EXIT-Chart Aided Hybrid Multiuser Detector Design for Frequency-Domain-Spread Chip-Interleaved MC-CDMA

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1 EXIT-Chart Aidd Hybrid Multiusr Dtctor Dsign for Frquncy-Domain-Sprad Chip-Intrlavd MC-CDMA Li Xu, Rong Zhang, Shng Chn and Lajos Hanzo School of ECS., Univ. of Southampton, SO7 BJ, UK. Tl: , Fax: Abstract With th advnt of EXtrinsic Information Transfr EXIT charts, w ar capabl of analyzing, prdicting and visually comparing th convrgnc bhaviours of diffrnt turbo Multi-Usr Dtctctor s. Th diffrnt s hav divrs EXIT charactristics and hnc thir suprposition allows us to crat a combind EXIT curv, which closly matchs that of th channl dcodr. Hnc a nar-capacity opration is facilitatd by combining th bnifits of diffrnt s and thrfor to crat a suprior. Thus in this contribution, w propos a novl hybrid combining schm, which combins th advantags of a high prformanc and low complxity in form of an advancd hybrid solution. Th transmittd bits ar unnown at th rcivr, hnc it is not fasibl to dirctly valuat th mutual information gain of th itrativ in conscutiv itrations, hnc w propos a ralistic algorithm for stimating this mutual information gain, which is thn usd for activating th most appropriat constitunt as and whn it is ncssary. Th constitunt s ar th Matchd Filtr MF basd Soft Intrfrnc Cancllation SoIC and th optimum Baysian s, which ar invod in th scnario of Frquncy-Domain-Sprad Chip- Intrlavd FDSCI Multipl Carrir Cod Division Multipl Accss MC-CDMA. Th rsultant hybrid is capabl of outprforming both th MF-SoIC and Baysian turbo s in th trms of th attainabl complxity and Bit-Error-Rat BER prformanc. I. INTRODUCTION Th Frquncy-Domain-Sprad Chip-Intrlavd Multipl Carrir Cod Division Multipl Accss FDSCI MC-CDMA schm considrd may b intrprtd as th multi-carrir vrsion of th Intrlav Division Multipl Accss IDMA philosophy dvlopd by Ping t. al. []. Th IDMA schm xchangs th classic position of DSsprading and intrlaving mployd in traditional CDMA systms, lading to chip-intrlaving instad of bit-intrlaving. Hnc th diffrnt usrs ar distinguishd by thir uniqu usr-spcific intrlavrs π, as sn in Fig.. Th IDMA rcivr of [] mploys turbo-styl itrativ joint Matchd Filtr basd Soft Intrfrnc Cancllation MF-SoIC aidd Multi-Usr Dtctctor combind with channl dcoding, whr th s front-nd procssing is carrid out on a chipby-chip basis. Howvr, MF basd dtction constituts a singlusr approach, which has a limitd ability to xploit any xtrinsic information and hnc its prformanc is intrfrnc-limitd. In contrast to th low-complxity MF-SoIC, th optimal Baysian imposs an xponntially incrasing complxity as a function of th numbr of usrs. EXtrinsic Information Transfr EXIT charts [] ar capabl of analyzing th convrgnc charactristic of concatnatd turbo componnts and constitut a convnint smi-analytical prformanc visualization tchniqu. Mor xplicitly, EXIT charts valuat th mutual information of th xtrinsic output and aprioriinput of th concatnatd dcodr componnts corrsponding to th associatd bits s. Th rsultant xtrinsic and aprioriinformation xchang btwn th itrativ Soft-In Soft-Out SISO blocs is thn portrayd, as dtaild in []. Thus th diffrnt mutual information gain of th s srially concatnatd with a SISO channl dcodr may Fig.. b c coding π S b c s d coding S π L DEC b i CDc DEC L a CDc c il Ds c i L CDc c i Transmittr of CDMA Joint coding and sprading Transmittr of Chip-intrlavd CDMA L a DEC s i L DEC s i Ds π π. L d i L a d i Itrativ Rcivr of chip-intrlavd CDMA Th transcivr of chip-intrlavd CDMA. d b visualizd at ach stp of th itrativ dtction procss in th EXIT chart. Thrfor, an advancd schm combining th bnifits of diffrnt s may b cratd. Hnc th novlty of this contribution is that w propos a hybrid, which activats diffrnt s in diffrnt itrations by xploiting a low-complxity mutual information vluation tchniqu. Spcifically, th proposd hybrid schm nabls us to circumvnt th prformanc limitations of th MF-SoIC by xploiting th suprior prformanc of th Baysian during a fw itrations only. This allows us to approach th optimum Baysian s prformanc at a modstly incrasd complxity in comparison to that of th MF-SoIC. As a furthr novl fatur, w propos an algorithm for th ral-tim monitoring of th actual mutual information xchang during th procss by valuating th avrag of th LLR magnituds at th output of th. Th rmaindr of this contribution is organizd as follows. In Sction II, our systm modl is introducd, whil th EXIT chart analysis is prsntd in Sction III, which will b usd in Sction IV for studying a rang of diffrnt turbo stratgis. Our systm prformanc rsults and discussions will b prsntd in Sction V, followd by our conclusions in Sction VI. II. TRANSCEIVER STRUCTURE Th uppr part of Fig. portrays th transmittr of th systm. Assuming that BPSK modulation is adoptd hr, th th usr s /8/$5. 8 IEEE 86

2 transmittd bit stram {b i; i =,,,M} is firstly channl ncodd at a rat of R = M/N c, yilding th ncodd stram {c i; i =,,,N c}. Thn th rsultant channl ncodd stram is Dirct Squnc DS sprad by a sprading cod having a sprading gain G, which is common for all usrs, yilding th squnc {s i; i =,,,N}. This squnc is thn chip-intrlavd mploying a usr-spcific random chip-intrlavr π, in ordr to form th chip stram {d i; i =,,,N}. Th rsultant chip stram is thn transmittd through th multipl accss channl supporting K usrs. This is in contrast to th concpt of a classic CDMA systm, whr th intrlavr is btwn th FEC coding and DS-sprading stags. Th lattr classic philosophy corrsponds to bit-intrlaving, which is also sn in th uppr part of Fig.. Thn ach usr s signal is OFDM modulatd [3]. At th rcivr, aftr OFDM dmodulation th u-th subcarrir s rcivd signal in th i-th OFDM symbol is dnotd by y = Hd + ν, whr H is th K dimnsional Frquncy Domain Channl Transfr Function FDCHTF vctor corrsponding to th K usrs, whil th K usrs data vctor is dnotd by d. Furthrmor, ν is th Additiv Whit Gaussian Nois AWGN having a zro man and a varianc of σ n. III. EXIT CHART ANALYSIS EXIT charts wr proposd by tn Brin [] for analyzing th convrgnc charactristic of turbo cods as a convnint visualization tchniqu. This tchniqu computs th mutual information of th output xtrinsic and input a-priori componnts corrsponding to th associatd bits s for ach of th itrativ SISO blocs. Mor spcifically, th mutual information of th LLRs and th lgitimat bipolar BPSK bits is givn by []: I = p Lx s s {+, } [ ] p Lx s log dx, p Lx ++p Lx whr p Lx s is th conditional probability distribution of th LLRs. W can now substitut th conditional probability distribution of th xtrinsic information L and that of th a-priori information L a into Eq. in ordr to driv th mutual information btwn ithr I E or I A and th lgitimat bipolar bits, rspctivly. Th rquird distribution of th LLRs in Eq. can b approximatd by th xprimntally gnratd LLR histogram or using th ubiquitous Gaussian distribution for modling th LLR distribution. IV. TURBO S A. MF-SoIC turbo Th rcivr of Fig. consists of a Soft-In-Soft-Out SISO and a ban of K individual SISO channl DECodrs DEC, whr th soft information xchangd btwn th rcivr componnts is constitutd by th xtrinsic Log-Lilihood Ratios LLRs. At th l-th itration, th MF outputs th xtrinsic information L d basd on th channl s output, combind with th aprioriinformantion L DECd providd by th SISO DEC. Th soft stimats ˆd of th th usr s signal ar rprsntd as: whil thir varianc is givn by: Ed =tanhl DECd /, 3 Vd = Ed. 4 Whn considring usr as th usr of intrst, w hav: y = H d + ξ, 5 whr ξ = j H d + ν dnots th intrfrnc plus nois. Th soft stimats of ξ can b rprsntd as Eξ = j H Ed, 6 whil th corrsponding varianc is xprssd as : V ξ = j H Vd +σ n. 7 Assuming that th rcivd signal is Gaussian distributd around th lgitimat transmittd symbol valus, th rsultant xtrinsic information L d can b xprssd as: L d = 4R{H y Eξ}, 8 V ξ whr R dnots th ral part of a complx variabl. Th calculation of Eξ and V ξ rquirs totally 4K 3 additions and multiplications, whn considring a singl transmittd chip. B. Baysian turbo Following th first itration, th aprioriinformation concrning th lilihood of all th lgitimat N b = K numbr of BPSK modulatd K-usr bit squncs bcoms availabl. Th joint PDF of th antnna array s output y and th transmittd chip stram d j {±}, j,...,n b of usr at th output of th channl ncodr can b xprssd as th suprposition of all th conditional Gaussian PDFs positiond at th lgitimat noislss channl outputs corrsponding to th transmittd symbols d =+ and d =, multiplid by th j-th lgitimat signal vctor s probabilitis, rspctivly, which can b xprssd as [4]: P y, d = ± = P d j j:d j =± y ȳ j σn. 9 ThntirstofN b = K numbr of lgitimat vctors of th K usrs is partitiond into two substs corrsponding to d =+ and d =. In Eq.9, ȳ j, j,...,n b constituts th noislss rcivd signal vctors, whr th Gaussian PDFs sn in Eq.9 ar cntrd. Th Euclidian distanc masurd from thir noislss cntr to th rcivd signal vctor is usd as th mtric of quantifying thir corrsponding probability. Furthrmor, P d j is th a-priori information to b dfind mor xplicitly blow. All th othr notations ar dfind as bfor. Providd that th chips of all th K usrs ar indpndnt, th probability P d j can b xprssd as : P d j = K = P d j,j,...,n b, whr P d j rprsnts th probabilitis of ithr P dj =or P d j =, dpnding on th l-th usr s bit at th j-th bit position, j,...,n b = L within th K-usr transmittd chip vctor, which is th a-priori information providd by th -th usr s SISO dcodr. Lt us us th conditional lilihood of th rcivd signal vctor as that of th stimatd bit dcision concrning th th usr s transmittd 87

3 .8.8 I,Ia DEC.6.4 Switch from Baysian bac to SoIC Switch from SoIC to Baysian IσLLR.6.4. Hybrid Trajctory Baysian SoIC NSC+Sprading I a,i DEC Fig.. Exit charts and simulatd trajctoris of th proposd hybrid whn supporting K =usrs at E b /N =db.. Iσ LLR I =.3σ LLR.3 σ LLR Fig. 3. Th mutual information I function of σ LLR and its linar approximation bit. Thn w hav: L d =ln P d =+ y P d = y ln P d =+ P d = =ln l j:d j =+ l:l P dj l j:d j = l:l P dj y ȳ j σ n y ȳ j. σn This will lad to th maximum-lilihood solution. Furthrmor, th complxity of th Baysian turbo can b rducd by mploying th tchniqus proposd in [5]. Th complxity of th abov-mntiond Baysian is constitutd by K K additions and multiplications rquird for computing th lgitimat channl output stats ȳ j, j,...,n b and 7 K additions of th Gaussian PDFs, plus th K xp function valuations sn in Eq., whn considring a singl transmittd chip. Hnc, w can approximat th total complxity of th Baysian as K 4K +6oprations. C. Hybrid Turbo Dsign Fig. portrays th EXIT curvs of both th SoIC aidd MF and of th Baysian s, whn supporting K = usrs with th aid of 4-chip Frquncy-Domain FD sprading squncs at E b /N =db. At th abscissa valu of unity, th EXIT curvs of both constitunt s convrg to th sam point, coinciding with that rcordd for a singl usr. This rvals that th multipl accss intrfrnc MAI is compltly liminatd by both th s, providd that prfct aprioriinformation is availabl. At th abscissa of zro, th Baysian turbo s EXIT curv xhibits a highr starting point than that of th MF-SoIC and provids a significantly widr EXIT tunnl, albit this is achivd at a cost of trmndously incrasd computational complxity. By contrast, th MF-SoIC rsults in rducd I valus in th EXIT chart at a significantly rducd complxity rquirmnt. Gnrally, if thr is an opn tunnl btwn th EXIT curv of th and that of th channl dcodr, th MF-SoIC would impos a lowr complxity than th Baysian turbo, whn aiming for achiving a nar-singl-usr prformanc. This implis that th MF- SoIC should b activatd instad of th mor complx Baysian, whn th formr is also capabl of achiving a sufficintly high th itration gain. Howvr, at a low SNR valu, thr may not b a sufficintly widly opn convrgnc tunnl whn using th MF- SoIC, but it may still b opn whn using th Baysian, as sn in Fig.. Our novl proposition is to us th MF-SoIC during th first a fw itrations and subsquntly to activat th Baysian for a fw furthr itrations to avoid ncountring th bottlnc rgion of th MF-SoIC. Byond th EXIT-chart s bottl-nc rgion w may thn safly activat again th MF-SoIC. As an xplicit bnfit, th proposd Hybrid bcoms capabl of achiving a similar prformanc to that of th Baysian at a dcrasd complxity in comparison to th convntional mthod, sinc th Baysian is only activatd during th critical itrations. In ordr to dtrmin th activation instant of th diffrnt s, w hav to monitor th mutual information gain btwn th s and th channl dcodr, as shown in Fig.. If th mutual information improvmnts ar monitord at th rcivr, thn it is intuitiv that th MF-SoIC should b activd whn its EXIT curv is abov that of th channl dcodr, whil th Baysian should b activatd whn th EXIT curv of th MF-SoIC is blow that of th channl dcodr. Howvr, in practic th nowldg of th mutual information is gnrally unnown at th rcivr. Thus, w hav to stimat of th xtrinsic information s absolut valu E L gnratd by th. Assuming that th LLRs oby a Gaussian distribution at th output of th having a zro-man and a varianc of σ LLR, th probability dnsity function PDF of th xtrinsic information s absolut valu L can b xprssd as: P L = σ LLR π xp L σ LLR. 88

4 Hnc, w hav: + E L x = xp x dx σ LLR π σllr = π σ LLR. 3 Similarly, Eq. can b rwrittn as []: Iσ LLR = x σ LLR / σ LLR πσllr log + x dx. 4 I,Ia DEC Hybrid Trajctory Baysian Trajctory SoIC Trajctory Baysian SoIC NSC+Sprading Th function Iσ LLR is monotonically incrasing with th LLR varianc σ LLR, as shown in Fig.3. It is also sn in Fig.3 that th mutual information Iσ LLR can b accuratly approximatd by a linar fuction in th rang of. < Iσ LLR <.8 as:. Iσ LLR.343 σ LLR This rang of [.,.8] typically includs th I valus xprincd during th itrativ procss. Furthrmor, using Eq.3, w arriv at: I E L π.343 E L.33, 6 whr I [.,.8]. Hnc, w can contriv a low-complxity schm of stimating th xtrinsic mutual information at th output of th basd on Eq.6. Mor xplicitly, th avrag valu of L within th transmission bloc is computd aftr ach itration, yilding E L. Thn, th corrsponding valu of th mutual information I can b drvid using Eq.6. In ordr to construct our hybrid, w rcord th xtrinsic mutual information gain G Il, namly that of th incrmntal valu of I,l during l-th itration compard to I,l of th prvious l - th itration, which is xprssd as: G Il =I,l π.343 I,l [E L,l E L,l ]. 7 Initially w activat th MF-SoIC, but onc th xtrinsic mutual information gain G Il of th l-th itration bcoms lowr than an xprintially dtrminatd thrshold of G Il < δ =.5, and simultanously th currnt I,l SoIC valu is blow th xprimntally dtrmind valu of I SoIC =.6, thn th mor complx but mor powrful Baysian is activatd. This allows th to travrs through th bottlnc rgion of I SoIC [.,.3] sn in Fig.. Subsquntly, whn th xtrinsic mutual information gain G Il of th l-th itration bcoms highr than anothr xprintially dtrminatd thrshold of G Il > Δ =., thn th lowcomplxity MF-SoIC is ractivatd for th sa of rducing th ovrall complxity. In ordr to avoid any potntial failur to convrg, th rquirmnt of maintaining a sufficintly high xtrinsic mutual information gain of G Il aftr switching to th MF-SoIC should rmain always valid. As and whn this condition is not satisfid, th Baysian should b ractivatd. In othr words, th proposd hybrid will activat th MF-SoIC during th ntir itrativ procss, whn th SNR valu is sufficintly high. Nonthlss, it achivs a similar prformanc to that of th Baysian at a lowr complxity, sinc it only activats th Baysian, whn th MF-SoIC would rsult in a BER floor. Th complxity of th hybrid is dtrminatd by th complxity of th MF-SoIC and that of th Baysian wightd by th corrsponding numbr of itrations I a,i DEC Fig. 4. Exit charts and simulatd trajctoris of th proposd hybrid whn supporting K =8usrs at E b /N =6dB. BER Fig Hybrid 8usrs Baysian 8usrs SoIC 8usrs Hybrid usrs Baysian usrs SoIC usrs Singl Usr E b /N db BER prformanc of th proposd systm MC-CDMA Systm Paramtrs Numbr of usrs 8, Numbr of rcivr antnnas Sprading factor Channl impuls 3-path SWATM rspons symbol-invariant [3] p.78 Numbr of subcarrirs 8 Lngth of cyclic prfix 3 Modulation BPSK Channl Coding Typ NSC, RSC Cod rat / Constraint Lngth 4 Turbo intrlavr bloc lngth,48 TABLE I SYSTEM PARAMETERS. 89

5 V. SIMULATION RESULTS AND DISCUSSIONS In this sction, th attainabl prformanc of th proposd hybrid is invstigatd in comparison to th two constitunt turbo s, namly that of th MF-SoIC and th Baysian. Our systm paramtrs ar summarizd in Tabl I. Each usr has a diffrnt random intrlavr. W will dmonstrat that th proposd hybrid stris an attractiv trad-off btwn th constitunt s mployd as bnchmarrs. As sn in Fig., th simulation-basd trajctory closly follows th EXIT curvs of th rcivr componnts. During th initial thr itrations, th MF-SoIC is activatd. As th incrmntal xtrinsic mutual information gain of ach additional itration is rducd, which is valuatd using th avrag absolut xtrinsic LLR diffrnc btwn th currnt and prvious itrations with th aid of Eq.7, th Baysian is activatd, in ordr to ovrcom th MF-SoIC s EXIT tunnl constriction. Whn th conscutiv itration gains of th Baysian bcom sufficintly high again, th MF-SoIC is ractivatd in th intrst of rducing th complxity imposd. Fig.4 shows both th EXIT curvs and th associatd simulationbasd trajctoris of all th s concrnd whn supporing K =8 usrs at E b /N =6dB. At this particular SNR thr is no nd to activat th Baysian, sinc vn th lowr-complxity MF- SoIC is capabl of maintaining an opn EXIT tunnl, hnc lnding to an infinitsimally low BER. Fig.5 portrays th attainabl BER prformancs of th MF-SoIC, of th Baysian and of th proposd hybrid as a function of th SNR as wll as of th numbr of usrs supportd. Obsrv in Fig.5 that at a high normalizd usr-load of γ = K/S f = /4, th MF-SoIC fails to convrg, whil th proposd hybrid and th Baysian achivs an infinitsimally low BER for E b /N > db. Explicitly, whn supporting for xampl K =usrs with th aid of S f =4-chip sprading squncs, th MF-SoIC bnchmarr fails to provid an adquat prformanc, whil th proposd hybrid achivs an infinitsimally low Bit Error Rat BER for E b /N > db at a high normalizd usr-load of γ = K/S f =/4, whn supporting K =usrs. This usr-load is thr tims highr than th numbr of chips pr FD sprading squnc. Furthrmor, th Baysian is also capabl of supporting K = usrs, but imposs a highr complxity than that of th proposd hybrid. A comparison btwn th complxity and BER prformanc of th diffrnt s supporting K =8usrs at E b /N =6dB as wll as supporting K =usrs at E b /N =db is listd in Tabl II. Th complxity was drivd by taing into account th complxity of th spcific s mployd and thir associatd numbr of itrations, whil th complxity imposd by th channl dcodr may b dmd insignificant compard to that imposd by th. It is clarly sn that th proposd hybrid outprforms both th MF-SoIC and th Baysian in trms of th complxity imposd, whil maintaining a simillar BER prformanc to th lattr. K =8, E b /N =6dB Typ of Complxity Opration BER SoIC = Baysian =48, Hybrid = K =, E b /N =db Typ of Complxity Opration BER SoIC = 8.34 Baysian =, 548, Hybrid =8, 849, 6 TABLE II COMPARISONS BETWEEN THE COMPLEXITY AND THE BER PERFORMANCE OF DIFFERENT S. by ach itration. Sinc it is not fasibl to masur th mutual information dirctly, w proposd a ralistic stimation of th mutual information gain. Fortunatly, th mutual information was found to b a nar-linar function of th xtrinsic LLR valus, whn assuming Gaussian distributd LLRs at th output of th. Th MF- SoIC and th Baysian wr combind in ordr to crat an advancd hybrid. Th simulation rsults guantifid th prformanc advantag of mploying th hybrid, which was capabl of supporting a high normalizd usr-load of γ = K/S f = /4. At this load th MF-SoIC faild to convrg, whras th proposd hybrid achivd an infinitsimally low BER, which was similar to that of th Baysian, whil imposing only about half th complxity. REFERENCES [] P. Li, L. Liu, K. Wu, and W. K. Lung, Intrlav-division multiplaccss, IEEE Transactions on Wirlss Communications, vol. 5, pp , Apr. 6. [] S. tn Brin, Convrgnc bhavior of itrativly dcodd paralll concatnatd cods, IEEE Transactions on Communications, vol. 49, pp , Oct.. [3] L. Hanzo, M. Münstr, B. Choi, and T. Kllr, OFDM and MC-CDMA for Broadcasting Multi-Usr Communications, WLANs and Broadcasting. Wily-IEEE Prss, 3. [4] S. Chn, B. Mulgrw, and S. McLaughlin, Adaptiv Baysian qualisr with dcision fdbac, IEEE Transactions on Signal Procssing, vol. 4, pp , 993. [5] L. Xu, S. Chn, and L. Hanzo, Exit chart analysis of low-complxity Baysian turbo multiusr dtction for ran-dficint multipl antnna aidd ofdm, in Proc. VTC 7, Baltimor, USA, pp. G7 3, Spt.3 Oct 3, 7. VI. CONCLUSION In this papr w proposd a novl hybrid turbo schm, which combins th bnfits of diffrnt s, namly that of low complxity and high prformanc. W analyzd and compard th convrgnc bhaviours of diffrnt s With th aid of EXIT charts, and thn dsignd a novl hybrid, switching btwn diffrnt s by monitoring th mutual information gain achivd It is worth noting nonthlss that according to Fig.4 at E b /N =6dB th MF-SoIC and Baysian s rquird I SoIC =9amd I Baysian =5 itrations, rspctivly. 8