Low-Complexity Turbo Receiver for MIMO SC-FDMA Communication Systems

Transcription

1 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. Low-Coplexiy bo Receive fo IO SC-FDA Coicaio Syses Fag-Bia eg, Y-Ka Chag ad Yig- Yag Absac liple-ip liple-op (IO) echologies ae adoped i ay sadads o ehace he daa ae ad he lik obsess. By cobiig IO echiqes wih he SC-FDA (Sigle Caie Feqecy Divisio liple Access) odlaio schee, IO SC-FDA syses ca achieve high daa aes ove boadbad wieless chaels. I his pape, we eploy he space-feqecy block code (SFBC) o each asied block fo he lise sceaio. A eceive side, i ode o edce he seachig coplexiy, we se he Layeed ORhogoal laice Deeco (LORD) algoih ad cobie he bo decodig o develop he low-coplexiy bo LORD lise deeco (D) fo IO SC-FDA syses. Soe silaio exaples fo plik sceaio ae give o deosae he effeciveess of he poposed schees. Idex es IO, space-feqecy block code, sigle caie feqecy divisio liple access W I. IRODCIO IRELESS asissios ee gea poplaiy owadays fo a wide vaiey of applicaios, sch as wieless liedia, wieless iee access, ad foh geeaio (4G) obile coicaio syses, hese applicaios have oivaed he develope of eos sigal pocessig ad coicaio echiqes fo ilizig hese esoces efficiely. hid-geeaio Paeship Pojec Log e Evolio (3GPP LE) epeses oe of he ajo advace sadads i he fe foh geeaio (4G) coicaios. he SC-FDA [] ad ohogoal feqecy divisio liple access (OFDA) has bee adoped fo plik ad dowlik asissio i 3GPP LE [], especively. SC-FDA cobies os of he well-kow advaages of OFDA wih he evelope flcaios of sigle-caie (SC) syses. hs, SC-FDA is wih lowe Peak-o-Aveage Powe Raio (PAPR) ha liis he oliea effecs ad avoids he se of expesive high powe aplifies a he obile saio. he PAPR poble is eve oe sige fo eials siaed a cell-edge, which ae ypically powe-liied ad ae sbjec o bad popagaio codiios. Fo hese eials, i is ieesig o se hei asi aeas i ode o iplee soe asi divesiy echiqes (ex. space-ie block codig) [3], allowig he o ipove he pefoace ad exed he coveage. Space-ie codig (SC) echiqes ca exploi boh spaial ad epoal asi divesiy o iigae lipah effecs ad sppess he ahos ae wih he Depae of Elecical Egieeig, aioal Chg-sig ivesiy, aiwa (e-ail: fbeg@ch.ed.w; chgyka@hoail.co; yag3@hoail.co). ISB: ISS: (Pi); ISS: (Olie) iefeece. O he ohe had, whe applied i feqecy doai, SFBC [4] ca exploi aohe fo of divesiy wih feqecy, ha is, specal divesiy. By space-ie pocessig ha cobies he IO syses wih space-ie block codig (SBC) ca povide high daa aes ove wieless chaels ad ipove he syse capaciy. Sch syses ay be a possible solio fo fe wieless ewoks o appoach hese deads. he se of liple aeas boh a he base saio ad a he eial ca ipove he pefoace by povidig spaial divesiy, icease he asied daa ae hogh spaial liplexig. oweve, lise IO (-IO) [5] ca accoodae liple ses as spaially disibed asissio esoces, a he cos of soewha oe expesive sigal pocessig. hs, -IO is also kow as spaial divisio liple access (SDA). -IO algoihs ae developed o ehace IO syses whe he be of ses, o coecios, bes geae ha oe. Ieaive lise deecio, also kow as bo lise deecio i coicaio syses is based o he bo piciple [6,7]. he chael decode ad lise deeco ieae sof ifoaio o cacel liple access iefeece (AI). IO SC-FDA [8] syse cobies he advaage of spaial ad feqecy divesiies wih feqecy doai eqalizes (FDE), as well as icease he plik syse capaciy. Possible deecio echiqes iclde zeo-focig (ZF) ad ii ea sqaed eo (SE) deecio, axi likelihood deecio (LD). Aog hese schees, LD is opial, b is coplexiy gows expoeially wih he be of sybols deeced. As a esl, hee ae deads fo ea LD schees ha povide siila pefoace wih less coplexiy. ay eseaches have sogh diffee liied-coplexiy deecio saegies, yig o appoach he ideal eceive pefoace a bes i ece yeas. I pacice, deecio ad decodig ae decopled, ad Sof-Ip Sof-Op (SISO) deecos sed i cojcio wih SISO decodes i ieaive schees [9] o appoxiae he ideal eceive hogh disjoi sages accodig o he bo piciple. bo deecos exploi he ifoaio fed back by he chael decode as a pioi ifoaio abo he asied vecos of sybols. Despie his siplificaio, he coplexiy of he opial axi A Poseioi (AP) ad axi Likelihood (L) deecos sill iceases expoeially. he sbopial deecio saegies y o appoach he ideal deeco wih liied coplexiy, ex., bo SE deecio o sphee deecio []. I ece yeas, oe of he os poisig poposals is he Layeed Ohogoal laice Deeco (LORD) [] [], ad is ieaive vesio, aely bo LORD (-LORD) WCE 5

2 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. [3]-[5]. LORD deecs he L hype-sybol, o close, depedig o he be of aeas ivolved. ha is paiclaly sied fo paallel ipleeaio ad sof-op bi deecio, ad pefos vey well i cobiaio wih sof decodes. foaely, LORD is o able o aage a pioi ifoaio, possibly fed back by he SISO chael decode. So, he -LORD is able o pocess a pioi sof ifoaio. I is desiged o be iclded i a ieaive eceive wih SISO decode ad is pefoace is vey close o he ideal AP deeco. I his pape, we eploy he space-feqecy block code (SFBC) fo he -IO SC-FDA syses. A eceive side, we se he LORD algoih ad cobie he bo decodig o develop he low-coplexiy bo LORD D fo -IO SC-FDA syses. his pape is ogaized as follows. I Secio, he syse odel of he -IO SC-FDA is descibed. he low-coplexiy bo LORD D fo -IO SC-FDA syses is poposed i Secio 3. Silaio esls ad coclsios ae povided i Secio 4 ad Secio 5, especively. oaio: ecos ad aices ae deoed by boldface lees; spescips of *,, ad deoe he coplex cojgae, aspose, eiia aspose ad ivese, especively; sads fo he cicla covolio; ad diag deoes a diagoal aix. II. SYSE ODEL I his secio, we coside obile ses accessig he sae spec i plik IO SC-FDA syses, each se has asi aeas, all ses ilize a covolioal ecodig wih code ae R /, ad afe ieleave, he qadae phase shif keyig (QPSK) odlaio schee ad space-feqecy block code (SFBC) schee ae eployed fo he asissio, as show i Fige. I his syse we deal wih he liple-access coicaio chael whee each se asi a idepede ifoaio via wo aeas sig Alaoi-like SFBC schee a he asie o a eceive eqipped wih aeas. All he liple-access ses ae o he sae spec o asi hei daa. Le he asied daa block of he -h se be wie as follows, x x x x... x () whee x ( ) deoes he -h sybols fo he se. ex, he sigal is asfoed o feqecy doai by -poi discee Foie asfo (DF) ad ca be wie as () () ()... ( ) F x () whee F deoes he oalized -poi DF aix wih ey o he a-h ow ad b-h col defied as F a, b exp jab, fo (3) a, b... I ode o povide asi divesiy, wo cosecive feqecy doai daa blocks ad ae i i asied acoss he wo asied aeas by he Alaoi-like SFBC schee fo each se ad he all sigals ae apped io he desigaed feqecy sbbad. Afe sbcaie appig, sigal ca be descibed as follows S,i P, i S,i P, i * * (4) S P S P,i, i, i,i, whee S is he asied block o he i -h feqecy a -h asi aea fo se ad P, deoes he sbcaie appig aix. he ie doai asied sigal ca be obaied by pefoig IDF opeaio o S, i ad ca be expessed as follows, S, F S,i S, F S,i * (5) S F S S F S F whee F,,i, i,i F is he -poi DF aix, ad is ivese is, ad, S is he asied block o he -h ie a he -h asi aea fo se. Fially, Cyclic Pefix (CP) wih legh loge ha delay spead is iseed o avoid ie-sybol iefeece ad sigals ae asied via he aeas i SC-FDA syses. III. LISER RECEIER FOR IO SC-FDA SYSES I his secio, we coside he lise IO eceive of SC-FDA syse wih eceived aeas. Asse ha pefec plse shapig ad chael sae ifoaio (CSI) ae achieved, ad asse ha all ses access he base saio i he sae sbbad wih powe cool sch ha all sigals fo obile saios aive a base saio wih he sae aveage powe. he afe eovig CP, he eceived sigal a he -h eceived aea deoed as i he ie doai ca be descibed as he saio of he cicla covolio of chael iplse espose h wih he asi sigal s, he h is assed o be saioay wihi a sybol daio ad kow i he base saio eceive. Fige is he block diaga of he eceive. he eceived sigal a he -h eceive aea ca be descibed as follows, h s q q (6) whee h ) h ()... h ( L ) h is he ( ie doai chael iplse espose wih of ode L bewee he -h asi aea ad he -h eceive aea fo se, deoes he -poi cicla covolio ad q is coplex addiive whie Gassia oise (AWG) wih zeo ea ad vaiace I. he sigal is descibed as follows, h s s (7) whee he chael aix is a cicla ISB: ISS: (Pi); ISS: (Olie) WCE 5

3 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. aix wih fis col eqal o he veco h, ( L). Afe he -poi DF opeaio ad sbcaie de-appig, he sigal is descibed as follows, F Λ q S η F s F he cicla aix has he followig popeies whee q (8) F Λ F (9) Λ is a diagoal aix wih diagoal eies eqal o he DF of he chael iplse espose. ha is, Λ is defied as Λ diag diag () F... h ( ) ( L) () Asse ha he cohee badwidh is ch lage ha he sb-caie badwidh, heefoe he sbchaels i eighbohood have alos he sae feqecy esposes. ha is, we ca ake he appoxiaio ha ( ) ( ) whee ad ae sbcaie idex i he sae desigaed bad. Afe sbcaie de-appig, we coside he Alaoi SFBC schee wih ses i he sae sbbad, he eceived sigal ca be wie as follows, () () () () () () () (), i, i, i, i, i,i () ()* () ()* () ()* () ()* (),i,i,i, i, i () () () (), i, i () ()* () ()*, i, i, i, i,i () () () (), i, i,i () ()* () ()*, i, i,i () Aagig he above wo eqaios i aix foa, we obai,i,i,i,i (), ()*, (), ()*, (), ()*, (), ()*, (), ()*, (), ()*, (), ()*, (), ()*, () i () i () i () i,i,i,i,i (3) Cobiig he eceived sigal a all eceived aeas, we have () () () η () () () (4) η Fo he geeal case of SFBC wih ses, each se eploys asi aeas, K feqecy asi divesiy, ad eceive aeas i he base saio, he above eqaio ca be exeded as follows () () () () () () ( ) () η ( ) () η ( ) ( ) η (5) he eqaio (5) ca be siplified as η (6) whee is a K aix, is a K aix, is a aix ad η is a K aix. ex, we eploy he LORD algoih o pefo he bo D. he LORD [] algoih cosiss of wo seps: ) Pepocessig: he asfoaio is siila o a QR decoposiio b i ca be copleed wiho ay oalizaios. ) Laice Seach: I povides paallelizable ipleeaio ha ca easily geeae eliable sof bi eics. he algoih solves he axi Likelihood (L) deecio poble o esiae he ses asied seqece, ha is ˆ ag i (7) I [] [], he eceived sigal ca be spli io eal ad iagiay pas, ) ( )... ( ) ( ) (8) ( Siila defiiios hold fo ad chael aix sch ha η. he he chael aix is QR decoposed, coespods o Ga-Schid ohogoalizaio (GSO) ehod wiho ecessay oalizaios, oly eqiig ha he cols of Q be ohogoal, wih abiay o. So he eceived sigal ca be asfoed io he followig foa, Q R η (9) whee R is he ppe iagla aix ad Q is he ohogoal aix. Oce eqaio (9) has bee obaied, siplified deodlaio algoihs ca be applied, he likelihood eic is ˆ R..., j j3 s i j he expessios fo, s i, j j s, j j3 j (), j ad oe deails ae povided i []. Based o he above expessio, we ca eploy he backwad ecsio algoih ha slices alog all sybols fo he lowes layes. Le ˆ be he collecio of he decided sybols, he above likelihood ca be expessed as a fcio of he wo lowes layes, ˆ ˆ,, () he ehod, hogh a exesive seach ove each pai, deecs he sybol close o ha of L deecio. A axi-a-poseioi (AP) deeco acceps he eceived veco ad he a pioi ifoaio, coig fo he decode, ad evalaes he likelihood of each se s possible asied sybols. I ca be easily ideified i he followig eic, b ˆ b i () whee i is a pioi ifoaio ad b is he -h bi of sybol. he copaio of he a poseioi LLRs ca be descibed as follows, ISB: ISS: (Pi); ISS: (Olie) WCE 5

4 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. l ax : b ( ) ˆ exp : b ( ) ˆ exp : b ( ) ˆ ax ˆ : b ( ) (3) he bo-lord [3] is based o a siplified b ea opial ehod o cope ax-log-ap appoxiaio eic (). he copaio of () eqies o ake io acco each possible cosellaio sybol. Fo his easo, sefl e-ogaizaio of he daa is eqied. Le Γ be he peaio aix, he eceived sigal ca be ewie as follows, ΓΓ ΓΓ η (4) I is coveie o pefo he QR decoposiio of he chael aix, ha is Γ QR (5) he fis e i () ca be wie as QRΓR ' R' (6) whee ' Q, ' Γ. We eed o seek he bes cadidae accodig o he disace cieio ad he a pioi pobabiliy cieio ha ca be descibed as follows, ˆ d ag i ag i ' R' (7) b ˆ a ag i b (8) he sigal is he pocessed by he ivese DF (IDF) opeaio, we he have he ie doai esiae ( xˆ... xˆ ˆ ) fo xˆ as ˆ F which is defied xˆ. Fially, de-ieleavig ad decodig ae pefoed o ecove he oigial daa esiae. Fige 3 is he syse block diaga of he poposed eceive. We popose o ilize bo piciple ha cobies AP deecio o pefo lise deecio. I his appoach, he lise deeco ilizes he exisic ifoaio fo AP decode o cacel he iefeece fo ohe ses o ipove he eceive pefoace. he decode ops o oly povide had bi decisios, b also he exisic ifoaio of all coded bi, icldig ifoaio ad paiy bis, which is sed as a pioi kowledge a he deeco (afe ieleavig). sig idepede a pioi ifoaio fo each bi of obai ( ) P b l (9) P b whee, we b is he - h bi of he sybol, wih,,..., b, whee b log / is he be of bis pe diesio. he sof esiae of he asied daa is as follows, x E P P P / (3) ah Pefoig DF opeaio ove x, we have he expeced vales of each se s feqecy-doai daa as follows, () ()... ( ) DF () ()... (3) x x x ( ) A he begiig of he ieaive pocess, o a pioi. I he sccessive ifoaio is available, so ieaios, Z deoes he eceived sigal which has all ohe ses iefeeces beig eoved. ha is ( ) ( ) Z (3) Whe he ieaive pocess coveges, he bi eliabiliy povided by he decode iceases ad he sof esiaes becoe close o he e asied vales []. I. SILAIO RESLS I his secio, we deosae he pefoace of he poposed ieaive lise IO deeco fo SC-FDA syse. he eployed IO echology fo he silaios is he Alaoi SFBC. he adoped chael odel is he spaial chael odel (SC) poposed i []. he chael is silaed ove sbba aea wih veical polaizaio aea i icocell. I his syse each se is wih wo aeas fo asie side, ad eceive side has wo aeas. he aea spacig a base saio is 6 waveleghs, while obile saio aea spacig is.4 ad waveleghs. he silaed bo coded IO SC-FDA syses has 8, 56 ad he Cyclic Pefix (CP) legh is. he eployed ecode is he ecsive covolioal codes (RSC) wih code ae R /, de hee diffee chael ecode (,, ), (,, 3) ad (,, 4) whee he las ey deoes he eoy ode ad he cosaied legh is +. he eployed ieleave is ado ieleave. he algoih fo he bo decode is he BCJR algoih. Fig. 4 ad Fig. 5 copae he bi eo ae (BER) pefoace of he sigle-se o-ieaive -LORD ad bo SE eceives wih he aea spacig fo obile saio eqal o.4 ad, especively. he base saio has eceive aeas ad he pefoaces ae wih ecodes (,, ) ad (,, 4). As we ca see, he -LORD pefoace is bee ha ha of SE eceive. We also fid ha he -LORD pefoace wih obile aea space eqal o is bee ha ha wih aea space 3 eqal o.4 a BER= whe (,, 4) covolioal code is sed. his esl cofis ha lage aea space ca achieve bee pefoace becase of lowe coelaio aog diffee pahs. Fig. 6 ad Fig. 7 copae he bi eo ae (BER) pefoace of he wo-ses o-ieaive -LORD ad bo SE eceives wih he aea spacig fo obile saio eqal o.4 ad, especively. Obviosly, i is show ha he -LORD schee ISB: ISS: (Pi); ISS: (Olie) WCE 5

5 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. ca cacel he iefeece fo lise IO syse. he pefoace of he -LORD eceive opefos he bo SE eceive a BER=. We also fid ha he -LORD pefoace wih obile aea space eqal o is bee ha ha wih aea space eqal o.4 a BER= whe (,, 4) covolioal code is sed. Figs. 8-9 depic he bi eo ae (BER) pefoaces of he -LORD deeco fo ieaive lise IO SC-FDA syses ad he aea spacig fo obile saio eqal o.4 ad, especively. he be of se is. As we ca see, iceasig he be of ieaios, he poposed eceive fhe ipoves he BER. We also fid ha he -LORD pefoace wih obile aea space eqal o is.7 db bee ha ha wih aea space eqal o 3.4 a BER=.. COCLSIO By cobiig IO echiqes wih he SC-FDA odlaio schee, IO SC-FDA syses ca achieve high daa aes ove boadbad wieless chaels. I his pape, we eploy he SFBC o each asied block fo he lise sceaio. A eceive side, i ode o edce he seachig coplexiy, we se he LORD algoih ad cobie he bo decodig o develop he low-coplexiy bo LORD D fo IO SC-FDA syses. he poposed lise deecio ehod pefos ieaive eqalizaio ad ca effecively cacel AI whe hee is liied be of ses i he sae sbbad o adeqae eceive aeas a he base saios. oeove, he silaio esls show ha he pefoace of he poposed bo LORD eceive opefos he bo SE eceive. []. Sellahai ad S. ayki, bo-blas fo wieless coicaios: heoy ad expeies, IEEE asacios o Sigal Pocessig, vol.5, o., pp , Oc.. [] L. G. Babeo,. Raaajah ad C. Coli, A low-coplexiy sof-io deeco based o he fixed-coplexiy sphee decode, i Poc. IEEE Ieaioal Cofeece o Acosics, Speech ad Sigal Pocessig, vol., o., pp , ach 8 []. Sii, ad. P. Fiz, Layeed ohogoal laice deeco fo wo asi aea coicaios, i Poc. Alleo Cofeece o Coicaio, Cool, ad Copig, Sep. 5. [3]. Sii ad. P. Fiz, A ovel Sof-Op Layeed Ohogoal Laice Deeco fo liple Aea Coicaios, i Poc. IEEE Ieaioal Cofeece o Coicaios, vol.4, pp , J. 6. [4] A. oasoi,. Sii,. Feai ad S. Bellii, Low Coplexiy, Qasi-Opial IO Deecos fo Ieaive Receives, IEEE asacios o Wieless Coicaios, vol.9, o., pp , Oc.. [5] A. oasoi,. Sii,. Feai ad S. Bellii, bo-lord: A AP-Appoachig Sof-Ip Sof-Op Deeco fo Ieaive IO Receives, IEEE Global elecoicaios Cofeece, vol., pp , ov. 7. [6] A. oasoi,. Sii,. Feai ad S. Bellii, adwae oieed, qasi-opial deecos fo ieaive ad o-ieaive IO eceives, ERASIP Joal o Wieless Coicaios ad ewokig, Feb.. [7] S.. Sog, G. L. Che, ad K. B. Leaief, Localized o ieleaved? A adeoff bewee divesiy ad CFO iefeece i lipah chaels, IEEE asacios o Wieless Coicaios, vol., o. 9, pp , Sep.. [8] S.. Alaoi, A Siple asi divesiy echiqe fo wieless coicaios, IEEE J. Selec. Aeas Co., vol. 6, o. 8, pp , Oc [9] D. Gesbe,. Koois, R. W. eah, J., C.-B. Chae, ad. Salze, Shifig he IO Paadig: Fo Sigle se o lise Coicaios, IEEE Sigal Pocessig agazie, vol. 4, o. 5, pp.36-46, Oc. 7. [] S. Li, ad D. J. Cosello, Eo Cool Codig, Peaso Peice all, 4. [] Spaial chael odel fo liple Ip liple Op (IO) silaios, 3GPP, vol. R 5.996, v..., Ap.. [] A. oasoi,. Feai, D. Gai, F. Osao ad S. Bellii, A Low Coplexiy bo SE Receive fo W-LA IO Syses, IEEE Ieaioal Cofeece o Coicaios, vol.9, pp.49-44, J. 6. REFERECES []. Gosalves ad K. Ioh, li-objecive Opiizaio fo Sofwae Develope Pojecs, i Lece oes i Egieeig ad Cope Sciece: Ieaioal licofeece of Egiees ad Cope Scieis, pp. 6. []. G. yg, J. Li ad D. J. Gooda, Sigle Caie FDA fo plik wieless asissio, IEEE ehicla echology agazie, vol., pp.3-38, Sep. 6. [3] Q. Li, G. Li, W. Lee,. Lee, D. azzaese, F. Cleckx ad Z. Li, IO echiqes i WiA ad LE: A feae oveview, IEEE Coicaios agazie, vol. 48, o. 5, pp. 86-9, ay. [4]. Jafakhai, SPACE-IE CODIG: EORY AD PRACICE, Cabidge ivesiy pess, 5. [5] C. Ciochia, D. Caselai, D. oie ad. Sai, Space-feqecy block code fo sigle-caie FDA, IEEE Elecoics Lees, vol. 44, o., ay 8. [6] C.-W. a ad A. R. Caldebak, lise deecio of alaoi sigals, IEEE asacios o Coicaios, vol.57, o.7, pp.8,89, Jl. 9. [7].. Poo, Ieaive lise deecio, IEEE Sigal Pocessig agazie, vol., pp.8-88, Ja. 4 [8]. üchle, R. Koee ad A. C. Sige, bo eqalizaio: piciples ad ew esls, IEEE asacios o Coicaios, vol.5, o.5, pp.754,767, ay [9]. Li,. e, W. Re ad S. Li, Evalaio of ea LD Algoihs i IO SC-FDA Syse Ieaioal Cofeece o Wieless Coicaios ewokig ad obile Copig, vol., o., pp.,4, 3-5 Sep. Fige : he asie of he lise IO SC-FDA syses. Fige : he eceive of he lise IO SC-FDA syses. Fige 3: he ieaive eceive of he lise IO SC-FDA syses. ISB: ISS: (Pi); ISS: (Olie) WCE 5

6 Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. Fige 4: BER pefoace of he -LORD ad bo SE wih o-ieaive lise deecio fo sigle se (S aea space.4 ). Fige 7: BER pefoace of he -LORD ad bo SE wih o-ieaive lise deecio fo wo ses (S aea space ). Fige 5: BER pefoace of he -LORD ad bo SE wih o-ieaive lise deecio fo sigle se (S aea space ). Fige 8: BER pefoace of ieaive IO eceives fo SC-FDA syses wih sigle se (S aea space.4 ), ad ecode is (,,3). Fige 6: BER pefoace of he -LORD ad bo SE wih o-ieaive lise deecio fo wo ses (S aea space.4 ). Fige 9: BER pefoace of ieaive IO eceives fo SC-FDA syses wih sigle se (S aea space ), ad ecode is (,,3). ISB: ISS: (Pi); ISS: (Olie) WCE 5