Multicode DS-CDMA With Joint Transmit/Receive Frequency-domain Equalization

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1 Muliode DS-CDMA Wih Join Tanmi/Reeive Fequeny-domain Equalizaion Kazuki TAKEDA iomihi TOMEBA and Fumiyuki ADACI Dep. of Eleial and Communiaion Engineeing, Gaduae Shool of Engineeing, Tohoku Univeiy 6-6-5, Aza-Aoba, Aamaki, Aoba-ku, Sendai, JAPA {kazuki, Aba Bi eo ae (BER pefomane of muliode dieequene ode diviion muliple ae (DS-CDMA in a fequeny-eleive hannel eveely degade due o ong ine-hip inefeene (ICI. Fequeny-domain equalizaion (FDE baed on he minimum mean quae eo (MMSE ieion an ake advanage of he hannel fequeny-eleiviy and ignifianly impove he BER pefomane. oweve, he pefomane impovemen i limied by he eidual ICI whih i peen afe MMSE-FDE. In hi pape, we apply a join anmi/eeive MMSE-FDE (alled double MMSE-FDE in hi pape fo muliode DS-CDMA ignal anmiion o fuhe impove he BER pefomane. We deive he ondiional BER fo he given hannel ealizaion and evaluae he ahievable aveage BER pefomane by Mone-Calo numeial ompuaion mehod. The BER pefomane i onfimed by he ompue imulaion. Keywod-omponen; FDE, DS-CDMA I. ITRODUCTIO Boadband wiele hannel ompie many popagaion pah having diffeen ime delay [. Thi eul in a evee fequeny-eleive fading hannel. In he hid geneaion mobile ommuniaion yem, die-equene ode diviion muliple ae (DS-CDMA uing oheen ake ombining i ued [. Coheen ake ombining an ahieve he pah diveiy and impove he bi eo ae (BER pefomane in a modeaely fequeny-eleive hannel. oweve, a he hip ae ineae, he hannel fequeny-eleiviy ge onge, poduing evee ine-hip inefeene (ICI, and he bi eo ae (BER pefomane ignifianly degade. The ue of imple one-ap fequeny-domain equalizaion (FDE baed on he minimum mean quae eo (MMSE ieion an ignifianly impove he BER pefomane of nonpead ingle-aie (SC ignal anmiion and DS- CDMA ignal anmiion [3,. Refeene [ eview oneap MMSE-FDE fo DS-CDMA ignal anmiion. Replaemen of ake ombining by MMSE-FDE edue he ICI and hene ignifianly impove he BER pefomane ompaed o ha wih oheen ake ombining. oweve, he pefomane impovemen i limied by he eidual ICI afe MMSE-FDE [5. Reduing he eidual ICI an fuhe impove he BER pefomane. One appoah o edue he eidual ICI i o inodue an ieaive ICI anellaion ehnique [6-8. The eidual ICI eplia i geneaed uing he log-likelihood aio (LLR and i ubaed fom he eeived ignal. In hi pape, we ake anohe appoah o edue he eidual ICI. One-ap FDE i joinly ued a boh he anmie and eeive. In [9, a join anmi/eeive FDE wa popoed fo SC anmiion, whee he anmi and eeive FDE weigh ae opimized uing an adapive algoihm. Sine he anmi and eeive FDE weigh inea eah ohe, i i quie diffiul if no impoible o heoeially deive an opimal e of anmi and eeive FDE weigh in he loed fom. In hi pape, we peen a ubopimal e of anmi and eeive FDE weigh baed on he minimizaion of he oal mean quae eo (MSE of he eeived DS-CDMA hip blok afe eeive MMSE fileing. We deive he ondiional BER of DS-CDMA uing join anmi/eeive MMSE-FDE (alled double MMSE-FDE in hi pape fo he given hannel ealizaion. The ahievable aveage BER pefomane i evaluaed by Mone-Calo numeial ompuaion mehod uing he deived ondiional BER and ompaed wih ha of onvenional eeive MMSE-FDE (alled ingle MMSE-FDE in hi pape. The ahievable BER i onfimed by he ompue imulaion. The e of hi pape i oganized a follow. Seion II peen he yem model. The MMSE weigh maix fo double MMSE-FDE i peened in Se. III. Seion IV deive he ondiional BER expeion. The BER pefomane i diued in Se. V. Seion VI onlude hi pape. II. SYSTEM MODEL Figue illuae he anmiion yem model of DS- CDMA uing double MMSE-FDE. Thoughou hi pape, hip-paed diee-ime ignal epeenaion i ued. I i aumed ha he pefe hannel ae infomaion (CSI i available a boh he anmie and eeive. Daa ymbol blok CP-emoval S/P Speading ode u ( -poin FFT Sambling ode ( Reeive FDE weigh W (k x -poin IFFT -poin FFT Tanmi FDE weigh W (k (a Tanmie Copy (b Reeive Depeading { ( u (} * Fig. Tanmiion yem model. x -poin IFFT Σ P/S CP-ineion Deiion vaiable A. Tanmie A he anmie, an infomaion bi equene i anfomed ino a daa-modulaed ymbol equene, whih i eial-o-paallel (S/P onveed ino U paallel eam {d u (i; i=,,,, }, u=~u. Then, eah eam i pead uing an ohogonal peading ode wih peading fao SF { u (; =~SF}, u=~u. U hip equene ae ummed up

2 o fom he muliode hip equene, whih i fuhe muliplied by a amble ode { (; =,,,, } o obain he muliode DS-CDMA hip blok. The eulan hip blok an be expeed uing he veo fom a x=[x(,, x(,, x( T, whee x( i given a U ( / SF x ( = d ( mod ( u= u u SF. ( The hip blok x i anfomed by uing an -poin FFT ino he fequeny-domain ignal X=[X(,, X(k,, X( T a X = Fx, ( whee F i an FFT maix given a ( ( ( π π j j = e e F. (3 (( j π (( j π ( e e One-ap anmi FDE i aied ou a S = C W X, ( whee W =diag{w (,, W (k,, W ( } i an diagonal anmi FDE weigh maix. C i he anmi powe nomalizaion fao, whih i inodued o keep he aveage anmi powe ina, and i given a C = / [. (5 An -poin IFFT i applied o S o obain he anmi ignal =[(,, (,, ( T =F S. Afe he ineion of g -ample CP ino he guad ineval (GI, he ignal blok i anmied. B. Reeive The popagaion hannel i aumed o be an L-pah fequeny-eleive blok fading hannel. The omplex-valued pah gain and ime delay of he lh pah ae denoed by h l and τ l, l=~l, epeively. The CP-lengh i aumed o be equal o o longe han he maximum hannel ime delay τ L. The eeived ignal blok =[(,,(,, ( T afe he CP-emoval an be expeed a E / T h + n, (6 = whee E and T ae he aveage anmi hip enegy and hip duaion, epeively, h i an iulan hannel maix given by h hl h h h hl h =, (7 hl h hl h and n=[n(,, n(,, n( T i he noie veo wih eah elemen n( being a zeo-mean addiive whie Gauian noie (AWG having vaiane /T ( i he one-ided noie powe peum deniy. An -poin FFT i aied ou on o obain he fequenydomain eeived ignal R=[R(,, R(k,, R( T a R F = E /T C W X +, (8 = whee =Fn and =FhF. Due o he iulan popey of h, he hannel gain maix =FhF i diagonal. The (k, kh elemen of i given by L l= l ( k = h exp( jπkτl /. (9 One-ap eeive FDE i aied ou a X = W R, whee W =diag{w (,, W (k,, W ( } i an diagonal eeive FDE weigh maix. Then, an -poin IFFT i aied ou on X o obain he equalized DS-CDMA hip blok x =[ x (,, x (,, x ( T a x = F X = E / T C F W W X + F W. ( Finally, depeading i applied o x o obain he deiion vaiable d u ( i fo d u (i a d ( i = (/ SF ( mod SF. ( u III. ( i + SF * * x( ( = isf u TRASMIT AD RECEIVE FDE WEIGTS A. Toal Mean Squae Eo (MSE The elaive eo veo e=[e(,, e(,, e( T beween he anmi hip blok x and he eeived hip blok x i defined, imila o Ref. [, a x E / T C x e =. ( E /( T [ E( xx C The oal MSE i given, uing Eq. ( and (, a e( W, W = [ E( ee = [( W W I( W W I + (( U / SF( E / [ W W [ W W (3, whee E i he aveage anmi ymbol enegy. B. Tanmi and Reeive MMSE-FDE Weigh Maie A onaenaion of he anmi FDE W and he popagaion hannel an be viewed a an equivalen hannel W. The MMSE oluion o he eeive FDE weigh maix an be deived fom Eq. (3 a W = [ + (/ (( U / SF( E / ( [ I. Subiuing Eq. ( ino Eq. (3 and epeening (/ ((U/SF(E / by Ω give e( = Ω [ (5 [( + Ω [ I, whih how ha he oal MSE i a funion of W W. Sine e(w i a onvex funion of W (k, k=~, he global

3 opimum oluion ha minimize Eq. (5 unde he anmi powe onain an be found. Le u inodue a powe onain ondiion [W W =. The opimaliy ondiion an be expeed a min. e( (6.. [ =, whoe oluion aifie he Kauh-Kuhn-Tuke (KKT ondiion [3-5. To deive he opimal W, fi, diagonal elemen of ae pemued in deending ode of (k, k=~, and he pemued diagonal maix i defined a G=diag{,,,, } (i.e., and =(q, ~, q =~. The ame odeing pemuaion a G i done o he diagonal elemen of W W and he pemued diagonal maix i defined a P=diag{,,,, }. Then, he opimaliy ondiion given by Eq. (6 an be ewien a min. e( P = Ω [ [( PG G + Ω [ I = Ω ( / ( ( + Ω ( P q P q G q P q (7 q = q =.. [ = and fo q = ~. Below, P =diag{p (,, P (,, P ( } epeen he global opimum oluion ha aifie he ondiion given by Eq. (7. Wihou lo of genealiy, we aume ha P ha ( m zeo diagonal elemen (<m and ha m zeo diagonal elemen. Sine e(p i a monooni deeaing funion of, ~, i an be aid ha P ( fo ~m and P (= fo m~. Lagangian funion J an be expeed a [5 J = + m { }, q q = + Ωq = + κ ψ q Ω + μ q m (8 whee κ, μ, and {ψ q ; ~ } ae he Lagange muliplie. P mu aify he KKT ondiion [3,. We obain ( J = fo ~, (9 P = P ( ( m = m ( = P (, ( P, ( P (, q = ~, ( ψ q, q = ~, (3 and ψ P ( =, q = ~. ( q Uing Eq. (8~(, we obain θm Ω Ω P ( =, ~m, (5 whee m m ( = ( Ω Ω θm = + (6 q G q G q and P (= fo m~. Afe finding he value of m ha aifie Eq. ( and (, we an find he global opimum oluion P ha aifie he opimaliy ondiion given by Eq. (7. Afe applying he onvee pemuaion o P, W W i obained a ~ = max[ θm Ω Ω ( Η,, (7 whee ~ =diag{ (,, (k,, ( }. The above join anmi/eeive MMSE-FDE i alled double MMSE-FDE (noe ha he ue of eeive MMSE-FDE i alled ingle MMSE-FDE. A een fom Eq. (7, W i a diagonal maix and heefoe, he low omplexiy popey of imple one-ap FDE i kep even wih double MMSE-FDE. IV. CODITIOAL BER When uing he above double MMSE-FDE, Eq. ( an be ewien, fom Eq. (, a x = E / T F Fx + F W, (8 whee = W W i an equivalen hannel gain maix whoe kh diagonal elemen i given by ( k =W (k(kw (k. The diagonal and off-diagonal elemen of F F podue he deied and eidual ICI omponen, epeively. The h elemen x ( of x i given a E x( = ( k x( T k = E τ + ( k x( τexp j k + n(. T π k = τ=, τ (9 Fom Eq. ( and (9, we obain he deiion vaiable d u ( i fo he ih anmi ymbol (i a d u E d ( u i = ( k du ( i + μici + μn, T (3 k = whee μ ICI and μ n denoe he eidual ICI and he noie afe he depeading, epeively. I an be een fom Eq. (3 ha d u ( i i a andom vaiable wih mean E / (/ T ( k d ( i k= u. A amble equene i ued o make he muliode DS-CDMA hip equene whie noie-like and heefoe, μ ICI an be appoximaed a a zeo-mean omplex-valued Gauian vaiable. The um of μ ICI and μ n an be eaed a a new zeo-

4 mean omplex-valued Gauian noie μ. The vaiane of μ i given by σ = E[ μ + E[ μ μ ICI = SF T n k = W ( k (3 U E ( + ( k k. SF k = k = The ondiional BER uing QPSK daa modulaion fo he given hannel ealizaion an be given a p b ( E,.5 ef[ (/ γ( E /, / whee [ x = ( / π exp( =, (3 ef d x i he omplemenay eo funion and γ(e /, denoe he ondiional ignal-o inefeene plu noie aio (SIR, given a E ( k E k = γ, = U E + W ( k = SF k ( k ( k k = k =. (33 The ahievable aveage BER an be numeially evaluaed by aveaging Eq. (3 ove poible ealizaion of. V. PERFORMACE EVALUATIO An L=6-pah fequeny-eleive blok Rayleigh fading having exponenially deaying powe delay pofile wih deay fao α (db i aumed. A blok anmiion uing =56 and g =3 i onideed. The peading fao i e o SF=56. QPSK i ued. Ideal hannel eimaion i aumed. A. One ho obevaion of he equivalen hannel Figue how one ho obevaion of he equivalen hannel een afe eeive MMSE-FDE (i.e., W (k(kw (k fo ingle MMSE-FDE and double MMSE-FDE when he anmi E b / (=.5(SFE / (+ g / =8dB and α=db. The double MMSE-FDE edue ampliude vaiaion in he equivalen hannel W (k(kw (k ompaed o hoe in he oiginal hannel (k when U=56, a een in Fig. (a. The ampliude of W (k given by Eq. (7 dop a ome fequenie. oweve, he fequeny-eleiviy of he equivalen hannel an be made weake by uing he double MMSE-FDE. A he ode muliplexing ode U deeae, he oal enegy of he anmi hip blok [xx / edue fo he fixed anmi E b /. Theefoe, mo of he oal enegy end o be alloaed o he fequenie having a good ondiion by uing he double MMSE-FDE and heefoe, he eeived ignal-o-noie powe aio (SR impove. Equvialen hannel gain ampliude Equvialen hannel gain ampliude Equvialen hannel gain ampliude.e+.e- QPSK, E b / =8dB, SF=56, U=56.E Fequeny index, k.e+.e- (a U=56 SF=56, U=6, QPSK, E b / =8dB.E Fequeny index, k.e+.e- QPSK, E b / =8dB, SF=56, U= (b U=6.E Fequeny index, k ( U= Fig. Equivalen hannel. B. BER Pefomane The ahievable aveage BER pefomane i evaluaed by Mone-Calo numeial ompuaion mehod. The e of pah gain {h l ; l=~l} i geneaed and he ondiional BER fo he given aveage anmi E / i ompued uing Eq. (3. The aveage BER i obained by aveaging he ondiional BER ove all poible hannel ealizaion. Figue 3 ompae he BER pefomane of DS-CDMA uing ingle and double MMSE-FDE a a funion of E b /. The ompue imulaion eul ae alo ploed o onfim he validiy of ou analyi baed on he Gauian appoximaion of ICI. A faily good ageemen beween he numeially ompued and ompue imulaed eul i een. The double MMSE-FDE povide bee BER pefomane han ingle MMSE-FDE iepeive of he degee of he hannel fequeny-eleiviy. When U=56, he eidual ICI afe he eeive MMSE- FDE i a pedominan aue of BER degadaion. In hi ae, ine double MMSE-FDE fuhe edue he hannel gain vaiaion ompaed o ingle MMSE-FDE (ee Fig. (a, he eidual ICI afe he eeive MMSE-FDE i fuhe uppeed. Theefoe, bee BER pefomane an be ahieved by double MMSE-FDE han by uing ingle MMSE-FDE. A U deeae, he noie afe he eeive MMSE-FDE beome a pedominan aue of BER degadaion. In hi ae, double

5 MMSE-FDE alloae mo of anmi powe o he fequenie having a good ondiion o impove he eeived ignal-o-noie powe aio (SR. Theefoe, double MMSE- FDE povide bee BER pefomane han ingle MMSE- FDE. Aveage BER Aveage BER.E-.E-.E-3.E- α=db, QPSK, SF=56.E-5 umeial.e E-.E-.E-3.E-.E-5 Aveage anmi E b / (db (a α=db α=6db, QPSK, SF=56 umeial Simulaed U= E Aveage anmi E b / (db (b α=6db Fig. 3 BER pefomane ompaion. Simulaed U= C. Impa of ode muliplexing ode, U Figue plo he equied E b / of double MMSE-FDE fo ahieving BER= 3 a a funion of ode muliplexing ode U when SF=56. Fo ompaion, he equied E b / of ingle MMSE-FDE i alo ploed. Fo U=56, double MMSE-FDE edue he equied E b / ompaed o he ingle MMSE-FDE by abou.db (.5dB when α=db (6dB. Alo, i i obviou ha double MMSE-FDE an ignifianly edue he equied E b / fo a low value of U. An E b / eduion of.db (.7dB i ahieved when α=db (6dB when U=. Requied E b / fo ahieving BER= QPSK, SF=56 α=6db α=db Code muliplexing ode, U Fig. Impa of ode muliplexing ode, U. VI. COCLUSIO In hi pape, we evaluaed he BER pefomane of DS- CDMA uing double MMSE-FDE. A ubopimal e of anmi and eeive one-ap MMSE-FDE weigh maie wa peened baed on he minimizaion of he oal MSE. Fo a lage oal anmi hip enegy, he anmi MMSE-FDE an edue he vaiaion of he equivalen hannel (kw (k and an uppe he ICI. On he ohe hand, fo a mall oal anmi hip enegy, mo of he enegy i alloaed o he fequenie having a good hannel ondiion and an impove he eeived SR. The aveage BER pefomane wa numeially evaluaed uing he deived ondiional BER expeion o how ha he double MMSE-FDE an ignifianly impove he BER pefomane. In hi pape, i wa aumed ha he CSI i available a boh anmie and eeive. Thee have been many udie on he CSI eimaion a he anmie [,. ow he impefe CSI affe he ahievable BER pefomane by he popoed join anmi/eeive MMSE-FDE i an impoan fuue udy. REFERECES [ J. G. Poaki, Digial Communiaion, h ediion, MGaw-ill,. [ F. Adahi, M. Sawahahi, and. Suda, Wideband DS-CDMA fo nexgeneaion mobile ommuniaion yem, IEEE Commun. Mag., Vol. 36, o. 9, pp , Sep [3 D. Falone, S. L. Aiyaviakul, A. Benyamin-Seeya, and B. Eidon, Fequeny domain equalizaion fo ingle-aie boadband wiele yem, IEEE Commun., Mag., Vol., o., pp , Ap.. [ F. Adahi, D. Gag, S. Takaoka, and K. Takeda, Boadband CDMA ehnique, IEEE Wiele Commun., Mag., Vol., o., pp. 8-8, Ap. 5. [5 Kazuaki Takeda and F. Adahi, Bi eo ae analyi of DS-CDMA wih join fequeny-domain equalizaion and anenna diveiy eepion, IEICE Tan. Commun., Vol. E87-B, o., pp. 99-3, O.. [6 S. Tomain and. Benvenuo, Ieaive deign and deeion of a DFE in he fequeny domain, IEEE Tan. Commun., Vol.53, o., pp , ov. 5. [7 R. Dini, R. Kalbai, D. Falone, and A.. Banihahemi, Ieaive layeed pae-ime eeive fo ingle-aie anmiion ove evee ime-dipeive hannel, IEEE Commun. Le., Vol. 8, o. 9, pp , Sep.. [8 K. Takeda and F. Adahi, Fequeny-domain inehip inefeene anellaion fo DS-CDMA downlink anmiion, IEEE Tan. Veh. Tehnol., Vol. 56, o. 3, pp. 86-9, May 7. [9 Y. Xiaogeng, O. Mua, and Y. Akaiwa, Ieaive join opimizaion of anmi/eeive fequeny-domain equalizaion in ingle aie wiele ommuniaion yem, Po. IEEE 68h Veh. Tehnol. Conf. (VTC, pp. -5, Canada, Sep. 8. [ Y. Zhu and K. B. Leaief, Fequeny domain pe-equalizaion wih anmi peoding fo MIMO boadband wiele hannel, J. Sele. Aea in Commun., Vol. 6, o., pp. 389-, Feb. 8. [ L. Sanquinei, I. Coovi, and M. Moelli, Channel eimaion fo MC- CDMA uplink anmiion wih ombined equalizaion, J. Sele. Aea in Commun., Vol., o. 6, pp , Jun. 6. [ F. Adahi, K. Takeda, and. Tomeba, Fequeny-domain peequalizaion fo muliode die equene pead peum ignal anmiion, IEICE Tan. Commun., Vol. E88-B, o. 7, pp , July 5. [3 W. Kauh, Minima of funion of eveal vaiable wih inequaliie a ide onain, M.S. Dieaion. Dep. of Mahemai, Univ. of Chiago, Chiago, Illinoi, 939. [. W. Kuhn and A. W. Tuke, onlinea pogamming, Po. of nd Bekeley Sympoium, pp. 8-9, Univ. of Califonia Pe, 95. [5 J. L. olinge, Digial ommuniaion ove fixed ime-oninuou hannel wih memoy, wih peial appliaion o elephone hannel, M.I.T. Lab., Eleon. Rep., Vol. 3, p. 6, 96.