Allocation Algorithm for Optimizing MC-CDMA Over Correlated Channel

Transcription

1 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader Alloation Algorithm for Optimizing MC-CDMA Over Correlated Channel Hassan EL GHAZI, Hamza DAHMOUI and awal BOUOUADE Department of Signal and Commniations, Institt ational des Postes et Téléommniations (IPT),. av Allal El Fassé, Madinat El Irfane, abat MOOCCO. Abstrat: In this paper, we address the problem of (Mltiple Aess Interferene) degrading the performane of a downlin MC-CDMA system in a freqeny seletive fading hannel. Or objetive is to develop a ode alloation strategy sbjet to se any ode family and any eqalizer. This alloation problem is formlated as a minimization problem of a ost fntion related to. Firstly, we bild the ost fntion from an approximation of the analytial expressions of the power for MC, EGC and MMSE eqalization. Then we propose an iterative algorithm based on the min-max riterion to selet the spreading ode of the ative sers. Simlation reslts show the effiieny of or alloation strategy verss ey parameters, in partilar the orrelation degree between the faded sbarriers. Keywords: MC-CDMA, hannel freqeny orrelation fntion, minimization, power approximation, spreading ode alloation Indeed, by hannel inversion, ZF (Zero Foring). Introdtion an eliminate bt in retrn-noise amplified on deeply faded sbarriers. The other tehniqes The MC-CDMA (Mlti-Carrier Code Division inlding MC (Maximm atio Combining), EGC Mltiple Aess) transmission [] [3] is a promising (Eqal Gain Combining) and MMSE (Minimm soltion for the physial layer of ftre broadband Mean Sqare Error) an not restore the orthogonality wireless ommniation systems whih will have to of odes and lead to residal. Therefore more spport mltimedia servies. By ombining OFDM advaned methods sh as MUD (Mlti-User (Orthogonal Freqeny Division Mltiplexing) and Detetion) [4] [7] have been developed. CDMA, we obtain a high speed transmission By exploiting the information from all sers, apability in mltipath environments and large they ahieve better performane, bt the main mltiple aess apaity. Unlie CDMA, MC- drawba is to strongly inrease the reeiver CDMA performs the spreading operation in the omptational omplexity, so the implementation in freqeny domain, mapping eah hip of the ser a mobile devie is still a tehnial isse. Another spreading ode on one sbarrier, and ths approah for improving MC-CDMA performane introdes freqeny diversity. However when the withot inreasing omplexity at the reeiver side MC-CDMA signal propagates throgh a freqeny onsists in seleting the set of spreading odes seletive fading hannel, the ode orthogonality is alloated to the ative sers, whih has a great destroyed and the reslting limits the system inflene on the level in a system transmitting performane. Several approahes have been throgh a realisti hannel with orrelated fading on proposed to mitigate and to improve signal sbarriers [8], [9]. The problem is then to define a detetion. The onventional single-ser detetion ode seletion strategy with the following properties: tehniqes, applying per sbarrier eqalization as in - possible se with any ode family and with OFDM systems and then orrelation with the ode of any eqalization tehniqe, the desired ser, offer poor performane. ISS: Isse, Volme, Febrary

2 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader - low omplexity in order to selet the best odes with an aeptable omptational ost, - qi management of load variations whih or very freqently in a elllar system, - the ode alloation shold not start eah time from srath. The proposed soltions in the sientifi literatre for ode seletion do not possess the three properties simltaneosly. Among the algorithms valid for any ode family and eqalization tehniqe, the one proposed by Mottier and Castelain in [] and then refined in [] ses a indiator of the interferene level, bt performs an exhastive searh among all possible ombinations of odes, so it has a very high omptational ost. To rede the nmber of examined ombinations examine, Morad et al. [9] propose an iterative algorithm, bt the power of the interferene between sers is allated at eah iteration and this allation reqires the nowledge of the hannel FCF (Freqeny Correlation Fntion) after eqalization. The athors not provide any analytial expression, so an additional stage is needed to estimate the FCF, whih introdes more omplexity. Other tehniqes an easily and qily selet the best sets of spreading odes, bt they are dediated to speifi MC-CDMA systems: Shi and Latva-Aho [] se a property only observed for Walsh odes in the freqeny domain and the wor of Tsai et al. on anellation [3] onerns a system sing Walsh odes and MC eqalization. The topi of this paper is to propose a ode alloation strategy meeting all reqirements previosly ited. To design an algorithm independently of the ode family and of the eqalization tehniqe, the problem is formlated in a general way. It then onsists in trying to find the optimal ode sets that minimize a ost fntion related to the affeting the ative sers of the MC-CDMA system, as in [9] []. Sine this optimization problem has no analytial soltion and the exhastive searh sffers from a prohibitive omptational ost, it is neessary to develop a faster and simpler solving tehniqe. To meet the low omplexity reqirement, we first bild a ost fntion whih an be evalated with few allations from an analysis of in a downlin MC-CDMA system. The analytial expression of the power is provided from the exat allation of the hannel FCF after MC, EGC and MMSE eqalization in the ase of a typial exponential PDP (Power Delay Profile). The ost fntion is then derived from an approximation of the exat expression. Low omplexity and handling of load fltations are strong argments in favor of an iterative solving proess. The proposed algorithm is based on the min-max riterion to garantee that no ommniation will be affeted by strong interferene. We show that the algorithm an be sed whatever the ode family and the eqalizer, and thans to its reded omplexity and to its iterative natre, it an also effiiently manage load variations. The remaining of the paper is organized as follows. Setion II presents the MC-CDMA system model and the hannel model. Setion III foses on the power and the formlation of the ode alloation problem as a minimization problem. The ost fntion is defined from an approximation of the power in setion IV. In setion V, an iterative algorithm is proposed to selet the optimal spreading ode alloated to sers and is ompared to different existing algorithms. eslts obtained for Walsh odes are presented in setion VI. The last setion draws some onlsions.. MC-CDMA model We onsider the downlin MC-CDMA system represented by Fig.. The system is synhronos, so we onsider orthogonal ode families inlding ommon binary odes: Walsh, Golay, orthogonal Gold and also omplex CI (Carrier Interferometry) odes [4]. The hannel is assmed to be slowly time varying and freqeny seletive over the total bandwidth. In mltiarrier systems, it is essential that eah sbarrier experienes a flat fading, so f mst be hose shorter than the hannel oherene bandwidth. This reqirement has two onseqenes. For high data rates, serial-to-parallel onversion mst be performed before spreading, as proposed in [5]. Moreover fadings affeting the different sbarriers are inherently orrelated.. Transmitter model Inpt data symbols are assmed to form an i.i.d. zero mean random proess with nitary power. After serial-to-parallel onversion of P symbols, the p th symbol of ser x p is spread with the ser ode ISS: Isse, Volme, Febrary

3 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader {,,..., } where z. The omponents of the spread seqene x p are then transmitted in parallel on sb-arriers seleted among a total amont of s p orthogonal sbarriers. To ahieve freqeny diversity, the gap between the sbarriers onveying the same symbol x is maximized, it is then eqal to P f as p in [6]. Conseqently the hips x p are sent on sbarriers p+p for,..., -. After the inverse FFT, the MC-CDMA symbol is extended with a CP (Cyli Prefix) longer than the hannel maximm exess delay. Considering all previos assmptions, the system is prevented from inter-symbol and intersbarrier interferene. Afterwards, to simplify notations and withot loss of generality, the index p is omitted. The sbarriers sed to transmit the symbol denoted x are jst identified by index varying from to -. Correlated hannel model We assme a WSSUS (wide sense stationnary norrelated sattering) ayleigh fading hannel modeled as a tapped delay line filter. The implse response is onstant over the MC-CDMA symbol dration T s and is written as: L h l l h( τ ) δ ( τ τ ) () Where L is the nmber of taps, h l the omplex gain and τ l the delay of the l th tap. Eah gain h l is a mtally norrelated omplex Gassian random proess with zero mean and powerσ l. We onsider an exponential PDP (Power Delay Profile) haraterized by an MS (oot Mean Sqare) delay spread σ,bease it is the most ommonly aepted τ PDP model for indoor hannels in aordane with theory and experimental data [7],[8]. The delays are mltiples of the sampling timeτ lt, the l l maximm exess delay is then eqal to (L )T whih is assmed large enogh ompared to σ, and σ l is related to the average vale of the PDP within the interval [ LT,( L+ ) T[. The FCF of the hannel model is obtained by Forier transform of the PDP. In the MC-CDMA τ system, the sampling time is T/(s f) and the freqeny spaing between two sbarriers and +n transmitting the same symbol is eqal to np fn(/s) f. If we denote H the omplex oeffiient orresponding to the hannel freqeny response on sbarrier, we get the FCF H (n) between H and H +n defined as: H ( n ) E * [ H H ] + n e s fστ e () n + j π s fστ.3 eeiver model Compared to the transmitter, the MC-CDMA reeiver applies inverse operations. After CP removal and OFDM demodlation by FFT, the signal obtained on the th sbarrier is given by: v v z v y H x + η (3) Where η is the AWG (additive white Gassian noise) with power σ at the FFT otpt. ext single-ser detetion is performed to deode the signal of ser. After sbarrier by sbarrier eqalization and dispreading with the ser ode, the deision variable y an be expressed as the smmation of three terms whih respetively orrespond to the sefl signal, the and the additive Gassian noise: n n z * y x H g + x + gη (4) Where g is the eqalization oeffiient on the th sbarrier. The term reslts from the mtal v interferene x z between the deteted ser and eah interfering ser v de to ode orthogonality alteration by the hannel and the eqalizer: z v * x x x H g v v v v (5) Several eqalization methods orresponding to different diversity ombining strategies have been proposed in literatre [5]. By hannel inversion, ZF restores orthogonality and totally eliminates when orthogonal odes are sed. Bt the performane is degraded by noise amplifiation on ISS: Isse, Volme, Febrary

4 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader sbarriers affeted by deep fading. In the following we are interested in minimization to improve the MC-CDMA system performane, so only MC, EGC and MMSE eqalizers are investigated. 3. power From (5) and statistial properties of the inpt symbols, the power of the affeting ser is written as: v v z P P z (6) v Where P z is the power of the mtal interferene between sers and v:, z v P ' H g ( ' ) z * z v z ' z v * ' (7) Fig.. Blo diagram of the MC-CDMA system for ser With (n)e[h g H +n *g +n ] the hannel FCF after eqalization. Whatever the eqalizer, the oeffiient H g affeting the th sbarrier an always be written as a fntion of H. Conseqently (n) an be derived from the joint density of ayleigh hannel envelopes given by Jaes [7]. After mathematial formlations, we obtains the freqeny hannel expressions for respetively MC, EGC and MMSE detetion, (n) is related to the absolte sqare of the hannel FCF before eqalization. As H (n) is also even and periodi with period : (n) (-n) ( -n) (8) Fig.. FCF of the eqalized hannel for MC, EGC and MMSE eqalization and for several vales of s fσ τ. 3. power and problem formlation In this setion, we first derive the analytial expression of the power from the hannel FCF after MC, EGC and MMSE eqalization in the ase of a typial exponential PDP. Then the ode seletion problem is expressed in a very general way with the aim of designing an algorithm independent of the ode family and of the eqalizer. Figre represents the normalized FCF (n)/ H () for the different eqalizers and for the following vales of s fσ τ :.6,.48 and.6. For all eqalizers, we an onsider that s fσ τ.6 orresponds to highly orrelated sbarriers, bease the FCF is almost onstant. For other vales, the FCF dereases, when the sbarrier spaing n inreases, from its maximm vale at n to get loser to a horizontal asymptote y ( /). The deay is all the more sharp sine the prodt s fσ τ is high. In MMSE ase, it also depends on the signal to noise ratio: Eb γ σ The figre also shows that the range of vales taen by the FCF depends on the eqalization tehniqe; it is larger with MC and very tighter with MMSE. Using (8), the expression (7) an be rewritten for an even vale of as: ISS: Isse, Volme, Febrary

5 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader P + / n () + ( n) [ ω ( ( n)] / ) [ ω ( / )] () z, z Where v ( n) is the PCF (periodi orrelation ω fntion) of the hip by hip prodt ω, * of the spreading odes of sers and v defined by:, * ( n) ω ω+ n ω () Finally the power obtained by sbstitting () in (6) depends on the following parameters: the ode length, the nmber of sers, the prodt s fσ τ, the ratio: E b / for the MMSE tehniqe, and the ode prodt PCF governed by the spreading odes alloated to the ative sers. At every moment, the first parameters are fixed while there is a degree of freedom to selet the ser odes among all available odes. Indeed, a CDMA based system almost never operates at fll load bease the apaity is first limited by Problem formlation In the most general way, the ode alloation problem is a minimization problem whih an be expressed as follows. Consider a spreading ode family with odes of length identified by a nmber ranging from to. In most ases (for Walsh, orthogonal Gold),. For CI odes, an tae vales p to. Let S{,,,-} be the set of all odes and S {z,z,,z - } S a sbset of odes that an be alloated to the ative sers of the MC-CDMA system. We loo for the optimal ode sbsets f(s ): S ( opt ) S (opt) that minimize a ost fntion arg min f ( S ) (3) S where f(s ) is related to the powers of the mtal interferene between the different pairs of odes from S. Bease the soltion to the minimization problem is a priori not niqe, we denote Ω the (opt ) (opt) set inlding all ode sbsets S leading to the minimm vale. Aording to the expression of z z v P, (), the eqation () annot be analytially solved whatever the exat ost fntion. Frthermore, solving (3) by exhastive searh reqires to evalate the ost fntion for the C ombinations of odes. When the ode length inreases, the searh spae beomes important that the omptational ost is too prohibitive. Therefore a simpler and faster solving tehniqe is needed. 4. Proposed fntion To bild the ost fntion, we propose an approximation of the mtal interferene power derived from the analysis of the eqalized hannel FCF. 4. power approximation Based on theoretial formlation aording to the eqation [], we show that The hannel FCF (n) after MC, EGC and MMSE eqalization dereases from its maximm vale at n to get loser to a horizontal asymptote y [ ( /)] when n inreases. To simplify expression (), we sppose that from a gap d between the sbarriers, the eqalized hannel oeffiients H g have a minimm orrelation: n) ( / ) n d. Then ( the power of the mtal interferene between two sers et v is approximated by: z P () + ( / ) [ w ( / ) + d n z, z v ( n) [ w ( n)] (4) P is the d th order approximation of the mtal interferene power between two sers. As shown in Appendix C, the ode prodt PCF verifies the following property for the different ode families (Walsh, orthogonal Gold, Golay and CI): w n ( n) (5) Using this property as well as the Hermitian natre and the periodiity with period of the PCF, the d th order approximation of the mtal interferene power () beomes: ISS: Isse, Volme, Febrary

6 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader P + d [ n () w ( n)]( ( / ) ( n) ( / )) (6) the power, only one rve is represented. Indeed the three vales are idential bease all sbsets ( 7) ( opt ) S lead to the minimm BE whih an be S ahieved. Whatever the eqalization tehniqe and the approximation order, the deviation from the exat vale of the power is expeted to derease when s fσ τ inreases. Indeed the eqalized hannel FCF (n) dereases more rapidly towards the asymptote and the proposed approximation is more arate. We an preise that the deviation is similar with MC and EGC tehniqes. With MMSE based detetion, the deviation is smaller bease of the lower range of vales taen by the FCF between n and n /, therefore the proposed approximation is more arate whatever the vale of s fσ τ. 4. Seletion riterion The d th order approximation of the mtal interferene power is now sed to define the ost fntion f(s ) Sine in many appliations, the minimm maximm riterion is nown to be more appropriate than the minimm average riterion [9], [], f(s ) is defined as the maximm vale of the d th power approximation over all oples (z,z v ) from S S. Among all possible ode ombinations S, we loo for the sbsets whih satisfy: S d arg S, min max P (7) (, ) S S By minimizing the maximm power, no ommniation will be affeted by strong interferene and hene, the overall will be ept at a low level. As previosly, the soltion to (5) is not neessarily niqe and we denote Ω the set inlding all ode sbsets S leading to the minimm vale. Figre 3 represents the BE of the MC-CDMA system with MC detetion and QPSK modlation when sing the sbsets of Walsh odes with length 6 provided by an exhastive searh from approximation orders d ranging from to 7. More preisely it shows the maximm, average and minimm vales of the BE obtained over the different ode sbset S fromω verss s fστ. For d 7, whih orresponds to the exat vale of Fig. 3. BE verss s fσ τ for several vales of the approximation order d. Maximm BE is plotted with a solid line and average BE with a dashed line. For d < 7, only the rves of average and maximm BE are plotted, sine the minimm BE over the sbsets S is eqal to the BE obtained with the optimal sbset, whih means that the following ( opt ) inlsion is always verified: S Ω. Whatever the approximation order, when s fστ inreases, the differenes between the BE rves get reded bease the aray of the approximations improves. For this reason, we onsider vales of s fσ τ below, beyond the differenes are very small. The rves of average BE and maximm BE get loser to the minimm BE rve when the approximation order inreases bease the searh for ode sbsets is refined. More preisely, from the 5 th order, the BE is lose to the minimm BE whatever the vale of s fσ τ.6. We an mae the same observations with EGC detetion, bt in MMSE ase, all BE rves almost merge bease the different approximations are more arate. Whatever the degree of orrelation between sbarriers, the first order approximation is sffiient to get a BE lose to the minimm BE. ISS: Isse, Volme, Febrary

7 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader 5. Spreading ode alloation algorithm The ost fntion defined by approahing the mtal interferene power an be evalated with few allations, bt solving the minimization problem (7) by exhastive searh still has a prohibitive omptational ost. For low omplexity and to reat qily to load hanges, we propose an iterative algorithm as in [9]. 5. Proposed iterative algorithm The priniple is to start from an initial state, here a spreading ode z seleted from the set S of the available odes. Then the following proess is repeated: at eah iteration, we ompare, for eah of the remaining odes, the vales of the approximate power of the mtal interferene with the odes already hosen in previos iterations. We selet the remaining ode z whih minimizes the maximm power over the first odes. After - iterations, we get a sbset of odes that represents a sboptimal soltion. To improve the effetiveness of the method, the proess is applied several times with different initial onditions. In total, sbsets of S ) z n,... z are bilt ( n... odes { } from the available odes. The final soltion is the best of the sboptimal soltions, i.e. the soltion that meets the minimm maximm riterion. The ode alloation algorithm, desribed in detail by table I, atally meets all reqirements: independene of the ode family and of the eqalizer, low omplexity and qi management of load variations. More preisely, the prohibitive omplexity of the exhastive searh is reded to an aeptable qadrati omplexity verss and. Assming the: ( -)/ vales of the mtal power are nown, the exhastive searh [], [] evalates the ost fntion for the( ) ombinations of odes and at eah evalation, the maximm over all the power vales is allated. The omplexity is then eqal to ο (( ) ). In the ase of the iterative algorithm, the ost fntion is only evalated on the ode sbsets whih are bilt. So the seond stage of the algorithm presents a omplexity eqal to ο ( ). Table I: CODE ALLOCATIO ALGOITHM It mst be added the nmber of operations performed dring the first step that bilds the sbsets. Sine for eah of the initial states, eah iteration onsists in allating a maximm over vales and a minimm over vales, the omplexity of this step is: ο ( ( )) ο( ) (8) Finally, the total omplexity of the iterative algorithm is eqal to ο ( ). Compared to the algorithm proposed by [9], ors reqires fewer operations to obtain the ( )/ power vales, sine it ses the approximated power instead of the exat power and the analytial eqalized hannel FCF instead of an estimated FCF. When sing the exat expression of the mtal interferene power (9), the allation of eah power vale onsists in the sm of ( /+) terms, after allating the / vales of the ode PCF, ω (n) and the (/+ ) vales of the hannel FCF (n). With the d th order approximation (4), the sm is limited to (d + ) terms and involves only d vales for the PCF and (d + ) vales for the FCF. Frthermore, by sing the analytial expressions of the hannel FCF [] and after respetively MC, EGC and MMSE ISS: Isse, Volme, Febrary

8 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader eqalization, the estimation stage is eliminated and the algorithm omplexity is reded again. Moreover the iterative natre of the algorithm maes easy and fast the reseletion of odes when ommniations are starting or ending in the MC- CDMA system. Assme that the sbsets (S (d) ) n {z n,, z } bilt dring the previos alloation of odes are stored. Then the seletion of a new sbset of odes only reqires pdating these sbsets and seleting the best one in aordane with the minimm maximm riterion. For this, one iteration mst be performed for every initial state z in the first step of the alloation algorithm. The objetive is to selet the missing odes z when the load hanges from to + ative sers and to sppress the last alloated odes z for a transition from to sers. In both ases, the seond stage of the algorithm remains nhanged. 6. eslts for the different eqalizers with Walsh odes In order to qantify the performane gain obtained throgh the proposed ode alloation strategy for the different eqalization tehniqes, the average BE of a MC-CDMA transmission has been obtained by simlation. Two different ases are onsidered: a system with alloation of the spreading odes by or algorithm, and a system with random alloation of the odes. eslts are given verss the ey parameters that inflene performane inlding the load, the degree of orrelation between the sbarriers and the signal to noise ratio. For simlation, the nmber of sbarriers is eqal to 64 as in IEEE 8.a/g standard, the sbarriers are QPSK modlated and the ode length is simply eqal to s. In this setion, we onsider the family of Walsh odes. 5. Performane verss the system load Figre 4 represents the BE of a MC-CDMA system verss the load for s fσ τ.48, Eb/ db and the different eqalization tehniqes: EGC, MC, MMSE. For eah of them, the figre shows two different rves when odes are alloated by or algorithm. They orrespond to two approximation orders, the first order and the th order whih always leads to the minimm BE. The first order approximation of the interferene power is arate enogh and also provides the minimm BE in MMSE ase whatever the load and in MC and EGC ases for a load above 6. evertheless for a lower load, it provides a BE smaller than 8 8 with MC and than 4 7 with EGC, so it leads to a signifiant improvement of the performane. Whatever the eqalizer, the performane gain provided by ode alloation is very important for a loading rate smaller than /4, is less important bt still signifiant for a rate between /4 and /, and strongly dereases when the rate exeeds / bease two effets ombine: the level inreases and the degree of freedom for hoosing the odes among the available odes dereases. More preisely, in a low loaded system, the MC tehniqe whih is the most sensitive to offers the most signifiant gain. For /G 6 (here the power of two G is eqal to 4 sine L 4 for s fσ τ.48), the performane remains onstant eqal to 8 when sing the ode sets alloated by the algorithm with the th order approximation. This BE vale orresponds to the optimal performane obtained for a single-ser transmission, bease the is ompletely aneled. For omparison, for 6, the BE obtained with randomly seleted odes is eqal to.4 3. However, one the limit of /G 6 sers is exeeded, the performane qily degrades. Even with ode alloation, the MC tehniqe remains very sensitive to. The performane gain is lower with the MMSE tehniqe, whih gives the best performane with random ode alloation. For 6, the BE is eqal to with the alloation and to with random alloation. Fig. 4 BE verss the nmber of sers for the different detetion tehniqes ISS: Isse, Volme, Febrary

9 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader ow in absolte, we an notie that the best performane is obtained when the alloation algorithm is opled with MC for a small load less than /G, with EGC for a load between /G and /, then with MMSE for a higher load. 6. Performane verss the sbarrier orrelation degree Figre 5 shows the BE of a qarter loaded MC- CDMA system verss s fσ τ whih haraterizes the degree of orrelation between sbarriers, for Eb/ db and for the different eqalization tehniqes. In aordane with Figre 4, or ode alloation algorithm ses the first order approximation in MMSE ase and the th order approximation with MC and EGC to get the minimm BE. First we an notie that whatever the vale of s fστ, the performane always benefits from sing the ode alloation algorithm. Bt the gain is more important for low vales of s fστ. For example, for s fσ τ.48, the average BE is respetively eqal to.4 3,.5 4 and with random alloation in MC, EGC and MMSE ases while it drops to 8, 7 and 4 6 with the proposed alloation. As previosly, the most signifiant gain is obtained with the MC tehniqe bease the is aneled when the MC-CDMA system ses the odes provided by or algorithm for /G, i.e. G / 4 (in simlations, L 4 for s fσ τ.48) and the performane gain is mh lower with the MMSE tehniqe. When s fσ τ inreases, i.e. when the orrelation degree between sbarriers dereases, the performane gain dereases for all detetion tehniqes, sine in the extreme ase of norrelated sbarriers, the BE performane is nown to no longer depend on the odes assigned to the ative sers [8]. Finally, the best performane is obtained when the proposed ode alloation algorithm is ombined with MC for low vales of s fστ (.5), with EGC for vales of s fστ between.5 and.7, and with the MMSE tehniqe for a lower orrelation between the sbarriers: s fστ.7. Fig. 5. BE verss s fσ τ for the different eqalization tehniqes 7. Conlsion In this paper, we propose a spreading ode alloation strategy for a downlin MC-CDMA system transmitting throgh a realisti orrelated ayleigh fading hannel. The alloation problem is formlated as a minimization problem of a ost fntion related to. The ost fntion is based on an approximation of the exat expressions of the power for MC, EGC and MMSE eqalization in the ase of a typial exponential PDP. The alloation algorithm is iterative and ses the minimm maximm riterion to selet the spreading odes of the ative sers. Via simlation reslts, we provide a omplete analysis of the alloation effiieny verss the ey parameters inlding the loading rate, the degree of orrelation between the faded sbarriers, the approximation order, the eqalization tehniqe and the family of odes. It shows that the proposed ode alloation algorithm always improves the performane of a MC-CDMA system withot additional omplexity at the reeiver. Using the sitable approximation order, the algorithm is able to provide the optimal ode sets and onseqently leads to the minimm BE. eferenes: []. Yee, J.-P. Linnartz, and G. Fettweis, Mltiarrier CDMA in indoor wireless radio networs, in Pro. IEEE PIMC, Sept. 993, pp ISS: Isse, Volme, Febrary

10 WSEAS TASACTIOS on COMMUICATIOS Hassan El Ghazi, Hamza Dahmoni, awal Bonoader [] K. Fazel and L. Pape, On the performane of onvoltionally-oded CDMA/OFDM for mobile ommniation system, in Pro. IEEE PIMC, Sept. 993, pp [3] [3] A. Choly, A. Brajal, and S. Jordan, Orthogonal mltiarrier tehniqes applied to diret seqene spread spetrm CDMA systems, in Pro. IEEE GLOBECOM, ov. 993, pp [4] S. Verd, Mltiser detetion. Cambridge, UK: Cambridge University Press, 998. [5] P. Castoldi, Mltiser detetion in CDMA mobile terminals. orwood, MA: Arteh Hose Pblisher,. [6] A. Yener,. Yates, and S. Uls, CDMA mltiser detetion: a nonlinear programming approah, IEEE Trans. Commn., vol. 5, pp. 6 4, Jne. [7] X. Wang and H. Poor, Spae-time mltiser detetion in mltipath CDMA hannels, IEEE Trans. Signal Proess., vol. 47, pp , Sept 999. [8] Q. Shi and M. Latva-Aho, Performane analysis of MC-CDMA in ayleigh fading hannels with orrelated envelopes and phases, IEE Pro. Commn., vol. 5, pp. 4, Jne 3. [9] A. Morad, A. Gegen, and. Pyndiah, Impat of the spreading seqenes on the performane of forward lin MC-CDMA systems, in Pro. ISSSTA, Sept. 4, pp [] D. Mottier and D. Castelain, A spreading seqene alloation proedre for MC-CDMA transmission systems, in Pro.VTC Fall, Sept., pp [] S. obilet, J. Helard, and D. Mottier, Spreading seqenes for plin and downlin MC-CDMA systems: PAP and minimization, Eropean Trans. Teleommn., vol. 3, pp , Ot.. [] Q. Shi and M. Latva-Aho, Simple spreading ode alloation sheme for downlin MC- CDMA, IEEE Eletron. Lett., vol. 38, pp , Jl.. [3] S. Tsai, Y. Lin, and C. J. Ko, -free MC- CDMA systems based on Hadamard-Walsh odes, IEEE Trans. Signal Proess. vol. 54, pp , Ag. 6. [4] B. atarajan, C. assar, S. Shattil, M. Mihelini, and Z. W, High-performane MC- CDMA via arrier interferometry odes, IEEE Trans. Veh, vol. 5, pp , ov.. [5] S. Hara and. Prasad, Overview of mltiarrier CDMA, IEEE Commn. Mag., vol. 35, pp. 6 33, De [6] Hara, S. Prasad,., Design and performane of mlti-arrier CDMA system in freqenyseletive ayleigh fading hannels, IEEE Trans. Veh. Tehnol., vol. 48, p , Sept [7] W. Jaes, Mirowave Mobile Commniations, nd ed. ew Yor : John Wiley and Sons, 994. [8] V. Ereg, L. Shmaher, P. Kyritsi, A. Molish, and et al., IEEE P8. Wireless LAs - TGn hannel models, IEEE 8.-3/94r4, May 4. [9] G. Shster, G. Melniov, and A. Katsaggelos, A review of the minimm maximm riterion for optimal bit alloation among dependent qantizers, IEEE Trans. Mltimedia, vol., pp. 3 7, Mar [] H. E. Ghazi, Strategie d alloation des odes d etalement por la tehniqe MC-CDMA, Ph.D. dissertation, 67 Universite de Valeniennes et d Hainalt-Cambresis, 8. Hassan El Ghazi reeived a PhD degree in eletrial engineering from Teleom Lille - UVHC, Frane in 8. He obtained a M. S in Wireless ommniations from UVHC in 4. In 7-9, he wored as researh engineer at TeSa. His researh interests are related to wireless ommniations, OFDM and traffi engineering. Hamza Dahmoni reeived a PhD degree in etwors and Compter Siene from Teleom Bretagne - EST, Frane in 7. He obtained a M. S in etwors from Paris-IV University in 3, and a M. S in Wireless networ design from Teleom SdParis - IT in. In 4-7, he wored as researh engineer at Frane Teleom. His researh interests are related to traffi engineering and performane evalation in heterogeneos networs. awal Bonoader PHD in progress in traffi engineering from Mohammed V University, she obtained an engineering diploma of teleommniation from IPT in 7. In 7-9 she wored as a projet manager in Mediteleom, here researh interests are related to KPI evalation of networs and wireless system (MIMO and OFDM). ISS: Isse, Volme, Febrary