Frequency-domain Eigenbeam-SDM and Equalization for High Speed Data Transmissions

Size: px

Start display at page:

Download "Frequency-domain Eigenbeam-SDM and Equalization for High Speed Data Transmissions"

Eunice Robertson
5 years ago
Views:

1 Fequeny-domain Eigenbeam-SDM and Equaizaion fo igh Speed Daa ansmissions Kazuyui Ozai Ainoi aajima and Fumiyui Adahi Dep. of Eeia and ommuniaions Engineeing Gaduaed shoo of Engineeing ohou Univesiy Sendai Japan Absa In ieess ommuniaions he hanne onsiss of many esovabe pahs ih diffeen ime deays esuing in a seveey fequeny-seeive fading hanne. he fequenydomain equaizaion an ae advanage of he hanne seeiviy and impove he bi eo ae BER pefomane of he singe-aie S ansmission. Reeny mui-inpu muioupu MIMO muipexing is gaining muh aenion fo ahieving vey high speed daa ansmissions unde imied bandidh. Eigenbeam spae division muipexing is non as one of MIMO muipexing ehniques. In his pape e popose fequeny-domain fo S ansmission. In fequeny-domain he ohogona ansmission hannes o ansmi diffeen daa in paae ae onsued a eah ohogona fequeny. A a eeive is used o suppess he ISI. In his pape fo high speum effiieny he ansmi poe aoaion and he adapive moduaion based on he equivaen hanne gains afe pefoming ae appied. he ansmission pefomane of he fequeny-domain in a sevee fequeny-seeive Rayeigh fading hanne is evauaed by ompue simuaion. Keyods- MIMO muipexing MMSE- S ansmission I. IRODUIO In he nex geneaion mobie ommuniaion sysems vaious boadband muimedia sevies ae demanded []. oeve sine he avaiabe bandidh is imied highy speum-effiien ansmission ehniques ae equied. Reeny mui-inpu mui-oupu MIMO muipexing [] has been aaing muh aenion. hee ae o ypes of MIMO muipexing. One is he spae division muipexing SDM [3-4] hee diffeen ansmi anennas ansmi diffeen daa simuaneousy. he ohe is he eigenbeam- SDM [5-6] in hih sevea ohogona hannes ae onsued based on he MIMO hanne infomaion shaed by he ansmie and he eeive o ansmi he diffeen daa simuaneousy. an be expeed o povide bee ansmission pefomane han SDM sine ohogona hannes ae onsued and he ansmi poe aoaion and he adapive moduaion an be appied. In mobie ommuniaions he hanne onsiss of many esovabe pahs ih diffeen ime deays esuing in a seveey fequeny-seeive fading hanne. he bi eo ae BER pefomane of singe-aie S ansmission signifiany degades due o he sevee ine-symbo inefeene ISI [7]. Reeny i has been shon ha he use of fequeny-domain equaizaion an signifiany impove he BER pefomane of S ansmission [8]. In his pape e popose fequeny-domain fo S ansmission hih foms ohogona hannes in fequenydomain and pefoms o suppess he ISI. Fuhemoe he ansmi poe aoaion based on he ae fiing heoem [9] and he adapive moduaion using a henoff bound of BER obained fom he equivaen hanne gains afe. he BER pefomane of fequeny-domain fo S ansmission is evauaed by ompue simuaion and is ompaed ih ha of he SDM using. he emainde of his pape is oganized as foos. Se. II desibes he poposed fequeny-domain fo S ansmission. he poe aoaion and he adapive moduaion mehods ae pesened in Se. III. Se. IV pesens he ompue simuaion esus fo he BER pefomane. Seion V onudes his pape. II. FREQUEY-DOMAI Fig. shos he ansmie/eeive suue of M fequeny-domain ih MMSE- hee is he numbe of ansmi anennas and M is he numbe of eeive anennas. A. ansmied signa A he ansmie binay infomaion sequene is onveed ino min M paae sequenes by seiao-paae S/ onvesion. is deemined by he poe aoaion and he adapive moduaion agoihm hih i be desibed in seion III. he h binay sequene is ansfomed ino he daa moduaed symbo sequene and divided ino a sequene of -symbo signa bos. he signa bos ansmied via ohogona hannes ae epesened using he veo epesenaion as x [ x x ] - hee x epesens he h signa bo and. is he anspose opeaion. -poin fas Fouie ansfom FF is appied o deompose eah signa bo ino fequeny omponens. he fequenydomain signa veo is expessed as X [ X X ] hee X is he h fequeny omponen of he h signa bo. Le be he -by- ansmi eigh maix o onsu he ohogona hannes i be deived ae. hen he fequeny-domain -by- ansmi signa veo X [ X X ] is obained as X X. Afe muipying by he ansmi eigh maix -poin IFF is appied o obain he ime-domain signa x n o be ansmied fom he nh anenna. he ime-domain -by- ansmi signas ae epesened by x [ x x ] /6/$ 6 IEEE

2 -. As shon in Fig. he as g symbos in eah bo ae opied and inseed as a yi pefix ino he guad ineva GI hih is paed a he beginning of eah bo. signa bos ae ansmied simuaneousy fom ansmi anennas using he same aie fequeny. B. Reeived signa A he eeive ansmied signas ae eeived by M anennas via a fequeny-seeive fading hanne hih onsiss of L-popagaion pahs ih diffeen ime deays. he M-by- eeived signa veo [ M ] a ime an be expessed as L h x n hee h and epesens he M-by- ompex hanne gain maix and he deay ime of h pah espeivey and n [ n n M ] epesens he M-by- noise veo hee n m is a zeo-mean ompex Gaussian noise poess ih vaiane. -poin FF is appied o deompose he eeived signa bos ino fequeny omponens. he M-by- signa veo R [ R R M ] a he h fequeny an be expessed as R X Π 3 hee and Π epesen he M-by- ompex hanne gain maix and he M-by- noise veo espeivey a he h fequeny and hey ae given by Info. S/ M anennas Π Mod. Mod. -GI -GI U o ansmie FF L Moduaion eve seeion FF M h exp jπ / n exp jπ / x. eigh maix muipie :oe maix IFF a ansmie hanne esimaion Eigenvaue deomposiion Rx. eigh maix muipie GI GI oe aoaion MMSE-. 4 FF U :hanne maix anennas U :Uniay maix fom eeive :Eigenvaue maix b Reeive Figue ansmie/eeive suue. De-mod. De-mod. S/ info. g symbos opy symbos Figue Fame suue. ime. De-muipexing he -by- eeived signa veo R [ R R ] is obained by muipying he eeived signa R by he -by-m eeive eigh maix. Using he eigenvaue deomposiion of he hanne maix e obain he ansmi/eeive eigh maies and o onsu he ohogona hannes. he eigenvaue deomposiion of he hanne maix is expessed as U U 5 hee U is he -by- uniay maix diag[ ] is he -by- diagona maix ih epesening he h eigenvaue of he hanne maix and. is he emi anspose opeaion. Fom Eq. 5 and an be obained as U U 6 hee diag[ ] is he -by- ansmi poe maix. is deemined by using he ae fiing heoem based on he equivaen hanne gains. Fo de-muipexing he ansmied signa bos R is muipied by he eeive eigh maix o obain R as R R 7 X Π hee he fis em is he desied signa omponens. Sine and ae he diagona maix he ansmied signa bos an be de-muipexed ihou suffeing he inefeene fom ohe anennas. D. Fequeny-domain equaizaion hough de-muipexing ihou suffeing he inefeene fom ohe anennas he ISI si emains. heefoe fo he suppession of he ISI e appy MMSE- o suppess he ISI and obain he -by- signa veo R [ R R ] hih is given by

3 Π X R 8 hee ] diag[ is he MMSE eigh maix ih [] 9 fo he given and hee is he ansmi poe of he h hanne and is he noise poe. Appying -poin IFF R is ansfomed ino he - by- ime-domain signa veo ] [ given by / exp / exp j j π π Π x x hee he fis em is he desied signa omponen he seond he ISI omponen and he hid he noise omponen. Afe paae-o-seia /S onvesion he eeived signa is daa-demoduaed o eove he ansmied binay infomaion sequene. III. OER ALLOAIO AD ADAIVE MODULAIO he ansmi poe and he moduaion eve ae deemined bo-by-bo based on he equivaen hanne gain. Fo he poe aoaion he ae fiing heoem [9] is used. he adapive moduaion o deemine he moduaion eve is based on he henoff uppe bound [9]. A. oe aoaion he oa hanne apaiy oa of he paae ohogona hannes is given by [] og oa γ hee γ is he eeived signa poe-o-he noise poe aio SR of he h hanne and is given as noise γ hee noise 3 is he noise poe. Using he Lagange muipie mehod he poe { } ha maximizes he oa hanne apaiy oa is deemined by he poe aoaion unde he onsained ondiion oa. Sine MMSE- is used i is quie diffiu if no impossibe o find heoeiay he bes poe aoaion using he Lagange muipie mehod. heefoe in his pape e assume ha ZF and MR eighs ee used in a eeive o deemine he poe aoaion. is found as max oa fo ZF 4 and max 3 3 oa fo MR. 5 B. Adapive moduaion he ondiiona signa-o-inefeene pus noise poe aio SIR γ of he h hanne is given as noise ISI γ 6 hee ISI is he inefeene poe of he h hanne and an be shon as ISI. 7 Based on he Gaussian appoximaion of he inefeene e ea he sum of inefeene and noise as a ne Gaussian noise. he BER is given as

4 γ BER a ef 8 b hee ef. is he ompemenay eo funion and a and b ae shon in abe []. In his pape he henoff uppe bound of he BER is used fo deemining he moduaion eve. he BER uppe bound fo he h hanne is given as γ γ BER aef a exp. 9 b b hen m bis pe symbo is used he uppe bound of he BER aveaged ove ohogona hannes is given as BER ave m BER m η a m γ exp b hee η m is he speum effiieny in bps/z. he moduaion eve is deemined as foos. Afe he pefoming poe aoaion using he ae fiing heoem using Eq. he opimum ombinaion of he moduaion eves m m hih minimizes he BER uppe bound is found fo he given speum effiieny η m. ABLE. a and b Moduaion a b mehod BSK / QSK / 8SK /3 /sin π/8 6QAM 3/8 64QAM 7/4 4 56QAM 5/64 7 IV. OMUER SIMULAIO he simuaion paamees ae given in abe. e assume an infomaion bi sequene of K4 bis. -by-m hannes ae assumed o be independen fequeny-seeive quasi-sai Rayeigh fading hannes i.e. f D hee is he symbo engh eah hanne having a symbo-spaed exponeniay deaying L6-pah poe deay pofie ih deay fao α. Idea hanne esimaion is assumed. e assume no feedba deay of he hanne infomaion fom he eeive o ansmie. Fis e disuss he unoded ase. e have ompaed he ahievabe unoded BER pefomanes of M fequenydomain hen ZF and MR eighs ae used fo he poe aoaion and found ha hee is amos no pefomane diffeene; heefoe in he fooing simuaion e use ZF eigh ony. he unoded BER pefomane of M fequeny-domain is poed in Fig.3 as a funion of he oa ansmied enegy-o-noise poe speum densiy aio SR. Fo ompaison he BER pefomanes of M SDM ih MMSE- and M SIMO ih MMSE- ae aso poed. I an be seen ha fequeny-domain is supeio o SDM and SIMO. hen α 6 db he equied SR of fequeny-domain fo he aveage BER -3 is smae by abou 5 7 db han ha of SDM. On he ohe hand he equied SR of 44 fequenydomain is smae by abou 6.5 and 9 db han ha of 44 SDM hen α and 6 db espeivey. his is beause in ohogona hannes ae onsued heeby poduing no inefeene fom ohe anennas and he adapive poe aoaion/moduaion is appied hie in SDM MMSE- anno ompeey suppess he inefeene fom ohe anennas and fuhemoe no adapive poe aoaion/moduaion is used. I an aso be seen ha he BER pefomane ih fequeny-domain is ess sensiive o he hanne fequeny-seeiviy o α sine he ISI aused by he fequeny-seeiviy is bee suppessed by pefoming as e as adapive poe aoaion/moduaion. ubo oding [3] is e non as a poefu hanne oding and has been used in he pesen hid geneaion mobie ommuniaion sysems [4]. he ubo oded BER pefomane of 44 fequeny-domain ih speum effiieny of 8 bps/s/z is poed in Fig.4. ubo enode ih oding ae R/ onsising of o 35 eusive sysemai onvouiona RS enodes is onsideed. Simia o he unoded ase fequeny-domain is aso supeio o SDM and SIMO. he equied SR of fequenydomain fo he aveage BER -4 is smae by abou 3.5 db han ha of SDM hen α 6 db. Fequenydomain povides he bee pefomane han SDM. oeve fequeny-domain is moe ompex han SDM sine he onsuion of ohogona hannes using eigenvaue deomposiion is neessay and he ansmi poe aoaion and he adapive moduaion ae appied. Fo exampe he numbe of muipy opeaions of fequenydomain is M imes ha of SDM as x. and Rx. eigh maies ae muipied in fequeny-domain E- SDM sysem. ABLE. Simuaion paamees. o. of Infomaion bis 4bis Daa moduaion BSKQSK8SK 6QAM64QAM56QAM o. of poins of FF/IFF 56 GI g 3 umbe of anennas M4 oe deay pofie L6-pah exponenia Deay fao α6db hanne esimaion Idea Feed ba deay one

5 Aveage BER Aveage BER Aveage BER.E.E-.E-.E-3.E-4 S fequeny-domain η 4 L 6 Fequeny-domain 56 g 3 SDMMMSE- SIMO6QAM Exponenia pofie αdb α6db.e SR db.e.e-.e-.e-3.e-4 Exponenia pofie αdb a M S 44 fequeny-domain η 8 L g Fequeny-domain SDMMMSE- SIMO56QAM.E-5 α6db SR db b M44 Figue 3 Unoded BER pefomane..e.e-.e- S 44 fequeny-domain η 8 L g.e-3 Exponenia pofie αdb α6db.e-4 Fequeny-domain SDMMMSE- SIMO56QAM.E SR db V. OLUSIOS In his pape e poposed fequeny-domain ha onsus he ohogona hannes in he fequeny-domain and pefoms o suppess he ISI. he poe aoaion based on he ae fiing heoem and he adapive moduaion using he henoff uppe bound ee appied. he aveage BER pefomane in a fequeny-seeive Rayeigh fading hanne as evauaed by ompue simuaion. I as shon ha he BER pefomane of fequeny-domain is supeio o SDM. efomane supeioiy of fequenydomain is signifian in he ase of ea fequenyseeiviy. REFEREES [] F. Adahi ieess pas and fuue-evoving mobie ommuniaions sysems IEIE ans. Fundamenas vo.e83-a pp Jan. [] G. J. Foshini e a. On of ieess ommuniaions in a fading envionmen hen using muipe anennas ieess esona ommun. vo.6 no. 3 pp [3] R. Van ee e a. Maximum ieihood deoding in a spae division muipexing sysem o. IEEE V-Sping vo. pp.6- May. [4] G. J. Foshini Layeed spae-ime ahieue fo ieess ommuniaion in a fading envionmen hen using muipe anennas Be Labs eh. J. vo. no. pp [5]. Sampah e a. Geneaized inea peode and deode design fo MIMO hannes using he eighed MMSE ieion IEEE ans. ommun. vo.49 no. pp.98-6 De.. [6] K. Miyashia e a. igh daa-ae ansmission ih eigenbeam-spae division muipexing in a MIMO hanne o. IEEE V -Fa vo.3 pp.3-36 Sep.. [7].. Jaes J. Ed. Mioave mobie ommuniaions iey e Yo 974. [8] D. Faone e a. Fequeny domain equaizaion fo singeaie boadband ieess sysems IEEE ommun. Mag. vo.4 pp Api. [9]. ove e a. Eemens of infomaion heoy J. iey & Sons In. 99. [] K. aeda e a. Join use of fequeny-domain equaizaion and ansmi/eeive anenna divesiy fo singe-aie ansmissions IEIE ans. ommun. vo. E87-B no.7 pp Juy 4. [] E. eaa apaiy of mui-anenna gaussian hannes Euopean ansaions on eeommuniaions vo. no.6 pp ov./de [] J. G. oais Digia ommuniaions fouh ediion MGa i. [3]. Beou ea Shannon imi o-oeing oding and deoding: ubo odes IEEE ommun. Mag. vo. 44 no. pp. 6-7 O [4] F. Adahi e a. ideband DS-DMA fo nex geneaion mobie ommuniaions sysems IEEE ieess ommun. Mag. vo. 36 Sep. 998 pp Figue 4 44 ubo oded BER pefomane.

Low-complexity Algorithms for MIMO Multiplexing Systems

Low-complexity Algorithms for MIMO Multiplexing Systems Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :