Space-Time Bit-Interleaved Coded Modulation over Frequency Selective Fading Channels with Iterative Decoding

Transcription

1 pace-me B-Ineeaved Coded Moduaon ove Fequenc eecve Fadng Channes wh Ieave Decodng Andea M. oneo DEI - Depamen of Eeconcs and Infomacs - Unves of Padova Va Gadengo 6/A Padova - Ia oneo@de.unpd. Absac- A space-me sea concaenaed codng appoach fo speca effcen and eabe communcaons ove fadng channes s pesened. he appoach s based on b-neeaved convouona coded moduaon wh mupe ansm anennas. he decodng pobem of such a scheme s addessed n fequenc seecve fadng channes, whee an eave pocedue s poposed. A he fs sep a mupe-sof-n mupe-sof-ou maxmum a poseo equaze s depoed. hen, a sof-n sof-ou maxmum a poseo convouona decode foows afe deneeavng. of nfomaon s exchanged beween he decode and he equaze hough mupe equazaon and decodng eaons. A bs/s/hz ssem depong wo ansm anennas s pesened. muaon esus show ha, wh jus one eceve anenna, few decodng eaons ed sgnfcan BER/FER gans n boh fequenc seecve boc fadng and fequenc seecve fas fadng ove he uncoded ssem wh dua eceve dves. I. IRODUCIO I s we nown ha he eab of weess communcaons s sgnfcan med b he aenuaon dsubances (fadng) noduced b he popagaon meda. Dves echnques ae ofen necessa o couneac he demena effecs of fadng. he povde he eceve wh epcas of he ansmed sgna ha ma expeence ess aenuaon hough he use of empoa, fequenc, poazaon, and spaa esouces []. Recen, schemes depong mupe ansm and mupe eceve anennas have ganed a o of aenon snce has been shown ha he capac of a weess n can be age nceased wh such an achecue []. In ode o enabe eabe and speca effcen weess communcaons, a ssemac appoach, nown as space-me codng, has been pesenen [3]. pace-me codng combnes he desgn of channe codng, moduaon, ansm and eceve dveses. In [3] pefomance cea ae deved o desgn spaceme es codes fo a fequenc non-seecve (.e. fa) Raegh fadng channe. Codng and moduaon ove mupe ansm anennas ae jon done,.e. combnen a snge en, hough a space-me exenson of he es coded moduaon concep [4]. hs appoach s efeed o as CM, space-me es coded moduaon. In CM a maxmum ehood decode jon decodes he sgnas ha Pa of hs wo was suppoed b LUCE ECHOLOGIE - BELL LAB. he auho s on eave fom Lucen echnooges, Whppan Laboao - J - UA. ae smuaneous ansmed fom dffeen anennas. he sucue of he space me code s such ha desucve supeposon s avoded. pace-me boc codes have been pesenen [5] whee s shown ha he ohogona sucue of hese codes smpfes he maxmum ehood decodng agohm, n fa fadng channes, o smpe nea pocessng. In hs pape we dea wh space-me codng ove fequenc seecve fadng channes ha noduce nesmbo nefeence. In pacua we foow he aenave and nove space-me codng appoach ha has been pesenen [6] fo he fa fadng case. he appoach s based on he sea concaenaon of a convouona encode a b-neeave and a space-me sgna conseaon mappe. We efe o as space-me b-neeaved coded moduaonbicm. he nfomaon bs ae encoded wh a convouona encode. hen, he ae appopae neeaved and sp no paae b seams ha ae mapped o sgna conseaon pons usng mu-eve/phase moduaos (e.g. M-PK, M-QAM moduaos). he paae smbo seams ae smuaneous ansmed fom sepaae anennas. he esung scheme s a space-me exenson o mupe ansm anennas of he b-neeaved coded moduaon concep [7-8]. he b neeave depoen BICM eeps he channe encode and he moduao sepaaed, n conas o CM [3]. Vaabe speca effcences can be eas obaned b appopae choce of he convouona code ae, he numbe of ansm anennas, and he sgna conseaon mappes. In [6] an eave demappng/decodng pocedue s apped ove fa fadng channes. Fuhe s shown ha he appopae desgn of he convouona code, he neeave and he b-o-smbo mappng ue, aows opmzng he codng gan, and fu expong he spaa and empoa dveses. Code consucon cea ae devsen [6] showng ha dffeen fom CM, he consucon of BICM wh eave decodng ams o maxmze he dsance popees (Hammng and Eucdean) a a b eve ahe han a a smbo eve. he dves gan and he codng gan depend on he Hammng dsance of cean coded b sub-sequences. Fuhe appopae b mappngs can enage he poduc Eucdean dsance of he code anncease he codng gan. In hs pape we addess he decodng pobem of BICM n a fequenc seecve fadng channe ha noduces me dspeson and consequen ne-smbo nefeence. he Goba Communcaons Confeence 000an Fancsco, UA, ovembe 7 - Decembe, /00/$ IEEE 66

2 poposed decodng saeg foows an eave pocedue ha s appcabe wh one o moe eceve anennas, and ha s consued of wo ndvdua opma seps. A he fs sep a mupe-sof-n mupe-sof-ou MAP equaze.e. based on he maxmum a poseo agohm [9-0], s depoed. hen, a sof-n sof-ou MAP convouona decode foows. of nfomaon s exchanged beween he decode and he equaze hough mupe equazaon and decodng eaons. Ieave decodng has ogna found appcaon n he conex of ubo codes decodng []. hen, has been apped o sevea deecon/decodng pobems such as eave equazaon of coded BPK moduaon [], eave demappng of coded QPK [3], aneave deecon/equazaon of coded M-DPK [4] n he pesence of co-channe nefeence. In he conex of BICM decodng, he poposed agohm s capabe of de-coupng wh few eaons he sgnas ha ae smuaneous ansmed b he mupe ansm anenna aa and ha expeence ne-smbo nefeence due o he fequenc seecve channe. Wh hs decodng saeg boh he spaa (mupe ansm and eceve anennas), he empoa (codng anneeavng), and he mu-pah (fequenc seecve fadng) dveses can be expoed. he pape s oganzed as foows. econ II evses he BICM concep [6]. econ III descbes he channe mode. econ IV addesses he decodng agohm n fequenc seecve fadng. In econ V, a bs/s/hz ssem ha depos wo ansm anennas s descbed, and pefomance esus fom smuaons ae epoed. Fna, econ VI concudes he pape. II. RAMIER BAED O BICM We consde a weess communcaon ssem compsng ansm anennas and eceve anennas [6]. A he ansme (Fg. ) he nfomaon b seam b s fs convouona encoded and hen b-neeaved o poduce he b seam. he neeaved b seam s /P conveed no seams d (=,...,, =-,..., ). Each paae seam s mappeno compex conseaon pons x (=,...,, =-,..., ) beongng o a mu-phase/eve sgna se (.e. M-PK o M-QAM sgna ses). A me (wh / smbo ae) he componens of he veco X = [ x... x ], afe puse shapng wh denca fes and RF moduaon, ae smuaneous ansmed each fom a dffeen anenna. he pupose of he b neeave s wofod. Fs, s used o de-coeae he fadng channe and maxmze he dves ode of he ssem. econd, emoves he coeaon n he sequence of convouona coded bs, and hs s an essena condon n he eave decodng agohm ha we popose n econ IV. We emphasze ha no ohogona consan s mposed on he anenna conseaons, and ha wh dea neeavng ndependen bs ae mappeno anenna conseaon pons. b convo. encode c b /P ne. / Fg.. BICM base band ansme. mappe mappe mappe he speca effcenc of such a scheme s R=R c og M bs/s/hz, wh R c convouona encode ae, and M moduaon ode. Dffeen speca effcences can be eas obaned b appopae choce of he convouona encode ae, of he moduaon ode and of he numbe of ansm anennas. In pacua a space-me b-neeaved coded modem fo communcaons a bs/s/hz s descben econ V. Ohe schemes wh dffeen speca effcences and/o depong a hghe numbe of ansm anennas ae pesenen [6] whee genea BICM desgn gudenes ae deved fom pefomance anass. III. CHAEL MODEL We consde popagaon hough a fequenc seecve fadng channe wh p esovabe -spaced as. One o moe eceve anennas ae depoed a he eceve. he eceved sgna, a each eceve anenna, s RF demoduaed, feed wh a fe mached o he ansm puse, and samped a ae /. he sequence of sampes a he -h anenna fe oupu s hen modeed as h,, p = = p= p p+ x x x h, x + n. () In () p epesens he p-h ap equvaen channe mpuse esponse of he n beween he -h ansm anenna and he -h eceve anenna, a me ; n s a sequence of..d. compex Gaussan vaabes wh zeo mean and vaance 0 / pe dmenson. Fuhemoe, he channe aps ae compex Gaussan dsbued wh zeo mean (Raegh fadng). he ae ndependen ove dsnc anenna ns and ove dsnc mu-pahs (.e. as) of a gven n. We consde boh he case of fas fadng,.e. empoa uncoeaed fadng coeffcens, and he case of boc fadng,.e. sac fadng coeffcens ove a boc of ansmed smbos, bu dsnc bocs expeence ndependen fadng. We defne he aveage b-eneg-o-nose-ao as foows We aso mae he foowng assumpons. he ansm and eceve fes geneae a qus esponse. he medum esponse s consan fo he duaon of he puse shape. he eceved sgna has no excess bandwdh. he ansm-eceve anenna ns have me-agned dscee mu-pah mpuse esponses. Wh hese assumpons he mode n () s mped, and he sequence of -spaced sampes eds a se of suffcen sascs. 67

3 E b o p Es = E[ hp, x p ] 0 og M + = () 0 og M = = p= whee we assume a nomazed smbo conseaon and a nomazed channe pofe,.e. E [ x ] = Es and p, E[ h = p = p, ] fo =,..., and =,...,. In veco noaon () can be wen as MIMO APP cacuao L e ( ) L e ( ) L e ( ) P/ / b dene. L a (c ) MAP convo. decode L e (c ) b ne. L(b ),, h... h x n =... = ,, h... h x n whee h = [ h,... h ] s he equvaen mpuse p, esponse of he channe a me of he - anenna n, and [... x ] [ x... x... x p +... x p + x = ]. Assumng o pocess bocs of s eceved sampes, s possbe o concse epesen he ovea sequence n (3) as = H x + n whee s he b s max of eceved sampes. he me evouon of (3) can be epesened wh a Maov chan. In fac, f we defne he sae a me - as = x... x +... x... x ], he nos sampe [ p p + depends on he sae and on he smbos ansmed a me on each anenna,.e. X = [ x... x ]. hs ( p Maov chan has = M saes, and M banches eavng and eneng each sae. ) IV. IERAIVE DECODIG OF BICM I FREQUECY ELECIVE FADIG Decodng of BICM s hee addessed fo he fequenc seecve fadng channe mode n econ III. I s based on he ubo-pocessng concep [-4] whee wo ndvdua opma seps can be eave epeaed (Fg. ). A he fs sep (efeed o as equazaon) fom he boc of nos channe obsevaons we compue he a poseo ogehood aos of he coded anneeaved bs (3) L ( d ) = og[ P( d = + ) / P( d = )] (4) fo each ansm banch =,...,. Assumng pefec nowedge of he channe sae nfomaon (.e. H), and nong ha we ae obsevng a Maovan souce n a memoess nos channe, he vaues n (4) can be compued b appcaon of he maxmum a poseo agohm [9-0]. nce n genea we have obsevaons fom an aa of eceve anennas, and we wan o compue sof vaues fo he bs ha ae ansmed on oveappng channes affeced b L a (d ) L a (d ) L a (d ) /P Fg.. Ieave BICM base band eceve. ne-smbo nefeence, hs modue can be nepeed as a mupe-sof-n mupe-sof-ou a poseo pobabes cacuao (MIMO-APP). Howeve when a snge eceve anenna s avaabe he agohm educes o a snge-sof-n mupe-sof ou modue (IMO-APP). In he second sep (efeed o as decodng) he a poseo og-ehood aos of he coded bs ae P/ conveed, deneeaved, and fed o a sof-n sof-ou convouona decode ha s mpemened accodng o he MAP agohm [0]. he convouona decode povdes boh he ogehood aos of he nfomaon bs L ( b ), and new/mpoved og-ehood aos of he coded bs L ( c ). Foowng he ubo decodng pncpe [] exnsc ogehood aos of he coded bs ae compued b subacng he decode npus fom he decode oupus, Le ( c ) = L( c ) La ( c ). he exnsc vaues ae neeaved, /P conveed, and fed bac o he equaze whee he can be usen a new eaon as an esmae of he a po ogehood aos of he coded bs on each ansm banch, L a ( ). In ode o mnmze he coeaon wh pevous compued sof nfomaon, exnsc nfomaon s aso compued a he equaze oupu, Le ( d ) = L( d ) La ( d ). B epeang sevea mes he above pocedue, s possbe o gea mpove he pefomance of he ssem, whee n he fna eaon he decoded sequence of nfomaon bs s obaned fom had decsons on L ( b ). ow, as we sad he compuaon of he og-ehood aos n (4) can be caed ou b appcaon of he MAP agohm. Hee we summaze he fundamena seps. he deas can be eas deved, and we efe he eades o [9-0], [4]. Le us assume o pocess bocs of s eceved sampes. Denong wh d ˆ, he b ha s mappeno he -h b poson of he -h compex smbo of he -h ansm anenna (=,..., ; =,..., s ; =,...,og M=), he 68

4 og-ehood aos n (4) can be compued as P( dˆ n P( dˆ,, = +, = n =, ˆ, ) D( d = + ) ˆ, ) D( d = ) p( p(,, (5),, whee ˆ, D ( ) s he se of a possbe sae ansons d ), fom me nsan (-) o me nsan, assocaed o he npu b d ˆ, = b, b = ±. he poduc of a fowad ecuson, a bacwad ecuson, and a anson pobab eds he jon pobabes p,, [0]. In un, he anson pobab s he poduc of he channe pobab dens funcon, and he a po pobab assocaed o he sae anson ). hus, unde he AWG and pefec CI nowedge assumpons, s gven b,, hp xˆ p+ + d ˆ, La ( d ) 0 = = p= = = γ = A e (6) ) p whee A s a consan. In (6) xˆ p and d ˆ, ae especve he conseaon smbos assocaed o he sae anson ), and he bs ha cause such a anson. A he fs pass hough he equaze no a po nfomaon on he coded bs s assumed, hus L, a ( d ) s se o zeo. In he foowng eaons, he a po og-ehood aos fo he bs of each ansm anenna banch assocaed o a sae ansons ae compued fom he decode oupus. hs a po nowedge heps mpove he mec qua, and decoupe he sgnas ha ae smuaneous ansmed b he ansm aa. Fna, fom a compex sand pon, he mpemenaon of boh he equaze and he decode MAP agohms can be smpfed b he nown max-og-map appoxmaon [0]. V. A BI//HZ MODEM BAED O BICM As an exampe we consde a BICM based ssem ha acheves a speca effcenc of bs/s/hz and depos = ansm anennas. We choose a a emnaed convouona code wh memo (4 saes) and ae R c =/. he code ponomas ae n oca noaon (7,5). We encode bocs (.e. fames) of 60 bs. he seam of 60 pa bs fom he fs ponoma s sen o he fs anenna whe he seam of 60 pa bs fom he second ponoma s sen o he second anenna. Each seam of bs s neeaved wh a sho andom neeave of engh 60. In hs wa, as shown n [6], he code acheves fu spaa ansm dves. Fna, he neeaved bs ae mapped o 4-PK conseaon pons accodng o he Ga ue. We have evauaed hough smuaons (fgues 3 and 4) he b-eo-ae BER and fame-eo-ae FER pefomance of hs ssem. We have assumed a wo equa powe as channe. he as ae spaced b one smbo peod, ae sasca ndependen, and Raegh faded. Boh a fas fadng scenao and a boc fadng (sac ove 30 compex smbos) scenao ae consdeed. I shoud be noed ha whe n he fome case he fadng channe s compee me-uncoeaed, n he ae case he nne neeave heen consdeed eaves he boc fadng channe compee coeaed. Howeve s depoed o de-coeae he sof decsons exchanged beween he equaze and he decode and o mnmze he eo popagaon fom feedbac. In pncpe, bee esus ae expeced wh onge engh neeaves ha, howeve wouncease he ansmsson dea. Fuhemoe, boh he equaze and he decode sages ae mpemened usng he max-og-map appoxmaon, and up o hee passes hough he decode ae consdeed. he equaze has 6 saes wh 6 ansons pe sae. Idea channe sae nfomaon s assumed. As a basene he pefomance of uncoded 4-PK n boh fa fadng and -a fadng s aso shown. In he ae case deecon s pefomed hough equazaon wh a MAP based equaze. I shoud be noed ha accodng o () he cuves do no show he anenna gan when wo eceve anennas ae depoed. A. BICM wh ansm and Receve Anennas Consde BICM wh wo ansm anennas and one eceve anenna. hen, Fg. 3 and Fg. 4 show ha BICM s capabe of oupefomng he uncoded ssem ha depos ehe one o wo eceve anennas. Runnng mupe eaons sgnfcan mpoves he pefomance of BICM. Mos of he gan s acheved a he second pass (cuves abeed wh =) hough he convouona decode. he gan n BER a BER=0-5 n boc fadng wh 3 eaons (Fg. 3a) s moe han 0 db ove he uncoded ssem wh a snge eceve anenna, and abou db ove he uncoded ssem wh dua eceve dves (ahough we do no consde he eceve anenna gan). In fas fadng (Fg. 3b), he gan n BER s moe han 6 db ove he uncoded ssem wh one eceve anenna, and 8.5 db ove he dua eceve dves uncoded ssem. he gan n FER a FER=0-3 n boc fadng wh BICM and 3 eaons (Fg. 4a) s moe han 3 db ove he snge eceve dves uncoded ssem, and abou 4 db ove he dua dves uncoded ssem. In fas fadng (Fg. 4b) BICM eds abou 9.5 db gan ove he dua dves uncoded ssem. he dves gan (sope of he cuves) of BICM ove he uncoded ssem s cea. BICM wh eave equazaon/decodng s capabe of expong he spaa, he mu-pah, and he empoa dveses. B. Pefomance of BICM wh ansm and Receve Anennas Pefomance can be fuhe mpoved b depong wo eceve anennas n he BICM scheme. hs mpovemen s moe ponouncen boc fadng, abou 6 db mpovemen n BER and 4 db mpovemen n FER ove he snge eceve anenna BICM ssem. 69

5 BER bs/s/hz Boc Fadng 4 PK x Rx fa 4 PK x Rx 4 PK x Rx BICM x Rx =0 BICM x Rx = BICM x Rx = BICM x Rx =0 BICM x Rx = BICM x Rx = x x x x x x bs/s/hz Fas Fadng x x x x x x x x x x Eb/o (db) Eb/o (db) a) b) Fg. 3a. B-eo-ae pefomance vesus aveage b-eneg-o-nose-ao, of BICM wh ansm anennas. Fames of 60 bs. Fequenc seecve boc Raegh fadng wh equa powe as. Boh one and wo eceve anennas ae depoed. Fo efeence he pefomance of uncoded 4- PK n fa fadng ( ansm/ eceve), and uncoded 4-PK n -a fadng wh MAP equazaon (-ansm/ and eceve) s shown. Fg. 3b. As a) assumng fequenc seecve fas Raegh fadng. FER bs/s/hz Boc Fadng PK x Rx fa 4 PK x Rx 4 PK x Rx BICM x Rx =0 BICM x Rx = BICM x Rx = 0 BICM x Rx =0 BICM x Rx = BICM x Rx = x x x x x x x x x x bs/s/hz Fas Fadng x x x x x x Eb/o (db) Eb/o (db) a) b) Fg. 4a. Fame-eo-ae pefomance vesus aveage b-eneg-o-noseao, of BICM wh ansm anennas. Fames of 60 bs. Fequenc seecve boc Raegh fadng wh equa powe as. Boh one and wo eceve anennas ae depoed. Fo efeence he pefomance of uncoded 4- PK n fa fadng ( ansm/ eceve), and uncoded 4-PK n -a fadng wh MAP equazaon (-ansm/ and eceve) s shown. Fg. 4b. As a) assumng fequenc seecve fas Raegh fadng. VI. COCLUIO A space-me codng appoach based on b-neeaved coded moduaon wh mupe ansm anennas, efeed o as space-me b-neeaved coded moduaon [6], has been pesened. Decodng of such a scheme has been addessen fequenc seecve fadng channes. he decodng saeg foows wo ndvdua opma seps n an eave pocedue. In he fs sep a MIMO sof-n sof-ou MAP equaze s depoed, foowed b a sof-n sof-ou MAP convouona decode. of nfomaon s exchanged BER FER beween he decode and he equaze hough mupe equazaon/decodng eaons. A bs/s/hz ssem depong ansm anennas s descbed, ans pefomance evauaed b compue smuaons, assumng pefec nowedge of he channe sae nfomaon. B appng he eave decodng pocedue wh jus one eceve anenna, such a ssem s capabe of oupefomng n BER/FER he uncoded ssem ha depos boh snge and dua eceve dves. Mos of he gan s acheved wh on wo eaons, hus wh a med decodng compex. he pefomance mpovemens ae obanen a fequenc seecve -a channe wh boh boc and fas fadng. As expeced hghe gans ae founn he fas fadng scenao. Howeve even fo he boc fadng case he gans ae emaabe. he pefomance of BICM n me-coeaed fadng channes wh pacca neeavng dephs sha be beween he bounds acheved wh he boc and fas fadng channe modes. Based on he above pefomance esusbicm s a pomsng aenave o space-me es codes [3] and spaceme boc codes [5] fo desgnng speca effcen and eabe weess ssems. A pefomance compason of spaceme b-neeaved coded moduaon and space-me boc and es codes s cuen unde nvesgaon, ncudng pacca esmaon of he channe sae nfomaon. REFERECE [] J. G. Poas, Dga communcaons, Y: McGaw-H, 995. [] G. Foschn, M. Gans, On ms of weess communcaons n a fadng envonmen when usng mupe anennas, Weess Pesona Comm., 998, pp [3] V. aoh,. eshad, R. Cadeban, pace-me codes fo hgh daa ae weess communcaon: pefomance ceon and code consucon, IEEE ans. Info. heo, Mach 998, pp [4] G. Ungeboec, Channe codng wh mueve/phase sgnas, IEEE ans. Info. heo, Jan. 98, pp [5] V. aoh, H. Jafahan, R. Cadeban, pace-me boc codng fo weess communcaons: pefomance esus, IEEE JAC, Mach 999, pp [6] A. oneo, pace-me b-neeaved coded moduaon wh an eave decodng saeg, Poc. of IEEE Vehc. ech. Conf. VC- 000-Fa, Bosonepembe 000. [7] E. Zehav, 8-PK es codes fo a Raegh channe, IEEE ans. on Comm., Ma 99, pp [8] G. Cae, G. acco, E. Bge, B-neeaved coded moduaon, IEEE ans. Info. heo, Ma 998, pp [9] L.R. Bah, J. Coce, F. Jene, J. Ravv, Opma decodng of nea codes fo mnmzng smbo eo ae, IEEE. Info. heo, Mach 974, pp [0] J. Hagenaue E. Offe L. Pape, Ieave decodng of bna boc and convouona codes, IEEE ans. Info. heo, Mach 996, pp [] C. Beou, A. Gaveux, P. hmajshma, ea hannon m eo coecng codng and decodng: ubo codes, Poc. of IEEE Inena. Conf. on Comm. ICC 993, pp [] C. Douad, A. Pca e a. Ieave coecon of nesmbo nefeence: ubo-equazaon, Euopean ans. on eecomm. ep./oc. 995, pp [3]. en Bn, J. pede, R.H. Yan, Ieave demappng fo QPK moduaon, IEE Eec. Lees, Ju 998, pp [4] A. oneo, Ieave MAP deecon of coded M-DPK sgnas n fadng channes wh appcaon o I-36 DMA, Poc. of IEEE Vehc. ech. Conf. VC- 99-Fa, Amsedamepembe 999, pp