Orthogonal Space-Time Discrete Multitone and Space-Time Filtered Multitone Coded Architectures

Transcription

1 Orhogonal Sace-ime Discree ulione and Sace-ime Filered ulione Coded Archiecures Andrea onello DIEG - Diarimeno di Ingegneria Elerica, Gesionale e eccanica Universià di Udine 33 Udine, Ialy - onello@uniudi Absrac In his aer we describe several sace-ime mulione archiecures for ransmission wih mulile anennas over fla and frequency selecive fading channels he idea behind hese schemes is o erform daa mulileing over boh he saial, and he frequency domain wo of hese archiecures are obained by eending he filered mulione F) modulaion conce o he mulile anenna scenario Anoher novel archiecure is based on he conce of deloying some form of cyclically refied discree mulione D) modulaion he archiecures aim a orhogonalizing he ime disersive channel, and ossibly he overlaing saial channels he efficien imlemenaion can be erformed via fas Fourier ransform FF), and low rae olyhase filering hese archiecures can be concaenaed wih ouer channel coding or daa sreading for sace-frequency diversiy eloiaion Keywords - Sace-ime coding, diversiy, fading channels, filered mulione modulaion, discree mulione modulaion, OFD I IRODUCIO I is well nown ha mulile-ransmi mulile-receive anenna archiecures can increase he caaciy of wireless communicaion sysems [3] o aroach he caaciy limis we need o deloy owerful sace-ime coding schemes ha eloi he saial-emoral diversiy of rich scaering environmens Several sace-ime coding schemes have been roosed iniially for ransmission over fla fading channels, for insance, he well nown sace-ime rellis codes SC) in [8], or he sace-ime bi-inerleaved codes SBIC) in [9] Alhough, for low ransmission raes, and small number of ransmi anennas good SC and SBIC have been found, he sace-ime coding roblem becomes more comlicaed if very high daa raes have o be achieved, ie, we deloy a high number of ransmi anennas wih high order modulaion On one hand, his is due o he difficuly of designing coding schemes ha are caable of achieving full saial diversiy and delivering high coding gains On he oher hand, he oimum decoding algorihm ha is based on he maimum-lielihood rincile is characerized by a comleiy ha limis he racical imlemenaion Aiming a simlify he decoding comleiy several sace-ime bloc codes wih simle decoding have been roosed, eg, he codes in [7], and he simle ransmi diversiy scheme by Alamoui When ransmission is over frequency selecive fading Par of his wor was suored by IUR under rojec FIRB "Reconfigurable laforms for wideband wireless communicaions" S--D S-F O-S--D O-S-F ABLE I ACROYS AD OAIO convenional sace-ime cyclically refied discree mulione modulaion sace-ime OFD) sace-ime filered mulione modulaion orhogonal sace-ime cyclically refied discree mulione modulaion orhogonal sace-ime filered mulione modulaion umber of ransmi anennas umber of ones µ µ ransmission eriod W/ ominal overall bandwidh f one sub-carrier) f/ one sacing Sub-channel daa eriod gn) Prooye sub-channel filer b umber of bis er comle daa symbol a l ) a l ) Daa symbol ransmied a ime l over sub-channel a, l ) Daa symbol ransmied over anenna and sub-channel channels, he same sace-ime codes roosed for fla fading channels can be deloyed However, equalizaion is required o counerac he inersymbol inerference, which ranslaes ino increased decoding comleiy [], [] In order o simlify he equalizaion as, i has been roosed o use cyclically refied orhogonal frequency division mulileing OFD) over each ransmi anenna, referred o as sace-ime cyclically refied discree mulione S--D) modulaion in his aer his allows for obaining a fla frequency resonse for each ransmi anenna lin hen, we can obain diversiy and coding gains via rellis coding [6], or bi inerleaved coding [5] across he ransmi anennas In he laer case, decoding is erformed hrough he ieraive concaenaion of a sof-in sof-ou bi demaer wih a sof-in sof-ou channel decoder Demaing can be erformed indeendenly over he OFD sub-channels However, oimal L/AP demaing sill has a comleiy ha increases eonenially wih he number of ransmi anennas [9] because each sub-channel sees he suerosiion of he daa symbols simulaneously ransmied by he anennas In his aer we describe several sace-ime mulione archiecures for ransmission over mulile anennas hey aim a orhogonalizing he ime disersive channel, and ossibly he overlaing saial channels In oher words, he goal is o ransform he mulile anenna, ISI channel in a number of non-overlaing sub-channels he idea behind hese schemes is o erform daa mulileing over boh he saial and he frequency domain For clariy, we lis in able I he acronyms ha will be used Firs, we review convenional sace-ime cyclically refied discree mulione S-- Proceedings of IEEE Vehicular echnology Conference Sring 4 VC 4 Sring ilan, Ialy ay 7-9, 4 IEEE 4 73

2 D) modulaion Second, we devise a scheme ha is obained by eending he filered mulione F) modulaion conce [] o he mulile ransmi anenna cone I is referred o as sace-ime filered mulione S- F) modulaion hen, we devise wo oher sace-ime archiecures whose objecive is o orhogonalize no only he ISI channel bu also he overlaing mulile anenna channels hey wor boh for fla fading channels and for frequency selecive fading channels hey are resecively referred o as orhogonal sace-ime filered mulione O-S- F) modulaion, and orhogonal sace-ime cyclically refied discree mulione O-S--D) modulaion he conce behind F modulaion over single inu channels single ransmi anenna) is o ransmi a number of low rae daa sequences over sub-channels ha are shaed wih an aroriae filer cenered on a given sub-carrier [], [3] Discree mulione modulaion D) is a aricular imlemenaion ha deloys recangular ime domain filers D is also referred o as OFD he design of he subchannel filers, and he choice of he sub-carrier sacing in an F sysem aims a subdividing he secrum in a number of sub-channels ha do no overla in he frequency domain In a D sysem, he orhogonalizaion of he ISI channel is obained wih he inserion of a cyclic refi longer han he channel ime disersion All he archiecures here described can be efficienly imlemened via FF and low-rae olyhase filering In S- F daa deecion may require sub-channel equalizaion in he resence of frequency selecive fading However, is comleiy is low since he equivalen sub-channel imulse resonse sans a small number of daa symbols In O-S-- D full sace-ime orhogonalizaion is obained, such ha he deecor simlifies ino a one-a equalizer er sub-channel as in convenional OFD over single inu-single ouu channels o he auhor's nowledge O-S--D is novel he mulione archiecures herein described can be concaenaed wih ouer coding A good oion is o use biinerleaved codes In his case decoding can be erformed via ieraive bi demaing and channel decoding Anoher idea o eloi diversiy is o use ouer direc sequence sreading [4] II CHAEL ODEL We assume o deloy ransmi anennas, and a single receive anenna he mulile receive anenna scenario is a simle eension he sace-ime archiecures ha we describe have an efficien discree-ime imlemenaion he filers in he digial-o-analog converer a he ransmier, and he analog-o-digial converer a he receiver are included in he equivalen discree-ime channel imulse resonse he channel is assumed o be frequency selecive such ha he equivalen imulse resonse for he -h anenna lin is ) P h n δ ) n ) is he ransmission eriod he a gains are Rayleigh faded, and are assumed o be ime-invarian over one or more ransmission frames of duraion each Furher, we assume < a, l ) a, l ) a, l ) a, l ) a, l ) a, l ) IFF IFF gn) gn) a, l ) gn) gn) a, l ) a l ) a l ) IFF n) n) yn) Fig Convenional Sace-ime D sysem f f f f n) n) yn) S/P -f -f g*-n) g*-n) Fig Sace-ime F sysem n) n) yn) Fig 3 Orhogonal Sace-ime D sysem a, l ) a, l ) a, l ) a, l ) IFF IFF S/P g, l ) g, l ) g, l ) g, l ) n) FF FF n) Join Dema b Bis z l ) z l ) Join Dema b Bis Join S Equalizer z l ) z l ) z l ) Join S Equalizer Dema b Bis z l ) Dema b Bis Fig 4 Orhogonal Sace-ime Criically Samled F ransmier III COVEIOAL S--D: SPACE-IE CYCLICALLY PREFIXED DISCREE ULIOE ODULAIO In convenional S--D ransmission, cyclically refied D modulaion is deloyed over each anenna [5] see Fig ) For each anenna of inde,, - we ae a bloc of, daa symbols a l ),,,-, we aly an oin inverse discree Fourier ransform IDF), we add a cyclic refi of lengh µ, and finally we ransmi he ouu, µ symbols Each daa symbol a l ) is assumed o belong o a comle consellaion, eg, -QA, and is n, obained by maing b bis he bloc of symbols l ), n,,, ransmied by anenna wih eriod, is generaed as follows j n µ ) n,, ) ) ) S D b l l n a l e ) he resuling ransmission bi rae is R / bis/s Wih he channel model ), and wih he assumion of using a cyclic refi longer han he channel ime suor, he 74

3 received signal reads for l,,, and n µ,, 3), n η y l n ) l ) l n ) where η n ) are assumed o be iid Gaussian random variables wih zero mean ow, demodulaion is accomlished by droing he received samles ha corresond o he cyclic refi of each received bloc, and alying an -oin discree Fourier ransform DF) o obain for he -h sub-channel ouu,, ) z l ) H a l ) w l ), H P, j e 4) wih w l being iid zero mean Gaussian random variables ha is, each DF ouu sees a fla faded channel However, alhough no inersymbol inerference ISI) is inroduced, he saial channels do overla herefore, o recover he ransmied bis, he oimal maimum lielihood demaer has o erform, for each of he frequency subchannels, bi demaing joinly over he saial channels Is comleiy grows eonenially wih he number of ransmi anennas Several demaing algorihms are described in [9], [], [] Finally, noe ha if he channel is fla here is no oin o deloy S--D IV S-F: SPACE-IE FILERED ULIOE ODULAIO A differen aroach is o use F modulaion [] insead of -D modulaion over each ransmi anenna he difference relies on he resence of sub-channel shaing ulses A general archiecure is shown in Fig he discreeime signal ha is ransmied by anenna is obained as follows, j f n n) a l) g n l) e π 5) l where g n ) is he rooye ulse ha is used o shae he sub-channels, while f / is he -h sub-channel one An efficien FF based imlemenaion is ossible resuling in a sace-ime eension of he one described in [] If he scheme is referred o as criically samled, oherwise if > he scheme is referred o as non-criically samled he rooye ulse is designed o be frequency concenraed, so ha sub-channels do no overla in frequency As an eamle, we can use square-roo-raised cosine ulses, or Gaussian ulses [3] he choice > allows for a beer sub-channel searaion he resuling ransmission bi rae is RS F b / bis/s, and can be higher han ha in S--D deending on he choice of, and consequenly of Wih he channel model ), he received signal reads y n ) n ) η n ) 6) Demodulaion is accomlished by firs deloying a ban of filers mached o he sub-channel ransmi ulses hen, we samle he ouus a rae / o obain for he -h mached filer F) ouu j π fn * ) ) ) n, j f ) j π f f n a l ) e e l n * gn l) g n m) w m) z m y n e g n m 7) Using Parseval heorem i can be shown ha if he sub-channels do no frequency overla, relaion 7) differs from zero only for his holds rue if G f ) for f > / ) Under such hyohesis ha can be me wih he aroriae sysem design we obain ha,, z m) a l) β m l) w m) l 8), j * n β m ) e g m n ) g n ) According o 8), he -h sub-channel ouu sees some ISI conribuion Furher, he saial channels overla herefore, o accomlish bi demaing we need o run a ban of equalizers each erforming join saial, and emoral equalizaion he oimal S-AP equalizer is described in [] ore in general, oimal mulicarrier AP equalizaion is described in [3] he ineresing feaure in his archiecure is ha he number of inersymbol inerferers is small noe ha each subchannel has as saced by muliles of ) hus, each equalizer can have moderae comleiy deending on he ransmission bandwidh, channel ime disersion, and number of ones he fac ha no cyclic refi is deloyed can ranslae in higher secral efficiency han wih S--D V O-S--D: ORHOGOAL SPACE-IE CYCLICALLY PREFIXED DISCREE ULIOE ODULAIO In his secion we roose a novel o he auhor s nowledge) scheme ha is sill based on he conce of deloying some form of cyclically refied D modulaion We sar from he observaion ha in boh convenional S--D, and S-F he saial channels do overla Indeed his allows for increasing he ea ransmission rae However, he oimal deecor/equalizer has a comleiy ha grows eonenially wih he number of ransmi anennas Furher, noe ha here is no oin o deloy S--D over a fla faded channel he scheme ha we describe in his secion aims a orhogonalizing he saial channels, and can be used in boh fla, and frequency selecive channels We refer o his scheme as O-S--D see Fig 3) We sar by aing a bloc of daa symbols a l ),,,- hen, we generae blocs of µ symbols each, as follows ), ) ) ) j π n n µ l l n a l e 9) for,, -, and n,,- Each bloc is ransmied 75

4 over a disinc anenna he above oeraion corresonds o aly a cyclic refi over boh ime and sace his can be beer undersood if we elicily wrie 9) in a mari! µ µ µ µ µ whose rows are ransmied over disinc anennas, and where j n/ n a l ) e π he resuling ransmission bi rae is RO S D b / bis/s oe ha in fla fading channels we can se µ, and Wih he channel model ), and wih he assumion of a cyclic refi ha saisfies he relaion µ, he received signal reads for l,,, and n µ,,, n y l n) l) η l n) ) ow, demodulaion is accomlished by droing he cyclic refi he samles of he l-h bloc corresonding o inde n, µ ), and alying an -oin DF o obain z l ) H a l ) w l ), H ) j e ) herefore, each DF ouu sees a fla faded channel, and he saial channels do no overla In oher words, we have ohogonalized boh he ISI channel, and he saial channels he comleiy of he oimal maimum lielihood bi demaer does no grow as he number of anennas grows ow he quesion is: wha is he advanage of such a scheme? he advanage is ha ransmission aes lace over non overlaing channels Furher, i can be roved ha he ran of he IO-ISI channel remains unchanged, and herefore he achievable diversiy gain In aricular if he channel as are indeenden, hen he ran of he P correlaion mari whose enries are * EH [ H ] is P Indeed, o eloi diversiy we need o deloy some form of coding We address his roblem in Secion VII VI O-S-F: ORHOGOAL SPACE-IE FILERED ULIOE ODULAIO A differen way o achieve saial, and emoral orhogonalizaion is o use a variaion of he S-F modulaion scheme of Secion IV I is obained by assigning disinc ones o disinc anennas If he sub-channels do no frequency overla, hen disinc saial channels occuy disinc orions of he available secrum, hus hey don' overla We refer o his scheme as O-S-F In formulae, he signal ransmied by anenna can be wrien as j n j n, l ) n ) e a l ) g n l ) e if we assume o inerleave he ones across he anennas, and we denoe he number of ones er anenna wih / he resuling ransmission bi rae is RO S F b / I can be higher han ha in O-S--D deending on he choice of, and consequenly of From ) an efficien olyhase imlemenaion can be derived For eamle, assuming a criically samled sysem, we have ha such ha he sequence of symbols ransmied by anenna reads n, n, n, ) ) ) ) l π j n j n n, n,, ) ) ) ) m m n g m l A l g l g l n e A l a l e 3) for m,,, n,, he imlemenaion is shown in Fig 4 ow, we need o deloy an IDF wih oins er anenna he ouu bloc of lengh is n, cyclically eended o obain he bloc A l ) of lengh n, hen, low-rae filering wih g l ) is erformed Finally, conversion follows Similarly, o he S-F modulaion case, demodulaion is accomlished by firs deloying a ban of filers mached o he sub-channel ransmi ulses Wih he channel model ), under he assumion of non overlaing in frequency) sub-channels, and under he assumion of deloying disinc ones over disinc anennas, he mached filer ouu samle reads,,,, β z m ) a l ) m l ) w m ) 4) ha is, he mached filer ouu of inde, ), for,, and,,, ehibis a conribuion only from he frequency sub-channel of inde, and he saial channel of inde herefore, also in his archiecure we have orhogonalized he saial channels However, some residual ISI can be resen which requires some form of emoral equalizaion, ie, a ban of indeenden single channel equalizers VII CHAEL CODIG In order o eloi saial and frequency diversiy we need o use some form of channel coding in all sace-ime archiecures ha we have described Coding has o ae lace across he sace-frequency sub-channels I is imoran o noe ha while in S--D and S-F he saial channels overla, in O-S--D and O-S-F he saial channels are orhogonalized For all archiecures a ossible good coding aroach is o use a sace-ime biinerleaved encoder [9] Decoding can be erformed via he urbo aroach ha is based on he ieraive concaenaion of symbol demaing, de-inerleaving, and channel decoding In S--D we have fla faded sub-channels each carrying he simulaneous ransmission of daa symbols Decoding can be erformed wih he ieraive S-AP algorihms in [9] In S-F we have sub-channels each carrying he simulaneous ransmission of daa symbols and each 76

5 - -3 BER -4-5 Fla Rayleigh Fading wo RX Anennas SR db) SR db) Fig 5 Performance of O-S--D wih ouer daa sreading 64, µ4, 4-PSK modulaion, wo receive anennas wih ZF deecion and RC combining U o 4 ransmi anennas BER 4 Pahs Rayleigh Fading Power Profile: [ ] wo RX Anennas 4 ehibiing moderae ISI Decoding can be erformed wih he ieraive S-AP equalizaion algorihms in [], [3] In O- S--D we have fla faded sub-channels each carrying a single symbol from a given anenna Similarly, in O-S- F he saial channels do no overla, however some moderae ISI can be resen We emhasize ha while for S- -D and S-F he comleiy of he demaing sage grows eonenially wih he number of anennas, in he oher wo schemes he comleiy of each sub-channel demaer is indeenden from he number of anennas he enaly is ha if we fi he daa modulaion order in he firs wo schemes he ea) ransmission rae increases linearly wih he number of ransmi anennas, while in he laer wo schemes is indeenden of he number of ransmi anennas However, his doesn' necessarily mean ha he secral efficiency is lower in racical scenarios I has also o be noed ha deending on he sysem design, is no he same for he four schemes yically, a sufficienly long cyclic refi is deloyed in he D schemes so ha, assuming b o be fied, we have ha RO S D RO S F RS D RS F o increase he ransmission rae in he laer wo schemes we can use higher order modulaion, eg, ma b bis er modulaed symbol A Orhogonal Sreading Anoher idea o eloi diversiy in he archiecures ha we have described, is o use daa sreading across he sacefrequency sub-channels [4] For sace limiaions we describe i for O-S--D only Le us consider an orhonormal mari, eg, Walsh-Hadamard mari, of size Le ci, ) i for,,- be he elemens of he i-h row Le b l ), i,, -, be a bloc of daa symbols o be ransmied hen, we aly he orhonormal ransform o generae he bloc of symbols a l i ) b l ) c i, ),,, -, i ha are ransmied by he O-S--D modulaor According o ) he ouu of he demodulaor now reads i z l ) H b l ) c i, ) w l ) Assuming nowledge i of he channel weighs, we can recover he ransmied daa symbols, for insance, wih simle coheren de-sreading ZF equalizaion) as follows * * z l ) ) / z l H H c, ) 5) desr he above rocedure does no add redundancy, ie, we ee he bi rae equal o b / bis/s I imlemens a form of sace-frequency daa sreading I is alied for diversiy eloiaion In Fig 5 we reor BER erformance for several scenarios assuming double receive diversiy and maimal raio combining Dee erformance imrovemens are found boh in fla fading and in frequency selecive fading VIII COCLUSIOS We have roosed several S mulione archiecures whose goal is o orhogonalize he ime disersive, wih mulile ransmi anennas channel hey can be concaenaed wih ouer codes and/or direc sequence sreading S-F and O- S--D are an ineresing oion for ransmission over ulin muliuser asynchronous channels see [4]) IX REFERECES [] S Ariyavisiaul, urbo sace-ime rocessing o imrove wireless channel caaciy, IEEE rans on Comm, , Augus [] G Cherubini, E Elefheriou, S Ölçer, J Cioffi, Filer ban modulaion echniques for very high-seed digial subscriber lines, IEEE Commun agazine, 98-4, ay [3] G Foschini, Layered sace-ime archiecure for wireless communicaion in a fading environmen when using muli-elemen anennas, Bell Labs ech Journal, 4-59, Auumn 996 [4] S Kaiser, "OFD code division mulileing in fading channels", IEEE rans Comm, 66-73, Augus [5] I Lee, A Chan, W Sundberg, Sace-ime bi-inerleaved coded modulaion for OFD sysems in wireless LA alicaions, IEEE Proc ICC 3, , ay 3 [6] Z Liu, Y Xin, G Giannais, Sace-ime frequency coded OFD over frequency selecive fading channels, IEEE rans Signal Proc, , Ocober [7] V aroh, H Jafarhani, A R Calderban, Sace-ime bloc coding for wireless communicaions: erformance resuls, IEEE Journal Selec Areas Comm, vol 7, 45-46, arch 999 [8] V aroh, Seshadri, A R Calderban, Sace-ime codes for high daa rae wireless communicaion: erformance crierion and code consrucion, IEEE rans Info heory, , arch 998 [9] A onello, Sace-ime bi-inerleaved coded modulaion wih an ieraive decoding sraegy, Proc of IEEE VC Fall, Boson, , Seember [] A onello, Performance of sace-ime bi-inerleaved codes in fading channels wih simlified ieraive decoding, Proc of IEEE VC-- Sring, Rhodes, ay [] A onello, Array rocessing for simlified urbo decoding of inerleaved sace-ime codes, Proc of IEEE VC--Fall, Alanic Ciy, 34-38, Ocober [] A onello, IO AP equalizaion and urbo decoding in inerleaved sace-ime coded sysems, IEEE rans on Comm, 55-6, February 3 [3] A onello, Asynchronous mulicarrier mulile access: oimal and suboimal deecion and decoding, Bell Labs ech Journal vol 7 n 3, 9-7, February 3 [4] A onello, A concaenaed mulione mulile anenna scheme for muliuser ulin communicaions, Proceedings of IG Worsho on Smar Anennas, unich, arch 4 77