A Spreadng Sequence Allocaton Procedure for MC-CDMA Transmsson Systems Davd Motter, Damen Castelan Mtsubsh Electrc ITE 80, Avenue des Buttes de Coësmes, 35700 Rennes FRAE e-mal: {motter,castelan}@tcl.te.mee.com Abstract A novel spreadng sequence allocaton procedure for mult-carrer code dvson multple access (MC-CDMA systems s proposed and nvestgated. Ths new technque, whch reles on an analytcal evaluaton of the multple access nterference (MAI, mtgates the nterference between dfferent users by optmzng the spreadng sequence selecton wthn a gven spreadng sequence famly. For low-loaded transmssons over dfferent realstc frequency correlated channels, t s shown that ths new selecton procedure outperforms systems where no specfc allocaton rule s employed. Furthermore, ths technque affects the emtted sgnals and ts performance mprovement s observed whatever the detecton technque used at the recever sde. Thus, ths technque mproves the capacty of MC-CDMA systems. 1. Introducton Among the multple access transmsson systems wth hgh bandwdth effcency, the MC-CDMA transmsson system proposed n [1] combnes the Orthogonal Frequency Dvson Multplex (OFDM modulaton and the CDMA scheme. The OFDM modulaton provdes robustness aganst multpath propagaton as well as good spectral effcency whle the CDMA allows the transmsson of dfferent users n parallel by allocatng to each one a dstnct spreadng sequence, whch s uncorrelated wth the sequences of other users. Instead of spreadng the nformaton n the tme doman as n the Drect Sequence CDMA technque, the MC-CDMA spreadng s performed n the frequency doman. Therefore, the orthogonalty among users has to be ensured n the frequency doman. To ensure ths orthogonalty, Walsh-Hadamard sequences are often retaned for spreadng[2],[3]. In order to lmt the peak-toaverage power rato, the asam or the Zadoff-Chu spreadng sequences may also be consdered [4]-[6] but at the expense of some orthogonalty losses. However, the transmsson channel s generally frequency selectve, whch breaks the orthogonalty among theses sequences, and the resultng MAI drastcally reduces the system performance. Many detecton technques have been proposed to reduce the MAI degradaton. The sngle-user detecton technques perform sngle tap equalzaton on each subchannel of the OFDM multplex, whch can consst n a smple phase equalzaton, a zero-forcng equalzaton, a Mnmum Mean Square Error (MMSE equalzaton or any other schemes as proposed n [2],[3]. Snce these technques do not take nto account all the characterstcs of a mult-user transmsson, they gve sub-optmal performance. Therefore, mult-user detecton technques were proposed n order to mprove the performance of the transmsson by consderng the sgnals of all actve users for the detecton of the desred sgnal of one partcular user [7]-[9]. These lnear and non-lnear methods are effcent but can result n some ncrease of complexty. In ths paper, we propose a smple MAI lmtaton technque for MC-CDMA transmsson systems, whch conssts n an optmzed spreadng sequence assgnment based on the network occupancy and the frequency correlaton of the transmsson channel. The spreadng sequence allocaton procedure s ndependent on the spreadng sequence famly. In secton 2, we present the MC-CDMA system confguraton and focus on the realstc case of frequency correlated fadng channels. We evaluate the analytcal expresson of the MAI for the case of a mult-user downlnk MC-CDMA transmsson, whch emphaszes the nfluence of the spreadng sequences. Based on ths observaton, we propose n secton 3 a selecton crteron of spreadng sequences wthn a gven spreadng sequence famly and derve a spreadng sequence allocaton strategy, whch s also presented through an example. In secton 4, we valdate ths optmzed spreadng sequence allocaton strategy by smulaton results of MC-CDMA transmssons over dfferent realstc transmsson channels and for dfferent
detecton schemes. Fnally, secton 5 sums up the results and provdes conclusons. 2. System Descrpton We consder the multple access system orgnally descrbed n [1] where users are transmttng smultaneously and synchronously usng OFDM modulaton wth N subcarrers, each havng bandwdth C f = 1/T S. We focus on the downlnk transmsson,.e. from the base staton to the moble staton. To dstngush the sgnals ssued from the dfferent users, a spreadng s performed n the frequency doman. Furthermore, spreadng codes of length N C are consdered. Snce the spreadng s performed over all the subcarrers composng the OFDM modulaton, the transmsson benefts from the maxmal avalable frequency dversty and no frequency nterleavng s needed. Fgure 1 represents a block dagram of the baseband model of the MC-CDMA transmtter for user j assocated wth the spreadng sequence C. The bnary nformaton s frst mapped to modulaton symbols d j, whch represents the k -th symbol of user j. Bnary source Symbol mapper Spread. Sequence Allocaton Procedure Fgure 1: Block dagram of the MC-CDMA transmtter for user j. Then, d j s duplcated tmes and multpled by the elements c,( 0,..., N 1 of the spreadng sequence d j C = ( c0, c1,..., cn c 1 = c IFFT(N C Guard Interval C. Each resultng value s assocated to a subcarrer and sent to the OFDM modulator, whch performs the Inverse Fast Fourer Transform (IFFT operaton and the guard nterval nserton. The sgnal of user j s then added wth the sgnals of other actve users and sent through the channel. The selecton procedure of the spreadng sequence C = ( c0, c1,..., cn 1 c for user j, depends on the network occupancy. In case of a fully loaded network, no spreadng sequence remans avalable and the new user s through the channel rejected. However, most of the tme, the network occupancy s relatvely low, e.g. 30% to 40% of averaged network occupancy s consdered n current French GSM network. Then, many spreadng sequences are not allocated whch gves a degree of freedom n the selecton of the spreadng sequence to be assgned. Currently, no specfc rule s employed to process the spreadng sequence allocaton for MC-CDMA systems. We propose to use ths degree of freedom to defne a spreadng sequence allocaton procedure n order to mnmze the MAI each tme the network occupancy s modfed. We focus on the realstc case of frequency correlated Raylegh fadng channels, e.g. non-lne-of-sght hgh-bt rate ndoor propagaton channels [10]. In ths stuaton, the delay spread τ m of the channel creates Inter Symbol Interference (ISI and s such that 1 / τ m > 1/ TS. We assume that ISI s avoded thanks to the guard nterval nserton so that only remans the channel frequency selectvty, whch s correlated. Furthermore, the fadng s assumed to be flat on each subcarrer and descrbed by a complex channel coeffcent followng a complex Gaussan dstrbuted random process. from the channel FFT(N C Fgure 2: Block dagram of the MC-CDMA recever for user j. A block dagram of the baseband model of the MC- CDMA recever for user j s represented on Fgure 2. The sgnal receved by user j durng the k -th symbol nterval s frst OFDM-demodulated by applyng an FFT of sze N C. The resultng components on each subcarrer can be wrtten as: r r j 0 r j r N C Spread. Sequence Generaton 1( ( ( = h [ d. c ] n (1 Equalzaton C m= 1 = ( c0, c1,..., cn c 1 for m = 1,..., and = 1,..., where h j denotes the complex channel coeffcent on subcarrer assocated to the sgnal propagaton from the base staton to the termnal of user j and n j represents Σ y j Symbol demapper Bnary decson
an Addtve Whte Gaussan Nose (AWGN on subcarrer. Among the dfferent schemes that can be consdered to proceed the detecton at the downlnk recever, we consder the sngle user detecton technque, whch conssts n a carrer-per-carrer equalzaton followed by a despreadng. The equalzaton coeffcent for subcarrer s denoted g j. Dfferent sngle user detecton technques have been proposed such as equal gan combnng (EGC, orthogonalty restorng combnng (ORC, mnmum mean square error combnng (MMSEC or any other methods as presented n [2],[3]. After equalzaton, despreadng wth the sequence allocated to user j and summng the components of each subcarrer, the sgnal for user j can be wrtten as: y = d 1 1 ( d m= 1, m j = 0 { g. h } C 1 { g. n } N = 0. = 0 ( { g. h. c. c } where the frst term represents the desred contrbuton of user j, the second term s the MAI comng from the other actve users and the thrd term s the contrbuton of AWGN. 2 From, the MAI power σ MAI,j assocated to user j s defned by relaton (3 as: 2 2R(1 w w 1 = 0 3 2 σ MAI, j = ( 1. R(0. 2R w w 2... where (k m= 1, m j = 0 2R( N C 1 w0 w 1 R s the autocorrelaton defned as R( p q = E[ ap aq ], a = h g s the real coeffcent affectng the -th subcarrer after equalzaton, (, ( w j = c c defnes the product between the chp element used by users j and k at the -th subcarrer. Relaton (3 emphaszes the nfluence of the w m w products, whch can greatly dffer dependng on the spreadng sequences to be assgned. An optmal MAI mnmzaton would be to properly desgn the spreadng sequences requred by the actve users as a functon of the fadng channel coeffcents and the assocated equalzaton scheme. However, snce ths method s not realzable, we consder a suboptmal technque that conssts n optmzng the selecton of the requred spreadng sequences among a gven famly of P ( P > spreadng sequences wthout takng nto account the precse channel n characterstcs. Ths selecton s dynamcally actvated,.e. each tme s modfed n order to satsfy a varable number of actve users. Snce equvalent performance s consdered for each user, we choose an teratve mnmax approxmaton of a cost functon computed over all the sequences as selecton crteron of the spreadng sequences. 3. Selecton Crteron and Allocaton Procedure Let Ω be a gven spreadng sequence famly and let NT be the number of elements of Ω. Let Ω be a subgroup of Ω that could be used n order to satsfy the requred number ( < NT of spreadng sequences n ( order to satsfy actve users. A cost functon J Ω s proposed and defned as: ( Ω (, k J = max I j (4 j Ω, k Ω, j k where I s a functon that s representatve of the nterference on the k -th spreadng sequence due to the transmsson of the j -th spreadng sequence. In other ( words, the J Ω only takes nto account the maxmal degradaton that s experenced by two of the spreadng sequences of Ω. Ths crteron suggests that the BER performance of a MC-CDMA mult-user transmsson over a frequency correlated channel manly results from the MAI caused by the two spreadng sequences that mostly nterfere each other. We defne I as: I = T ( W (5 (, j (, j where W denotes the vector of N C components w n ( n = 0,..., 1 resultng from the chp-to-chp product between the -th and the j -th spreadng sequence at the n -th subcarrer, and T (x defnes the number of transtons of vector x ( T ( x 0 : N c 2 = 0 1 T ( x = sgn( x 1 sgn( x (6 2 ( Comng back to relaton (3, mnmzng J Ω leads to retan a group of spreadng sequences for whch the (, j dfferent product vectors W present a maxmum number of transtons. Ths leads to make the multplcaton coeffcent of R (1 n relaton (3 be a large negatve value that can mtgate the large postve value of the frst term. The allocaton procedure s performed for the spreadng sequences on the bass of the crtera presented
through relatons (4 and (5 among a gven spreadng sequence famly. Ths procedure re-allocates all the needed spreadng sequences each tme the value of s modfed. Among a total number of N T spreadng NT! sequences, the!.( N dfferent groups Ω! of T spreadng sequences are compared n order to mnmze (4, so that the subgroup s retaned accordng to: Ω ( opt = arg mn [ J Ω Ω = arg mn [ ( Ω (opt Ω k max I Ω Ω j Ω, k Ω, j k ] As the spreadng sequence famly s pre-defned by the transmsson system, the optmum selecton subgroup (opt Ω can be computed a pror for each and the result can be stored n a look-up table. Accordng to the spreadng sequence famly, t may happen several equvalent optmal subgroups. Then, the selecton procedure can be done arbtrary between these subgroups or t can nclude other system crtera n order to select the proper subgroup. As an example, let us consder the Walsh-Hadamard sequence famly wth length N C = 4 that s composed of (0 4 spreadng sequences: C = ( 1, 1, 1, 1, (1 (3 C = ( 1, 1, 1, 1, C = ( 1, 1, 1, 1, C = ( 1, 1, 1, 1. Let us suppose also that = 2 spreadng sequences are needed and that the use of the sequence C s mandatory as frst allocated sequence. Then, 3 subgroups Ω of 2 spreadng sequences ncludng C have to be evaluated accordng to (7: Ω (0 0 = { C, C }, {, (1 Ω 1 = C C } and (3 Ω 2 = { C, C }. The cost functon s then computed over the 3 possble subgroups whch leads to Ω 0 Ω 1 J = 3, Ω 2 J = 2 and J = 1. Then, accordng to (opt (7, the optmal subgroup Ω of 2 spreadng sequences s Ω (0 0 = { C, C } snce 0 s mnmum,.e. t has the largest negatve value. J Ω 4. Performance Evaluaton In ths secton, we present smulaton results that llustrate the performance of dfferent spreadng sequences allocaton strateges n the realstc case of MC-CDMA transmssons over frequency correlated fadng channels. We consder a smulaton envronment that s qute smlar to the ETSI BRAN HIPERLAN/2 physcal layer,.e. an ndoor transmsson wth 64FFT-based OFDM modulaton. The data rate s 20 MHz so that the subcarrer bandwdth s 0.31 MHz. Two propagaton channels ssued from [10] are taken nto account wth a dfferent ] (7 coherence bandwdth B c, as presented n Table 1. In order to deal wth multple access and to beneft from the maxmal frequency dversty, a synchronous transmsson wth Walsh-Hadamard spreadng sequences of length 64 s consdered, whch wll allow a maxmum number of 64 smultaneous actve users. Wth no restrcton on the results, we assume that an actve user only uses one sequence. Sngle-user detecton based on EGC or MMSEC technques are used at the recever sde. The sgnals of all actve users are transmtted wth equal power, the guard nterval s desgned to entrely compensate the ISI and the channel transfer functon s power normalzed. Table 1: Characterstc of the channel models [10]. Channel A BC = 2.5 MHz Channel B BC = 1.3 MHz We compare the performance of our optmsed spreadng sequence allocaton procedure to other allocaton choces n terms of averaged Bt-Error-Rate, whch s computed after demodulaton and detecton over all the actve users. Fgure 3 represents the results for Channel A and EGC detecton, where the curves dffer by the spreadng sequence allocaton strategy and/or the number of smultaneous actve users. Average BER 1E-01 1E-02 1E-03 opt. allocaton: 2 users bad allocaton: 2 users opt. allocaton: 30 users bad allocaton: 30 users 0 1 2 3 4 5 6 7 8 9 10 11 12 Eb/N0 (db Fgure 3: Performance comparson of dfferent Walsh-Hadamard spreadng sequence allocaton strateges. (Channel A, EGC detecton. For 2 users wth a bad spreadng sequence allocaton, BER=10-3 s acheved for a Eb/N0 equal to 9.1 db whle our optmzed allocaton procedure requres 1.7 db less. As bad allocaton for 2 users, we choose the all one
Walsh-Hadamard sequence and the sequence wth one transton 1/-1 n the mddle of the sequence. Moreover, the transmsson of 30 actve users based on the optmzed procedure performs better that the transmsson of 2 actve users wth a bad allocaton. Compared wth the optmzed allocaton for 30 actve users, the transmsson of 30 actve users wth a bad allocaton requres 5 db more to acheve BER=510-3. Ths result emphaszes the great mpact of the spreadng sequence allocaton strategy that can drastcally ncrease the multple access nterference and then the BER, even f only one user nterferes on the desred one. In order to evaluate the nfluence of the channel frequency correlaton, Fgure 4 depcts for a transmsson over Channel B the nfluence of the allocaton strateges that were compared on Fgure 3. 1E-01 Fgure 5 represents the BER obtaned for dfferent spreadng sequence allocaton strateges for a transmsson over Channel A when the detecton s performed by a MMSEC algorthm, whch s known to provde better performance than EGC detecton [3]. For comparson, the BER obtaned after EGC detecton (Cf. Fgure 3 for the transmsson of 2 users wth optmzed and bad spreadng sequence allocaton s also plotted. Compared wth the optmzed allocaton strategy, a degradaton of 2.6 db s experenced to acheve BER=10-3 for 2 users wth MMSEC detecton f a bad allocaton strategy s chosen. Ths degradaton s much hgher than the degradaton of 1.7 db that s experenced wth EGC detecton as plotted n Fgure 3. Wth an optmzed allocaton procedure, the MMSEC detecton performs better than the EGC detecton,.e. t requres 0.5 db less to provde BER=10-3 : the spreadng sequence allocaton lmts the MAI n the transmsson and the ntrnsc performance of the MMSEC detecton s acheved. 1E-01 Average BER 1E-02 1E-03 opt. allocaton: 2 users bad allocaton: 2 users opt. allocaton: 16 users opt. allocaton: 30 users Average BER 1E-02 0 1 2 3 4 5 6 7 8 9 10 11 12 Eb/N0 (db Fgure 4: Performance comparson of dfferent Walsh-Hadamard spreadng sequence allocaton strateges (Channel B, EGC detecton. For a transmsson of 2 actve users, the optmzed spreadng sequence allocaton requres almost 1.7 db less to acheve BER=10-3 than a bad allocaton. Moreover, compared wth the case of a bad allocaton for 2 users, 16 users can be tolerated wth an optmzed allocaton to acheve the same BER. If 30 users are transmttng wth an optmzed allocaton, then a large degradaton occurs. Compared wth the results of Fgure 3 where 30 users were tolerated, the smaller frequency correlaton of the channel,.e. the smaller coherence bandwdth BC = 1.3 MHz, lmts the performance mprovement due to the allocaton strategy n terms of addtonal number of users. These results confrm the nfluence of the multplcaton coeffcent of R (1 n relaton (3, whch s lower for Channel B than for Channel A. 1E-03 opt. alloc.: 2 users MMSEC bad alloc.: 2 users MMSEC opt. alloc.: 30 users MMSEC opt. alloc.: 2 users EGC bad alloc.: 2 users EGC 0 1 2 3 4 5 6 7 8 9 10 11 12 Eb/N0 (db Fgure 5: Performance comparson of dfferent Walsh-Hadamard spreadng sequence allocaton strateges (Channel A, MMSEC detecton. In contrast, f a bad allocaton s performed for 2 users, then the MMSEC detecton performs worse than the EGC detecton. Thus, the ampltude equalzaton seems to make the recever less robust n case of a bad allocaton. At last, as n Fgure 3, the transmsson of 30 actve users wth optmzed spreadng sequences gves much better performance than the transmsson of 2 users wth a bad spreadng sequence allocaton. Ths result confrms the great mpact of the spreadng sequence allocaton procedure.
5. Conclusons In ths paper, a MAI mtgaton scheme for MC-CDMA transmsson systems was nvestgated. The proposed technque s based on a partcular selecton, wthn a gven spreadng sequence famly, of the spreadng sequences that are requested by the network to satsfy a gven number of actve users. On the bass of an analytcal evaluaton of the MAI, a spreadng sequence allocaton procedure was derved. The effcency of ths technque was llustrated by smulaton results for Walsh-Hadamard spreadng sequences wth dfferent realstc channel confguratons and dfferent detecton algorthms. On one hand, because of the frequency correlaton of the channel, the performance of MC-CDMA systems s dependent on the spreadng sequences that are selected wthn a gven spreadng sequence famly wth unform characterstcs n AWGN transmsson condtons. On the other hand, the non-full-loaded network occupancy, whch s a frequent transmsson case, gves a degree of freedom n the allocaton of spreadng sequences so that ths allocaton can be optmzed n order to mprove the performance of the transmsson. Besdes, snce ths technque affects the emtted sgnals, t s lkely to mprove the system capacty whatever the detecton method used by the recever. It s also applcable to any spreadng sequence famly and s smple to mplement. Further research wll consst n a performance evaluaton of ths technque wth more robust detecton algorthms such as mult-user detecton ones. References [1] N. Yee, J.P. Lnnartz, G. Fettwes, Mult-Carrer CDMA n ndoor wreless rado networks, Proc. of PIMRC 93, pp. 109-113, Vol.1, 1993. [2] S. Hara, R. Prasad, Overvew of Multcarrer CDMA, IEEE Communcatons Magazne, vol. 35, pp. 126-133, Dec. 1997. [3] S. aser, Mult-Carrer CDMA Rado Systems Analyss and Optmzaton of Detecton, Decodng, and Channel Estmaton, PhD. Thess, VDI-Verlag, Fortschrttberchte VDI, Seres 10, No. 531, 1998. [4] B.M. Popovc, Spreadng Sequences for Multcarrer CDMA Systems, IEEE Trans. on COM, Vol.47-6, pp. 918-926, Jun. 1999. [5] B.J. Cho, E.L. uan, L. Hanzo, Crest-Factor Study of MC-CDMA and OFDM, Proc. of VTC Fall 99, pp. 233-237. [6] H. Xng, J. Rnne, M. Renfors, The Performance Analyss of Mult-Carrer CDMA Systems Usng Dfferent Spreadng Codes n Frequency Selectve Fadng Envronment, Proc. of 2 nd Int. Workshop MC-SS 99, pp. 141-148, Sep. 1999. [7] D.N. alofonos, J.G. Proaks, Performance of the multstage detector for a MC-CDMA system n a Raylegh fadng channel, Proc. of IEEE GLOBECOM 96, pp. 1784-1788, Nov. 1996. [8] S. aser, J. Hagenauer, Mult-Carrer CDMA wth Iteratve Decodng and Soft-Interference Cancellaton, Proc. of IEEE GLOBECOM 97, pp. 6-10, Nov. 1997. [9] J.Y. Baudas, J.F. Hélard, J. Cterne, Mult-Carrer CDMA usng Interference Cancellaton, Proc. of 2 nd Int. Workshop MC-SS 99, pp.251-258, Sep. 1999. [10] J. Medbo. Channel Models for HIPERLAN/2 n Dfferent Indoor Scenaros. ETSI BRAN doc. 3ERI085b, March 98.