms as specified by he FCC ad ETSI are se i pulse rais, hey iherely provide a meas o avoid false posiives due o radom ierferece. A iellige algorihm ha akes he pulse widhs ad spacig afer iiial pulse ideificaio is ecessary o deermie wheher a radar pulse is prese or o. For his work, we assume ha a umber of cosecuive radar pulses mus be ideified i order for he algorihm o be successful, ad hus we mus fid he probabiliy of a umber of cosecuive pulses ladig wihi he receive porio of he WiMAX frame. II. BACKGROUND To make beer use of he limied RF specrum, goverme specrum sharig i he form of dyamic frequecy selecio (DFS) sared i 24 [5]. The basic premise of DFS is o allow privae users access o he uder-uilized radar bads i he 5 GHz rage. Because of he demad ha goverme users place o he probabiliy of radar deecio, he privae

2 W() α τ r() T R TT T T T P = = T Fig.. Sigal Model Fig. 2. Sceario for Case : T P < T T users access o hese bads are subjec o hem implemeig quie sric cogiive-radio-based sharig echiques. Sice he DFS sadards were iroduced, sudies have show he effeciveess of co-exisece of radar ad widebad commuicaio sigals [6]. I [6], DFS was esed usig a IEEE 82.a RLAN sysem operaig i he viciiy of a Doppler weaher radar sysem. The coclusio was ha he RLAN iroduced addiive, ucorrelaed oise, from he radars perspecive. The auhors oe ha he DFS would deec he radar sooer ha he RLAN would corrup he radar. As meioed i he iroducio, a TDD sysem ha implemes DFS will experiece some mued periods durig which he receiver is ured off. This work focuses o deermiig he probabiliy ha a porio of a radar burs will arrive a a BS durig he period whe i is i receive mode, ad hus he probabiliy ha specific radar ypes ca be deeced i TDD mode. A. Sysem Model Our model cosiss of wo sigals: ha of he periodic rasmi/receive modes of he BS ad ha of he arrivig radar pulse. Power levels are o cosidered. Fig. demosraes a sample composie waveform, where a sigle sample es radar waveform cosisig of fory pulses overlaps hree cosecuive receive frames. Each TDD frame is of duraio T. O ay give frame, he firs T T secods is for rasmi, while he remaiig T R = T T T is for receive, durig which radar deecio is possible. We use a coiuous-ime samplig fucio, W(), o deoe he receive widow of he TDD radio; durig he receive porio of a frame, W() =, oherwise, W() =. The radar burs arrival ime is α [,T], wih he radar waveform iself deoed r(). The radar burss cosis of N pulses, each separaed by τ secods, where τ is he PRI. The oal duraio of he radar pulse rai is he T P = (N )τ. The variable P is he umber of pulses ha lad i W(). B. Assumpios A umber of assumpios ad defiiios are used o simplify he followig aalysis. For he radar burs, he pulses cosidered are ake from he FCC ad ETSI sadards, ad ca vary i duraio from µs o 2 µs. To simplify he mah, his aalysis assumes ha hey are ui impulses. Jusificaio for his ca be made by examiig he raio of he pulse repeiio ierval (PRI) o he pulse widh, which varies from abou o 428; his relaes o a duy cycle of % o.7%. We also assume ha for a sigle radar burs arrivig i he curre ierval [,T], he arrival ime α is uiformly disribued, ad ha he PRI τ lies i [τ mi,τ max ] ad is also uiformly disribued. These assumpios are cosidered valid give ha we oly cosider a sigle radar burs. I real sysems, here may be subseque burss, bu his case is o cosidered i his work. III. PULSE DETECTION Our goal is o fid he probabiliy ha radar pulses of a give radar ype lad durig he receive porio of a TDD frame (while W() has a value of ). The sysem desiger ca use hese echiques o specific limis o he receive-orasmi raio of he radio sysem ad deermie he maximum umber of pulses he radar deecio algorihm should search for [4]. Firs, we will aemp some aalysis o wo special cases: Case, where he radar pulse rai is less ha T T ad herefore will oly effec a sigle frame, ad Case 2, if he radar pulse rai is greaer ha T + T R, ad herefore will effec a leas wo frames. I boh cases, we will cosider oly a sigle frame, so he domai of W() is resriced o [,T]. The, o accommodae for a greaer variey of radar ypes, a more deailed simulaio model will be devised ad used for compariso. As a maer of oaioal coveiece, he probabiliies Pr(P = N) are codiioed o he oal duraio of he icomig radar burs T P. I his work, he radar ypes are o cosidered as radom variables, ad hus he codiioal saemes do o porray ay sochasic depedece. A. Case : T P < T T Case iself ca be divided up io wo scearios: if he eire radar pulse lads wihi W(), ad if less ha N pulses lad wihi W(). As meioed i Secio II-B, we assume ha α is uiformly disribued ad ha he pulses are impulse fucios. This meas ha, give ha α is disribued from [,T], he probabiliy of α beig wihi W() (or (T T α T)) is (T T T )/T or T R /T. I is possible ha o all radar pulses will fi wihi W(). The maximum umber of pulses ha ca lad i W() ca be foud as he raio bewee T R ad τ o be X P = T R /τ () If X P N, Pr(P = N T P < T T ) is o-zero, where N is he umber of pulses i r() ad P is he umber of pulses ladig i W(). Usig he above resul for he probabiliy of α ladig i W(), we ca fid he probabiliy ha all N radar pulses lad wihi W() whe T P < T R o be Pr(P = N T P < T T ) = (T R T P )/T (3) = T P /T,

3 Pr(P X P T P > T +T R ) = Pr(P = X P T P > T +T R ) = T Rlog(τ max τ mi ) τ max τ mi X P + Pr(P > X P T P > T +T R ) =. (2) ad oherwise. The receive o full frame raio is defied as = T R /T. We ca see ha if T P T, he his probabiliy reduces o, while if T P > T R, he he probabiliy goes o zero. If X P < N, we mus sar wih fidig he probabiliy ha P = X P. This probabiliy is depede o he umber of pulses ha will o fall i W() whe P = X P, which is N X P. To calculae Pr(P = X P T P < T T ), defie a excess ime ɛ which is he slack i he burs arrival ime durig which P = X P as ɛ = T R (X P )τ. (4) Normalizig ɛ by T gives he probabiliy of P = X P for a sigle se of pulses (i.e. he firsx P pulses). The, cosiderig ha here are N X P pulses ha do o fall i W(), he probabiliy ha P = X P for all combiaios is Pr(P = X P T P < T T ) = (N X P +)ɛ/t (5) The probabiliy ha P < X P mus be foud boh for whe he las pulses lie wihi he sar of W() ad whe he firs pulses lie wihi he ed of W(). Also, sice he pulses are evely disribued wihi a sigle pulse rai, he probabiliy of oe pulse ladig i W() is he same as wo pulses ladig i W(), ad so o. The we ca work ou P < X P o be Pr(P = p p < X P,T P < T T ) = (6) Pr(T T τ α T T )+ Pr(T T P +τ α T T P +2τ) = 2τ/T. By summig over he probabiliies, we ca break he probabiliy of or more pulses ladig i W() io wo expressios: codiioed o X P N ad X P < N, so we ge Pr(P X P N,T P < T T ) = (7) Pr(P = N T P < T T )+ N i= Pr(P = i T P < T T ), Pr(P X P < N,T P < T T ) = (8) Pr(P = X P T P < T T )+ N i= Pr(P = i T P < T T ). Fig. 3. T +T R T P Sceario for Case 2: T P > T +T R To iclude he radom aure of he PRI τ ad he umber of pulses N [3], we ake he expecaio of (7) ad (8) wih respec o τ ad N. Doig so, we ge Pr(P X P N,T P < T T ) = (9) ( N ) τ/t +2(N )τ/t, Pr(P X P < N,T P < T T ) = () ( N XP + ) ɛ/t +2(N )τ/t, where τ = E[τ] ad N = E[N]. B. Case 2: T P > T +T R I his Case, oe receive frame i W() is guaraeed o compleely overlap wih he radar burs (X P < N). Also, as log as τ < T R, a leas oe pulse of he pulse rai is guaraeed o lad. The probabiliy of P = X P ca be calculaed by usig he fac ha he pulses are equi-spaced ad iiially lad wih uiform probabiliy, so Pr(P = X P T P > T +T R ) = T R /τ T R /τ () = T R /τ (X P ), which is he raio remaiig afer removig he X P pulses ha are guaraeed o lad i W(). The reaso ha Case ad Case 2 are o equal whe P = X P is because i Case, he domai ha α ca occupy i order for P = X P is α [T T P,T T ], while he domai for Case 2 is α [,T]. The probabiliy ha P > X P pulses lad i W() is zero because of he equal spaced pulses, ad he probabiliy ha P = X P is Pr(P = X P T P > T +T R ), o accou ha eiher X P or X P pulses are guaraeed o lad i W() i a frame. Afer akig he expecaio wih respec o τ, he codiioal probabiliies are provided for T P > T +T R i (2). C. Simulaio Model Sice he radar ypes defied i [2] ad [3] have radom compoes ad will usually o fi io eiher of he Case or Case 2 caegories, a more deailed model is creaed. Usig he radom radar burs arrival ime α ad he radom PRI τ

4 Pr(P ).4.2 =.5 ANA =.7 ANA Pr(P ).4.2 =.5 ANA =.7 ANA Fig. 4. Probabiliy of FCC ype 2 pulses ladig i W() Fig. 5. Probabiliy of FCC ype 3 pulses ladig i W() as show i Fig., we ca represe he full radar pulse rai r() as he sum of Dirac dela fucios r() = N = ( ) δ ( )τ α (2) To deermie he umber of pulses ha lad i W(), he iegral of W()r() ca be ake as P (α,τ) = T T T W ()r()d (3) Noe ha if T P > T T, he some pulses may lad i subseque receive frames. This case is o cosidered i he aalysis of he Case ad Case 2, ad hus we ca expec he simulaed resuls usig (3) o be more accurae (i.e. more pulses may be capured i subseque frames). IV. RESULTS AND SIMULATIONS We cosider he es radar pulses described i [3], specifically Radar Types, 2, 3, 4 ad 6. FCC Radar Type 5 is o cosidered as i is a chirp pulse, ad herefore sigificaly differe i srucure ha he ohers. For Radar Type 6, we cosider oly a sigle burs of ie pulses. The parameers of hese es pulses are give i Table I, icludig he required deecio probabiliy rae (De. Prob.) i he FCC specificaio [3]. Noe ha for Radar Types hrough 4, he aggregae deecio probabiliy is show; he miimum probabiliy is 6%. For calculaio of (3), he oal legh of he burs is cosidered, ad ay pulses ha lad i subseque frames are icluded i he resuls. This resul is compared o he aalyical resuls of Case (for Radar Types 2, 3, 4, ad 6) ad of Case 2 (for Radar Type ). The simulaio resuls are show afer Moe Carlo simulaio over N usig 4 samples, wih N, α ad τ beig uiformly disribued. Pr(P ).4.2 Fig. 6. =.5 ANA =.7 ANA Probabiliy of FCC ype 4 pulses ladig i W() Moe Carlo simulaio usig (3) is used o geerae values for Pr(P ), usig 4 samples. Fig. 4, 5, 6, ad 7 show Pr(P ) (refereced wih SIM) ad Pr(P T P < T T ) (refereced wih ANA) for each of he es pulses. Curves for =.3,.5, ad.7 are show, wiht = ms. Obviously, as icreases, he probabiliy of seeig a pulse icreases, as he mued porio of he frame is shoreed. However, by reducig, he proporio of uplik o dowlik raffic is reduced, wih ramificaios for load balacig. I may be argued ha a miimum of hree pulses are required o ideify a radar burs; ay less may be oise. A horough aalysis ivolvig SNR ad hreshold values is required o verify his rule of humb, bu laboraory experi-

5 Pr(P ) Pr(P ).4.2 =.5 ANA =.7 ANA Fig. 7. Fig. 8. Probabiliy of FCC ype 6 pulses ladig i W() =.5 ANA =.7 ANA Probabiliy of FCC ype pulses ladig i W() mes provide evidece of his, ad so we will use his value i he followig example. For =.5, Pr(P = 3) is approximaely 9% for Radar Type 2. Similarly, Pr(P = 3) is approximaely 9% for Radar Type 3 ad 8% for Radar ype 4. Due o he shor burs duraio of Radar Type 6, here is oly a 65% probabiliy ha hree pulses will lad i W(). Noe ha for Radar Type 3 ad 4, if =.7, Pr(P = 3) is %. This resuls from a combiaio of a large T P ad T R. The aalyical resuls follow he simulaio resuls closely. As expeced, he geeral red is for he aalyical resuls o show a lower probabiliy of pulse deecio, give ha subseque frames are o cosidered. However, sice our aalysis icludes a average over N ad τ, here is some variaio, paricularly whe he probabiliy of deecig greaer ha pulses is low. For Case 2, Radar Type is evaluaed. Due o he large PRI TABLE I FCC TEST PULSE PARAMETERS Tes Pulse Pulse Widh (µs) τ (µs) N De. Prob % % % % % of Radar Type, here is o way ha more ha four pulses ca be deeced wihi a sigle 5 ms receive frame. Subseque receive frames ca be used o help i radar pulse ideificaio, or, a lower umber of pulses ca be used. However, he odds are good ha a small umber of pulses will be see: here is a % chace ha hree pulses will lad i a receive frame for T R = 5 ms. V. CONCLUSIONS Due o he geeral aure of ime divisio duplexed (TDD) sysems, implemeaio of dyamic frequecy selecio (DFS) echiques will eed o deal wih periodic dow ime whe he local rasmier is acive. However, radar pulses may sill be arrivig durig hese dow imes. This paper provides a aalysis o he probabiliy of wheher a radar pulse rai ca be deeced i he case of TDD sysems. Usig he example radar pulse rais specified by he FCC for he 5 GHz U-NII bads, simplified expressios for pulse observaios are provided. The aalysis ad simulaios provide he sysem desiger wih ools o decide which specific rasmi o receive raios are compaible wih he DFS limis specified by he FCC ad ETSI. Fuure work will iclude fidig opimal values for rasmi ad receive raios. Sice he rasmi ime is resriced by DFS i TDD sysems, he cocep of furher ierleavig he rasmi ad receive widows will also be cosidered. REFERENCES [] FCC, Tile 47 CFR, Par 5 Subpar E, Federal Commuicaios Commissio, 28. [2] ETSI, ETSI EN 3 893, Europea Telecommuicaios Sadards Isiue, 28. [3] FCC, Appedix: Compliace measureme procedures for Ulicesed- Naioal Iformaio Ifrasrucure devices operaig i he MHz ad MHz bads icorporaig Dyamic Frequecy Selecio, Federal Commuicaios Commissio, 26. [4] M. We ad L. Hawe, Radar deecio for 82.a sysems i 5 GHz bad, i IEEE I. Cof. o Wireless Commu., Neworkig ad Mobile Compuig, 25, pp [5] M. J. Marcus, Sharig goverme specrum wih privae users: opporuiies ad challeges, IEEE Wireless Commu., vol. 6, o. 3, pp. 4 5, 29. [6] A. L. Bradao, J. Sydor, ad W. Bre, 5 GHz RLAN ierferece o acive meeorological radars, i IEEE 6s Veh. Tech. Cof., 25, pp