Turbo Coded MIMO Multiplexing with Iterative Adaptive Soft Parallel Interference Cancellation

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1 Turbo Coe MIMO Mulplexg wh Ierave Aapve Sof Parallel Ierferece Cacellao Akor akaja, eepshkha Garg, a Fuyuk Aach ep. of Elecrcal a Coucaos Egeerg Tohoku Uversy, Sea, Japa akaja@oble.ece.ohoku.ac.jp Absrac Ierave aapve sof parallel erferece caceller (ASPIC) s propose for urbo coe ulple-pu ulpleoupu (MIMO) ulplexg. ASPIC s apple o rasfor a MIMO chael o sgle-pu ulple-oupu (SIMO) chaels for axu rao versy cobg (MRC). I he erave ASPIC, replcas of he erferece fro ffere ras aeas are geerae a subrace fro he receve sgals. The log-lkelhoo rao (LLR) sequece obae as he urbo ecoer oupu s feback for erave erferece cacellao. A he raser, he forao b sequeces a pary b sequeces are rase fro ffere aeas. The achevable b error rae (BER) perforace of he urbo coe MIMO ulplexg wh he propose erave ASPIC a Raylegh fag chael s evaluae by copuer sulao. Keywors- MIMO ulplexg, Ierave ASPIC, Turbo cog, Log-lkelhoo rao I. ITROUCTIO Recely, here have bee reeous eas for hghspee aa rasssos oble coucaos []. However, he avalable bawh s le, so hgher specru effcecy s requre. Oe of he prosg echques s he ulple-pu ulple-oupu (MIMO) syse [], [3] ha uses ulple ras a receve aeas. Oe such echque o prove hgh spee aa whou requrg aoal bawh s space vso ulplexg [4], [5]. I such MIMO ulplexg, ras aa sequece s rasfore o parallel sequeces a each sequece s rase fro a ffere ras aea a he sae e wh he sae carrer frequecy. Therefore, he oal rassso rae creases proporo o he uber of ras aeas. A he recever, s ecessary o separae he sgals rase fro ffere aeas. Varous ehos for he separao of he rase sgals are kow, e.g., axu lkelhoo eeco (ML) [6], u ea square error (MMSE) [6], zero forcg (ZF) [6], V-Bell Laboraores layere space-e archecure (V-BLAST) [7] a so o. I oble rao coucaos, chael sae s chagg every oe. Ths pheoeo s calle ulpah fag [6]. I a ulpah fag evroe, b error rae (BER) perforace egraes rascally. Effecve echques o reuce he averse effec of fag are aea versy cobg a chael cog. Recely, urbo cog [8],[9] ha has powerful error correcg capably s he ceer of aeo. Therefore, s esrable o corporae chael cog a aea versy cobg o MIMO ulplexg for creasg he rassso aa rae whle provg he rassso perforace. I hs paper, a erave aapve sof parallel erferece caceller (ASPIC) s propose for urbo coe MIMO ulplexg. A he recever, for he geerao of sof ecso values, he MIMO chael s rasfore by ASPIC o he sgle-pu ulple-oupu (SIMO) chaels for axu rao versy cobg (MRC) [6] o reuce he effec of fag. The log-lkelhoo rao (LLR) sequece obae as urbo ecoer oupu s feback for erave erferece cacellao. A he raser, he forao b sequeces a pary b sequeces obae by urbo cog are rase fro ffere aeas. The achevable b error rae (BER) perforace of he urbo coe MIMO ulplexg wh he propose erave ASPIC a Raylegh fag chael s evaluae by copuer sulao. The reaer of hs paper s orgaze as follows. Seco escrbes he urbo coe MIMO ulplexg wh he erave ASPIC. Seco 3 preses he copuer sulae BER perforace of urbo coe MIMO ulplexg wh erave ASPIC a Raylegh fag chael. Seco 4 coclues he paper. II. MIMO MULTIPLEXIG WITH ITERATIVE ASPIC Fgure shows a rassso syse oel of (, r ) MIMO ulplexg wh erave ASPIC, where a r represe he uber of ras aeas a ha of receve aeas, respecvely. The bary forao b sequece {b ; =(I-)} of legh I (for splcy we assue ha I s a eve eger) s urbo coe o he coe sequece {x j ; j=(i/r-)} by a rae-r urbo ecoer. The urbo coe sequece afer erleavg s rasfore o parallel sequeces such ha forao (syseac) b sequeces a pary b sequeces are rase a he sae e fro ffere aeas as uch as possble. Ths esures ha he LLR of he forao bs a he recever ca be use o crease he relably of he pary bs rase a he sae e bu fro a ffere aea. Ths s furher explae eal here wh a R/ urbo coe.

2 M MRC MRC The erleave urbo coe sequece s ve o / forao (or syseac) b sequeces a / pary b sequeces by seral-o-parallel (S/P) coverso. Each sequece s rasfore o QPSK oulae sybol sequece. The forao sybol sequeces are rase fro he h( /-)h ras aeas a he pary sybol sequeces are rase fro he /h( -)h ras aeas. The sybol rase fro he h aea s eoe as. I s assue ha he sgals rase fro ras aeas experece epee Raylegh fag a are receve by r receve aeas. The sgal r receve by he h receve aea ca be expresse usg he equvale low-pass represeao as r = S ξ = _ +, () for = r -, where S s he average receve sgal power o each aea, ξ _ s he coplex ga of he fag chael bewee he h ras aea a he h receve aea, a s he ave whe Gaussa ose (AWG) process a he h receve aea, whch has a zero ea a a varace of σ /T ( s he sgle se AWG power specru esy a T s he QPSK sybol legh). ML s perfore o oupu he har ecso sybols { ; = } for he rase sybols usg he r receve sgals { r ; = r }. Whe urbo cog s use, s ecessary o geerae sof values for he pu o he urbo ecoer. I hs paper, he sof values are geerae by usg he erave ASPIC a MRC. Iforao B Sequeces aa Turbo Ecoer QPSK Mo. & Ierleaver S/P QPSK Mo. Pary B Sequeces Ierave P/S ASPIC ML MRC r (a) Traser RC Ierleaver QPSK Mo. QPSK Mo. & Sof QPSK o. (b) Recever Receve Sof QPSK eo. aa & e Ierleaver & Turbo ecoer LLR Fgure. Syse oel of (, r) MIMO ulplexg wh erave ASPIC. A. ASPIC a MRC Fgure shows he ASPIC a MRC srucure ha geeraes he sof ecso values. The su of sgals rase by aeas s receve by each of he r receve aeas (see Eq.()). I ASPIC, he sybol rase by he h aea, = -, s exrace fro he receve sgal for each receve aea. Thus, a MIMO chael s rasfore o SIMO chaels. The r sgals receve by each SIMO chael s equvale o r aea versy recepo wh sgle aea rassso. The r sgals receve by each SIMO chael are coherely cobe usg MRC o geerae he sof value eee for urbo ecog. The operao prcple of ASPIC s escrbe below. Usg he har ecso sybol oupus { ; = -} of ML, he ASPIC geeraes he replcas of erferece a perfors he parallel erferece cacellao (PIC). Whe ML s correc, har PIC excessvely subracs he erferece, so he use of har PIC creases he erferece. Therefore, he aapve sof cacellao wegh base o he ecso relably of ML s rouce. The oupu r _ fro ASPIC for he sgal rase fro he h ras aea a receve by he h receve aea ca be expresse as r _ = { r S for = r -, where esae for ξ _ a ξ S _ } + ξ _ = _, () ξ represes he chael ga s gve by = λ Re[ ] + jλ I[ ], (3) _ c _ s where λ _ c a λ _ s are he aapve sof cacellao weghs ( λ _ c a λ _ s ). The use of λ _ c = λ _ s = leas o har PIC. r _, = r -, are coherely cobe usg MRC. The MRC oupu r for he sgal rase fro h ras aea ca be expresse as r = r = r ξ, (4) where eoes he coplex cojugae operao. Afer MRC, he MRC oupus are parallel-o-seral (P/S) covere o a seral sequece a sof QPSK eoulao s perfore, followe by urbo ecog. r r r = ξ _ ξ Fgure. ASPIC a MRC. _ r _ ξ _ r _ ξ _ r ξ _ r ξ _ r ASPICMRC ξ _ r

3 B. Aapve Sof Cacellao Wegh As sae Sec.A, whe ML eeco s correc, he use of har PIC creases he erferece. Hece, aapve sof cacellao wegh s rouce o avo he crease he erferece. I s ffcul o heorecally f he opal wegh, so we ake a heursc approach base o he ecso relably of ML. Whe he ecso relably of ML s hgh (oherwse), we use a large (sall) cacellao wegh. The operao prcple s as follows. ML s carre ou o oupu he har ecso sybol vecor = [,,, ] ha zes he log lkelhoo L: = = _ L r S ξ. (5) = r The, ML fs wo caae sybol vecors, he os relable sybol vecor ha has he lowes log lkelhoo value a he seco os relable sybol vecor ha has he seco lowes log lkelhoo value, a hey are copare b-by-b. We use he followg aapve sof cacellao wegh: λ _c (λ _s, f hes () bs ) = he wo sybols are he sae exp( α L), oherwse (6) for QPSK, where L s he fferece of log lkelhoo bewee he os relable caae vecor a he seco os relable oe, a α s he aapvy paraeer ha corols he exe o whch L corbues o he cacellao wegh. C. Ierave Process I a erave process, he sof ecso forao sybol sequece s geerae fro he LLR sequece gve by he urbo ecoer, a he pary sybols are aga eece ML usg he sof ecso forao sybols. These forao a pary sybol sequeces are pu o he ASPIC aga. The ASPIC rasfors he MIMO chael o SIMO chaels, a MRC cobg s perfore aga. Below hs h erave process s explae, <. Afer he LLR sequece, obae as he urbo ecoer oupu, s chael-erleave by a erleaver, he sof ecso value ( ) of he forao sybol sequece rase by he h aea, = /-, s geerae as ( ) ( = ) _ c _ s where Ω( β Λ ) + j Ω( βλ ), (7) Ω ( x) = [ exp( x)] /[ + exp( x)]. (8) ( ) Λ ( ) Λ I Eq.(7), _ c a _ s are he LLRs of urbo ecoer oupu, obae afer he -h erao of ASPIC, ha correspo o he QPSK forao sybol (of bs) rase by he h aea a β s he paraeer whch s opze by copuer sulao. The, he / pary sybols are separae by perforg ML o oba he har ecso pary sybols { ; = / } by usg he r receve sgals. The esae pary sybols obae afer ML ca be expresse as L / ( ) ( ) = r ( _ + r S ξ _ ) = = = / ξ, (9) ( ) Afer ML s perfore, he sof ecso pary sybols, = /, are geerae by usg LLR of forao b correspog o ha pary b, as ) _ c Λ _ s ( ) Re[ ] ( ) I[ ( = Ω β Λ + j Ω β ], () where Λ _ c a Λ _ s are he LLRs of forao bs he QPSK sybol correspog o he QPSK pary sybol rase by h ras aea. These sof ecso forao a pary sybols are aga pu o he ASPIC whch aga geeraes he replcas a cacels he erferece. The oupu r _ fro ASPIC ca be expresse as r _ = { r S ξ } + = _ S ξ _, () oe ha ( ) =. The, MRC s perfore by usg Eq.(4). Afer MRC, urbo ecog s perfore. The repeo of he above process s calle erave ASPIC. For R>/, sce he uber of pary bs s less ha he uber of syseac bs, soees, oly syseac bs wll be rase fro all he aeas. Ths oes o har he ASPIC perforace, as he relably of all syseac bs ca be prove ASPIC by usg LLRs obae fro he urbo ecoer. However, for R</, he uber of pary bs s ore a soees oly pary bs wll be rase fro all ha aeas. For such pary bs, he relably cao be prove as urbo ecoer oupu cosss of he syseac-b LLR oly. III. SIMULATIO RESULTS Table shows he sulao coo. The rassso of forao b sequece of legh I=996 bs s cosere. Fgure 3 shows he srucure of he urbo ecoer. A rae-/3 urbo ecoer cossg of wo (7,5) recursve syseac covoluoal (RSC) ecoers [9] s eploye. The pu o he

4 seco RSC ecoer s he erleave verso of he forao sequece pu o he frs RSC ecoer. The eral erleaver s a S-rao ( S = I ) erleaver []. The wo pary b sequeces obae by he wo RSC ecoers are pucure o crease he cog rae o R/. The urbo coe sequece legh s -b a a 5 4-b block chael erleaver s use. MIMO chael s assue wh r epee frequecy-oselecve Raylegh fag chael, a chael esao s assue o be eal. The axu oppler frequecy f oralze by he coe b rae /T b s assue o be f T b =.. SIMO s as sall as.6b. O he oher ha, whe (, r )=(4,4), he requre E b / for average BER -4 s abou.b less ha ha whou erao, a he E b / egraao fro perfec SIMO ca be reuce by abou.b..e- Iforao B S-rao Ierleaver Fgure 3. Turbo ecoer. Traser Recever TABLE I. Turbo ecoer Syseac B RSC Pary B RSC Pary B SIMULATIO COITIO (7,5)RSC ecoer o. of aeas,4 Chael esao Turbo ecoer Oupu P/S copoe Rae / S-rao erleaver Ieal Log-MAP 9 eraos o. of aeas r,4.e-3.e-4.e-.e-3 (, r )=(,) E b / =3B = = β (a) (, r )=(,) Fg.4 plos he average BER of urbo coe (, r )MIMO ulplexg wh erave ASPIC as a fuco of β. I s assue ha α s opze all he sulao resuls. A broa opu s see β, bu he opu value s see o be β=. a.4, whe (, r )=(,) a (4,4), respecvely. Fg.5 plos he average BER perforaces of urbo coe (, r ) MIMO ulplexg wh erave ASPIC as a fuco of he average receve E b / per receve aea. Here, perfec SIMO refers o he coo whe PIC s eal. I ca be see ha ASPIC proves beer BER perforace ha har PIC. As he uber of eraos creases, he BER perforace proves, bu alos o aoal provee s see afer 4 eraos. Whe (, r )=(,), he requre E b / for average BER -4 ca be reuce by abou.7 B wh 4 eraos fro ha whou erao, a he egraao fro perfec o. = of eraos= (, r )=(4,4) 3 =3 E 4 b / =-B.E β (b) (, r )=(4,4) Fgure 4. Ipac of aapvy paraeer β o average BER.

5 .E-.E-.E-3.E-4 (, r )=(,) ASPIC (β=.) = Har PIC IV. COCLUSIO I hs paper, MIMO ulplexg wh erave ASPIC, whch rasfors he MIMO chael o SIMO chaels for MRC versy cobg, was propose. The sof ecso values eee for urbo ecog s geerae by usg he ASPIC. The achevable urbo coe BER perforace of MIMO ulplexg usg erave ASPIC was evaluae by copuer sulao assug a Raylegh fag chael. Irouco of ASPIC proves he BER perforace sgfcaly. Furher perforace provee ca be acheve by he use of erave ASPIC. For (,) or (4,4) MIMO ulplexg, he erave ASPIC ca acheve he BER perforace close o he perfec SIMO by abou.6b or.b, respecvely. Perfec SIMO.E Average receve E b / per receve aea (B) (a) (, r )=(,).E- (, r )=(4,4) ASPIC (β=.4) =.E-.E-3.E-4.E-5 Har PIC Perfec SIMO -5 5 Average receve E b / per receve aea (B) REFERECES [] F. Aach, Wreless pas a fuure-evolvg oble coucaos syses, IEICE Tras. Fuaeals, vol.e83-a, pp.55-6, Ja. [] G. J. Fosch a M. J. Gas, O Ls of wreless coucaos a fag evroe whe usg ulple aeas, Wreless Persoal Cou., vol.6, o. 3, pp , 998. [3] S. M. Alaou, A sple ras versy echque for wreless coucaos, IEEE J. Selec. Areas Cou., vol.6, o.8, pp , Oc [4] R. va ee, A. va Zels, a G. Awaer, Maxu lkelhoo ecog a space vso ulplexg syse, Proc. IEEE VTC -Sprg, vol., pp.6-, May. [5] G. J. Fosch, Layere space-e archecure for wreless coucao a fag evroe whe usg ul-elee aeas, Bell Labs. Tech. J., vol., o., pp.4-59, 996. [6] Joh G. Proaks, gal Coucaos, fourh eo, McGraw-Hll,. [7] P. W. Wolasky, G. j. Fosch, G.. Gole, a R. A. Valezuela, V-BLAST: a archecure for realzg very hgh aa raes over he rch-scaerg wreless chael, Proc. ISSSE, pp.95-3, 998. [8] C. Berrou, A. Glaveux, a P. Thajsha, ear Shao l error-correcg Cog a ecog: urbo coes, Proc. IEEE I. Cof. o Cou., pp.64-7, May 993. [9] J. P. Wooar a L. Hazo, Coparave suy of urbo ecog echques: a overvew, IEEE Tras. Veh. Techol., vol.49, o.6, pp. 8-33, ov.. [] O. F. Ackel a W. E. Rya, Pucure urbo coes for BPSK/QPSK chaels, IEEE Tras. Cou., vol. 47, o.9, pp.35-33, Sep (b) (, r )=(4,4) Fgure 5. perforaces of urbo coe (, r)mimo ulplexg wh erave ASPIC.