Research on Efficient Turbo Frequency Domain Equalization in STBC-MIMO System

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1 Research o Effcet urbo Freuecy Doma Eualzato SBC-MIMO System Wau uag Bejg echology ad Busess Uversty Bejg R. Cha Abstract. A effcet urbo Freuecy Doma Eualzato FDE based o symbol-wse mmum mea-suare error MMSE flterg s roosed for a ovel sace-tme bloc code SBC MIMO system. he trasmtter seds a searate data bloc va SBC usg two ateas er grou to get dversty ga. he recever ca effectvely utlze ter-atea terferece IAI ad ter-symbol terferece ISI followed by freuecy doma eualzato to rocess soft terferece cacellato SIC. After freuecy doma flterg e symbol Log-lelhood rato LLRs calculated from e oututs of eualzer s as e uts of e soft- soft-out SISO decoder. Smulato results show at our roosed scheme rovdes a furer substatal ga whle ot creasg comlexty at e recever. Keywords: MIMO; MMSE; sgle carrer; SBC; urbo FDE. Itroducto I s aer we develo a teratve detecto ad decodg algorm of SC-FDE based o [] for a ovel SBCMIMO wreless system. he recever ca effectvely utlze ter-atea terferece IAI ad ter-symbol terferece ISI followed by freuecy doma eualzato to rocess soft terferece cacellatosic ad symbol Log-lelhood rato LLR s calculated as e uts of e soft- softout SISO decoder usg e oututs of eualzer. So t ca realze teratve chael eualzato ad chael decodg at each terato. heory aalyss ad smulato results bo show at our roosed algorm ca mrove e system erformace remarably comared w geeral MIMO system. System Overvew Wau uag female master ayag ea rovce lecturer. Research drecto: Comuter Alcato etwor ecoomc maagemet. el: E-mal: huagw@.btbu.edu.c hs wor was suort by a grat from Research Fud for Youg Scholars I Bejg echology ad Busess Uversty.R.ChaO. QJJ0-6 Bejg hlosohy ad socal scece lag rojects.r.chao. JGB08 ad he Geeral rogram of Bejg Mucal Educato Commttee.R.ChaO.SM000008research result of stage. CCA 03 ASL Vol SERSC 03 07

2 roceedgs he d Iteratoal Coferece o Comuter ad Alcatos We defe at t x =... ; t = v v + ; v =0... s e t bloc sgal o e stream before sace-tme bloc codg. After trasferrg each sgal bloc to freuecy doma by -ot Fast Fourer rasform FF corresodg sgal s t t X x = s e t bloc sgal o trasmtted atea atea o e stream after beg ecoded accordg to SBC rcle. Where t t t t x = x x... x t t t t X = X... X X t t t t x = x... x x t t t+ t+ Bloc-wse SBC rcle s show as x = x x = x t t+ t+ t x = x x = x e At e recever after dscardg e C e tme doma sgals o t bloc ca be exressed as freuecy doma sgal s R atea for t r = Qad e corresodg receved t t t t.where t r = r r... r t t t t R = R R... R I order to exress clearly we defe t t+ t t+ Let E [ e e e ] x x x... x x = X = X X X X R = R R R R =... t t+ t t+... t t+ t t+... Q Q = where e deotes e ut vector at ca get freuecy doma sgal at e =0 - toe ca be wrtte as R = E F x+ Z = X + Z 5 Where = Q Q... Q Q Q Q... Q Q 3 Freuecy Doma MMSE urbo Eualzato We descrbe t t+ t t+ x= x x... x x x x... x = A. Soft ISI ad IAI Cacellato he estmate of e desred symbol ca be roduced by a freuecy doma MMSE flter after e ISI ad IAI cacellato e freuecy doma. We assume e symbol o e atea x =... ; =... s e desred

3 Research o Effcet urbo Freuecy Doma Eualzato SBC-MIMO System symbol. I e aer e exected IAI ad ISI for x ca be reseted as α α = E F x 6 β resectvely ˆ = E F xˆ β 7 ˆ xˆ = Where 0 x x x+ x 8 xˆ = 0 0 xˆ 00 0 ˆ ˆ ˆ xˆ ˆ = x ˆ x 0 x + x after SIC e sgal e freuecy doma at toe s wrtte as Y = R α β = E F xx x + Z ˆ ˆ ˆ ˆ = E F x x + Z Cosderg all freuecy toes e soft terferece cacellato model ca be exressed as follows Y = R = F x xˆ + Z α β 0 After soft terferece cacellato sgal to terferece lus ose rato SIR of sgal Y has bee mroved comared w orgal receved data. he freuecy doma MMSE eualzato s mlemeted whle soft terferece s gored terato zero sce ere s o ror formato. B. Effcet Freuecy Doma MMSE Flterg Symbol-wse MMSE crtero ca be wrtte as order to detect e desred symbol { } m x. E D Y x D = arg D { } E DY x Y = Accordg to e orogoalty rcle we have he 0 s substtuted to w a assumto at ere s o correlato betwee data symbols ad AWG. 0 { } D { } { } D F E xxˆ x xˆ F + E ZZ E x x xˆ F = 0 3 We assumed at e symbols are deedet ad e ror formato about e x desred symbol should ot be used e evaluato e we have 4 E x ˆ x x =Φ = 0 0 σ s 0 0 = σ s e { } = + { ˆ ˆ } { =Γ ϒϒ ϒ ϒϒ ϒ} E x x x x = dag 5 + where ϒ j = dag { ϒ j ϒ } j ϒ j j ad ϒ j m s varace of symbol xj 9 ad 09

4 roceedgs he d Iteratoal Coferece o Comuter ad Alcatos o e bass of ror formato from decoder. τ = dag ϒ ϒ ϒ σ ϒ + ϒ ad σ s e symbol eergy. { } s cov m m m x x ϒ = 6 j j j =Φ F F Γ F + σ I 7 Fally we obtaed D s Q C. Extrsc LLR Calculato After eualzato e estmate of tme doma symbol x ca be obtaed by IFF = = + = + xˆ D Y D F x xˆ Z D F e x xˆ xˆ D Z 8 I 8 we ca see at e frst term s e exected symbol multled by a factor e secod term s e resdual terferece from oer ateas ad symbols e rd term s AWG. As e terato cotue e ror formato becomes more ad more exact. So a assumto s made [9] at e outut of MMSE eualzer has udergoe a euvalet Gaussa chael φ λ x = x + 9 ˆ he e soft-ut soft-outut decoder ca utlze extrsc formato from eualzer whch s treated as e ror formato to calculate extrsc LLR accordg to e exectato ad varace of eualzed data symbol. As descrbed x ca be comuted [3] exectato µ = D F e 0 σ s wrtte as σ ˆ ˆ reew x µ x x µ σ s Varace he fucto of reew. s to reew = as a orgal modulated symbol. he extrsc LLR for e symbol ca be obtaed xˆ µ Le x = σ D. Low Comlexty Imlemetato As e eualzato s rocessed based o symbol-wse t s hard to mlemet due to e comlexty. Cosderg at e dagoal elemets of e freuecy doma Θ = F Γ 7 are costat w e same value F covarace matrx ω j = γ j j 3 = he off-dagoal elemets ca be gored because e dagoal elemets s larger a e off-dagoal elemets. herefore we aroxmate ω = γ 4 = s 0

5 Research o Effcet urbo Freuecy Doma Eualzato SBC-MIMO System After smlcato Θ = dag { ω I ω I νi ω I ω I } 6 + Accordgly eualzer coeffcets are gve by D =Φ F Θ + σ I 7 Q s 4 Smulato Results he BER erformace of our roosed turbo eualzato algorm for SBC- MIMO system s showed Fg.. It s obvous at our roosed teratve eualzer acheves sgfcat erformace comared w e tradtoal o-teratve oes esecally uder well chael codto. As e terato tmes creases e erformace of e roosed system s better but e teratve gas become comaratvely smaller esecally after 3 teratos. Fg.. BER erformace of our roosed eualzer for SBC-MIMO 5 Cocluso I s aer we roose a ovel urbo FDE based o symbol-wse detecto for sgle carrer SBC-MIMO system. he trasmtter ateas double to get dversty ga wout creasg recevg ateas. hs algorm ca effectvely utlze ter-atea terfereceiai ad ter-symbol terfereceiai followed by freuecy doma eualzato to rocess soft terferece cacellatosic. Smulato results have show at our roosed algorm acheves better BER erformace comared to bo e tradtoal o-teratve oes ad oes w geeral MIMO system. Refereces. Baoj L Zhfeg Rua ad Yogyu Chag Effcet urbo Freuecy Doma Eualzato Based o Symbol-Wse Detecto IEEE Iteratoal Coferece o Commcatos 08 to be ublshed.. A. Dejoghe ad L. Vadedore urbo-eualzato for multlevel modulato: a effcet low-comlexty scheme IEEE ICC 0 May C M. uchler ad J. ageauer Lear tme ad freuecy doma turbo eualzato IEEE VC 0 May C453