26 IEEE Nnth Internatonal Symposum on Spread Spectrum Technques and Applcatons Improved Throughput over Wrelnes wth Adaptve MC-DS-CDMA Mattheu CRUSSIÈRE, Jean-Yves BAUDAIS and Jean-Franços HÉLARD Electroncs and Telecommuncatons Research Insttute of Rennes IETR INSA, 2 avenue des Buttes-de-Coësmes, 3543 Rennes, France {mattheu.crussere,jean-yves.baudas,jean-francos.helard}@nsa-rennes.fr Abstract In ths paper, we present a fnte-granularty loadng algorthm for multcarrer drect sequence code dvson multple access MC-DS-CDMA. The resultng adaptve scheme represents an extenson of classcal dgtal multtone DMT wth spreadng n the tme doman. The presented algorthm assgns subcarrers, spreadng codes, bts and energy per code n order to maxmze the data rate n a sngle user network, or to maxmze the mnmum data rate n a multuser network. The optmzaton s realzed at a target symbol error rate and for a gven power spectral densty PSD. Optmal allocaton s performed through analytcal study, and smulaton results of the new scheme are presented n sngle user dgtal subcrber lne DSL and multuser power lne communcaton PLC contexts. Compared to DMT, t s shown that the tme spreadng component of MC- DS-CDMA system yelds throughput mprovement aganst a weak ncrease of complexty. I. INTRODUCTION DIGITAL mult-tone DMT modulaton, also known as orthogonal frequency dvson multplexng OFDM, s a flexble and effcent soluton to transmt nformaton over wrelnes [1]. Wth multcarrer modulaton, the channel s dvded nto multple subchannels that are essentally ntersymbol nterference-free, and ndependent addtve whte Gaussan nose channels. The man property of wrelne channels s ts statc, or quas-statc mpulse response. It can then be advantageously assumed that the transmtter has perfect channel state nformaton, and can perform adaptve resource allocaton. Under constrants, lke power budget, power spectrum densty PSD, peak power, QoS, or throughput, the queston s how to fnd power and bts allotment on each subchannel n order to maxmze performance. The optmal soluton s known as the waterfllng-based method wth adaptve modulatons. Many dscrete algorthms for allocatng subcarrers, power, and bts have been developed. The frst proposed [2] gves an optmal soluton usng a greedy algorthm but leads to computatonal complexty and would be mpractcal when the number of bts to be transmtted per DMT symbol s large. Many suboptmal algorthms wth less computatonal complexty have been developed see, for example, [3] and references nsde for an extensve overvew, and multuser extenson has been carred out [4]. All these algorthms compute the bt loadng subcarrer per subcarrer. However, for long lnes or deep frequency fadngs, many avalable subcarrers cannot bear any bt wth DMT system, and only few subcarrers are used to transmt data. Carrer mergng [5], [6] has been proposed to reduce the bt loadng quantfcaton loss and allows to use more avalable subcarrers. Moreover, fnte order modulatons lke quadrature ampltude modulatons QAM and PSD constrant accentuate ths quantfcaton loss. To crcumvent ths problem, trells coded modulaton can be used wth varable rates, leadng to an mportant ncrease of complexty, contrary to carrer mergng. In ths paper we propose to use the multcarrer drect sequence code dvson multple access MC-DS-CDMA technque, frst ntroduced n wreless context [7], to perform symbol mergng as bt loadng quantfcaton loss reducton. Ths merge s realzed n the tme doman own to the spreadng sequences of the MC-DS-CDMA system, n contrast to carrer mergng whch realzes mergng n the frequency doman. Thus, the bt loadng algorthm has to take nto account not only the subcarrer but also the spreadng component of the system to perform bt, power and code allotment. Ths paper s organzed as follows. Secton II presents the MC-DS-CDMA system model. Secton III recalls the DMT system capacty n multuser context. Secton IV gves the mathematcal soluton of maxmzaton MC-DS-CDMA throughput problem under PSD constrant, and secton V gves the correspondng algorthm. The performance of MC-DS- CDMA system s gven n secton VI and compared to the performance obtaned wth the DMT system n ADSL Asymmetrc dgtal subscrber lne sngle user context, and PLC Power lne communcaton multple user context. Fnally, secton VII concludes the paper. II. MC-DS-CDMA SYSTEM The studed MC-DS-CDMA system results n multcarrer modulaton appled to CDMA sgnal. The MC-DS-CDMA transmtter modulates the data substreams on subcarrers wth a carrer spacng proportonal to the nverse of the chp rate to guarantee the orthogonalty between spectrums of the substreams after spreadng [7]. The data stream s frst converted onto parallel low rate substreams, before applyng the spreadng on each substream n the tme doman, and modulatng onto each subcarrer. Due to code dvson multple access, several data of substreams are transmtted at the same tme by a gven subcarrer. Let N s be the number of used subcarrers whch s equal to the number of low rate substreams, N c be the number of smultaneous transmtted symbols by subcarrer, andl c the number of chps per code of subcarrer,.e. the length of the code. Note -783-978-/6/$2. 26 IEEE 143
that, N c also corresponds to the number of used codes related to subcarrer. To smplfy the notaton and the presentaton of the system we suppose n the sequel that N c = N c and L c = L c. QAM symbols are transmtted by blocks of sze N s N c, denoted Xn = x,j n < N s, <j N c. The same spreadng code matrx C =c j,k <j Nc, <k L c s appled to all subcarrers [8]. These spreadng codes are orthogonal codes extracted from the Hadamard matrx of sze L c L c.thenth spread symbol expressed before multcarrer modulaton s Y n =[Y 1 n... Y Lc n] = Xn C. 1 The multcarrer modulaton s appled to the vector Y k n = [y k,1 n... y k,ns n] T, and the MC-DS-CDMA scheme needs L c DMT symbols to transmt one full MC- DS-CDMA symbol. To make the notaton more compact and wthout loss of generalty, the tme varable n s omtted n the followng. The multcarrer component of MC-DS-CDMA sgnal s assumed to be adapted to the channel, and the channel s constant over L c DMT symbols,.e. over one MC-DS-CDMA symbol. In that case, the channel can be modeled by one sngle complex coeffcent per subcarrer [9]. After multcarrer demodulaton wth guard nterval removal and fast Fourer transform, channel correcton wth zero forcng ZF, and despreadng, the receved sgnal carred by the th subcarrer and the jth code s [1] L c ζ,k z,j = L c x,j + c j,k, 2 h k=1 where h s the frequency channel coeffcent of subcarrer, and ζ,k the sample of complex background nose assumed to be Gaussan and whte, wth varance N, k ofsubcarrer and kth DMT symbol. Because of transmtted PSD constrant, the power of the transmtted sgnal depends on the length L c of the code. The matrx of the receved symbols over all subcarrers and all codes s Z = L c X + G W C T wth G the dagonal equalzaton matrx such that g, =1/h,and W =w,j < Ns, <j N c. III. MULTICARRIER BIT LOADING DMT or OFDM modulaton decomposes the channel nto a set of N s orthogonal subcarrers. The total system capactes s then the sum of the capacty of each subcarrer C DMT = log 2 1+ h 2 e, 3 N where h 2 e /N s the sgnal to nose rato SNR of subchannel at the recever sde. Wth PSD constrant, the maxmum energy e per symbol and per subcarrer s lmted to E,.e., e E. The throughput n R s gven by R DMT = R = log 2 1+ h 2 E, 4 Γ N where Γ s the SNR gap or normalzed SNR that s calculated accordng to the gap-approxmaton analyss [1]. In sngle user context wth QAM constellatons, the relable throughput per subcarrer s R, where s the floor functon. Only subcarrers wth R 1 are used to transmt data. In multple user context, a smple soluton to share the resources s frequency dvson multple access FDMA; the set of subcarrers s then dvded between the users. The optmal soluton that maxmzes the mnmum throughput needs lots of subchannel swappngs, and a suboptmal soluton as the one proposed n [4] already acheves results close to the optmal soluton. Ths algorthm allocates the subcarrers one by one to each user. At each step, the user wth the smallest rate s beng assgned the subcarrer, among the remanngs, that leads to the hghest ncrease of ts rate. In ths paper, a modfed verson of ths algorthm s appled to the MC-DS- CDMA scheme to perform multple access. IV. MC-DS-CDMA BIT LOADING In ths secton, the bt loadng strategy appled to MC-DS- CDMA s presented n the sngle user case. The algorthm has to assgn bts and energy per code, and also to fnd the number of codes that maxmze the throughput per subcarrer. Due to orthogonalty n frequency and code spaces, each receved symbol z,j s estmated ndependently wthout ntersymbol nterference, as evdent from 2. Thus, the total system capacty s the sum of the system capactes assocated wth each subcarrer and code j. The capacty, expressed n bt per MC-DS-CDMA symbol, of the MC-DS-CDMA system usng ZF detecton s then where and C MC-DS-CDMA = j=1 = log 2 1+ j=1 var [z,j x,j ]= C MC-DS-CDMA,j E [z,j u x,j ] var [z,j x,j ] E [z,j u x,j ] 2 = L 2 c e,j, L c k=1 Then, t comes C MC-DS-CDMA = j=1 2 c 2 j,k h 2 var [ζ,k] =L c N h 2., 5 log 2 1+L c h 2 e,j. 6 N e,j s the energy of the chp of the code j n the subcarrer. The PSD constrant s expressed as [1,N s ] j=1 where E s gven by the maxmal PSD. e,j E. 7 144
Proposton 1: Gven an energy transmsson level E and QAM constellatons, the relable MC-DS-CDMA throughput s R MC-DS-CDMA = R = =j R,j = L c R /L c + Lc 2 R/Lc R/Lc 1, wth R = L c log 2 1+ h 2 E Γ N,andΓ the normalzed SNR of the QAM constellaton. The throughput R s the maxmum throughput acheved n R. Ths maxmum throughput s obtaned wth a number of codes equal to the length of the codes,.e. full load case N c = L c, and wth a unform dstrbuton of energes,, j e,j = E/L c. Followng proposton 1, t s now possble to optmally assgn one modulaton to each code on the dfferent subcarrers. Ths proposton, wth the proof gven n [11], says that maxmum MC-DS-CDMA throughput s obtaned on each subcarrer f R /L c +1 bts are assgned to L c 2 R/Lc R/Lc 1 codes, and R /L c bts are assgned to the other codes,.e. L c L c 2 R/Lc R/Lc 1 codes. Ths proposton gves the number of used codes N c = L c, and the energy e,j that should be assgned to the code j of the subcarrer s e,j = 2 R,j 1 N Γ L c h 2, 8 wth R,j the number of tranmtted bts over ths code j and ths subcarrer. Note that such an energy allocaton yelds a null nose margn because each modulated symbol receves the exact amount of energy to transmt the number of bts determned by proposton 1 for a gven Γ. The transmsson system wll therefore meet the targeted error probablty related to Γ. V. BIT LOADING ALGORITHM In sngle user context, the bt loadng algorthm apples the proposton 1 to perform the bts, codes and energes allotment across the spectrum. In multuser context, each user uses ts own channel, and we am at maxmzng the smallest throughput of all users, whch s equvalent to maxmzng the total throughput of the system whle ensurng equal rates between users. Let N u be the number of users, and B u the subset of subcarrers used by user u. Because of frequency dvson multple access between user, we have u u, B u B u =. The throughput of the system wrtes R MC-DS-CDMA = R u = = u=1 c N u=1 B u j=1 u=1 R u B u R u,j, 9 where R u,j { R u /L c, R u /L c +1 } accordng to proposton 1, and where the superscrpt u ndcates that the dfferent values are calculated usng the channel coeffcents of user u, h u,j. Let us now enounce the proposed allocaton algorthm n three steps. 1 Intalzaton a Compute u α u = R u, wth B u =[1,N s] b Set u R u =, B u = 2 Whle u B u = a Fnd u =argmn αu cardb u= u b For the found u, fnd the best unused subcarrer,.e. wth the best lnk budget c Update B u, R u : B u = {}, R u = R u 3 Whle there exsts unused subcarrer a Fnd u =argmn R u u >, b For the found u, fnd the best unused subcarrer c Update B u, R u : B u = B u + {}, R u = R u + R u To realze multple access, the prncple of the subcarrer allocaton algorthm n [4] s used, except that the N u frst subcarrers are assgned see step 2 wth respect to a prorty order among the users based on the achevable throughput R u of each user, and except that the user whch cannot mprove ts rate see condton n 3a s no more taken nto account by the allocaton procedure n step 3. The user wth the smallest R u s beng allocated at frst, and then are the others n second step. Any subcarrers cannot been dedcated to one user wth zero bt transmsson n thrd step. Of course the thrd step s stopped when no more user can mprove ts throughput. Wthout condton n 3a,.e. wthout R u >, the user wth the worst channel would mpose ts throughput on all the others user, whch would reduce the total throughput. VI. SIMULATION RESULTS MC-DS-CDMA system uses L c DMT symbols to transmt one MC-DS-CDMA symbol. To compared DMT and MC- DS-CDMA performance, the throughput must be expressed usng the same unt. All the throughputs are expressed per DMT symbol, hence the MC-DS-CDMA throughput wrtes R MC-DS-CDMA /L c. Wth L c =1the MC-DS-CDMA system amounts to the classcal DMT. We use the 2 q -ary QAM constellatons specfed for DSL. Results are gven for a targeted SER of 1 3 wthout channel codng, correspondng to an SNR gap Γ =6dB. A. Sngle user ADSL context In ths context, the generated MC-DS-CDMA sgnal s composed of N s = 22 subcarrers transmtted n the band [.146 ; 1.14] MHz. The ADSL transmsson lne s a standard European lne wth a dameter of.4 mm. The spectrum mask s lmted to 39 dbm/hz and the PSD of the statonary background nose s 14 dbm/hz. The equvalent subcarrer SNR at the recever takng nto account the SNR gap Γ s dsplayed Fg. 1 for a length of the lne equal to 35 m. Furthermore the rate transmtted by each subcarrer are exhbted for DMT dashed lne and MC-DS-CDMA sold lne wth L c =4. The step ampltude of the starcase curve s lower for MC- DS-CDMA L c =4thanDMTL c =1 due to mergng 145
effect. The spreadng component of MC-DS-CDMA allows to gather the energes of the dfferent chps of the codes, and then provdes throughput gan. Contrary to DMT, the proposed system collects an explots teh resdual energes, lost on each subcarrer of the DMT system because of the fnte granularty of the QAM constellatons. 6 4 2 Subcarrer SNR db 2 55 11 165 22 15 Subcarrer rate bt/dmt symb. B. Multple user PLC context In ths context, the generated MC-DS-CDMA sgnal s composed of N s = 188 used subcarrers transmtted n the band [1.6 ; 2] MHz. In smulatons, we use power lne channel responses that have been measured n an outdoor PLC network by the french power company Électrcté de France EDF. Note that the allocaton problem formulaton holds n both forward and backward lnks, snce multple access s realzed through an FDMA approach. We appled the proposed algorthm to the case of a 4-user multple access communcaton over the above-mentoned PLC channels. The background nose level s 11 dbm/hz, we assume a transmsson level of 4 dbm/hz, and a average channel attenuaton of 5 db. 2 db DMT load 1 MC DS CDMA rate 1 loaded subcarrers 5 DMT rate 1 55 11 165 22 Fg. 1. ADSL subcarrer SNR and rate vs. subcarrer ndex, L c =4 2 3 6 9 12 15 18 2 db MC DS CDMA load 19 Throughput bt/dmt symb. 1 loaded subcarrers 165 14 1 Fg. 2. 115 99 25 5 75 1 code length ADSL throughput vs. code length L c The throughputs obtaned for dfferent code lengths are dsplayed Fg. 2. Wth DMT,.e. L c =1, the throughput s R = 992 bt/dmt symb., whereas t reaches 165 bt/dmt symb. wth L c = 8. The throughput gan obtaned wth ths reasonable spreadng factor corresponds to 8% of the maxmum achevable gan gven at L c = 1. Ths throughput gan represents an ncrease of the DMT throughput of about 1%. 2 3 6 9 12 15 18 Fg. 3. PLC load vs. subcarrer ndex, L c =8, N u =4 The equvalent subcarrer SNR of the 4 used channels are dsplayed Fg. 3. Furthemore the loaded subcarrers are ndcated by marker n the DMT and the MC-DS-CDMA cases. As expected, a larger number of sucarrers are exploted by the proposed adaptve MC-DS-CDMA scheme due to the symbol mergng effect. Wth DMT, the mnmum SNR needed to transmt some data s roughly db. Due to spreadng gan, ths mnmum SNR s 1 log 1 L c lower wth MC-DS- CDMA. As prevously presented n the ADSL sngle user case, 146
16 15 14 13 12 25 5 75 1 46 42 38 + 34 + + + + + + + +++ + + + + + + + + + + + + + + + System throughput bt/dmt symb. Throughput of user bt/dmt symb. strategy s based on a greedy approach whch represents a suboptmal but practcal soluton to the stated problem. We analyzed the performance of the new system and compared the results to those obtaned wth the DMT system. We hereby hghlghted that DMT s equvalent to the proposed MC-DS-CDMA system wth L c = 1. The spreadng component was shown to provde throughput gan especally for low channel gans. Ths behavor was explaned by the energy gatherng capablty of MC-DS-CDMA wthn each spread symbol. Contrary to DMT, the proposed system can explot the resdual energy conveyed by each subcarrer because of the fnte granularty of the QAM modulatons. Furthermore, t rased a trade-off concernng the spreadng factor choce. On one hand, t was to be suffcently large to ncrease the throughput, and on the other hand, t was to reman relatvely small to ensure low process delay. For well-chosen spreadng factors, we then concluded that the proposed adaptve system was able to transmt hgher rates than DMT. + #1 #2 #3 #4 3 25 5 75 1 Fg. 4. PLC user and system throughput vs. code length, N u =4 the total throughput s ncreased n the PLC multple user case wth MC-DS-CDMA, Fg. 4. For example, DMT transmts xxx bt/dmt symb. whle MC-DS-CDMA transmts xxx bt/dmt symb. for L c = 4. The throughput gan s hgher than 2% for L c 4. The mnmum throughput s also ncreased of 1% wth L c =4. For low values of L c, user #4 s the only one who s able to explot the hghest frequences of the spectrum. VII. CONCLUSION In ths paper, we proposed an adaptve MC-DS-CDMA system sutable for wrelne networks. We ntroduced a novel loadng algorthm that handles the subcarrer, code, bt and energy resource dstrbuton among the actve users of the system. We focused on the system throughput maxmzaton constraned to PSD lmtatons and fnte order modulatons. We derved the optmal soluton n the case of sngle user transmssons and proposed a smple algorthm n the case of multple user transmssons. The subcarrer dstrbuton REFERENCES [1] J. Coff, A multcarrer prmer, ANSI T1E1.4/91 157, Commttee contrbuton, Tech. Rep., 1991. [2] D. Hughes-Hartogs, Ensemble modem structure for mperfect transmsson meda, U.S. Patent 4 679 227, July, 1987. [3] C. Wong, R. Cheng, K. Letaef, and R. Murch, Multuser OFDM wth adaptve subcarrer, bt, and power allocaton, IEEE Journal on Selected Area n Communcatons, vol. 17, no. 1, pp. 1747 1758, Oct. 1999. [4] W. Rhee and J. Coff, Increase n capacty of multuser OFDM system usng dynamc subchannel allocaton, n Proc. IEEE Vehcular Technology Conference VTC-Sprng, vol. 2, May 2, pp. 185 189. [5] O. Isson, J.-M. Brosser, and D. Mestdagh, Mult-carrer bt-rate mprovement by carrer mergng, IEE Electron. Lett., vol. 38, no. 9, pp. 1134 1135, Sept. 22. [6] S. Maller, F. Nouvel, J.-Y. Baudas, D. Gardan, and A. Zeddam, Multcarrer CDMA over copper lnes comparson of performances wth the ADSL system, n Proc. IEEE Internatonal Workshop on Electronc Desgn, Test and Applcatons DELTA, Jan. 22, pp. 45 452. [7] S. Kondo and L. Mlsten, On the use of multcarrer drect sequence spread spectrum systems, n IEEE Mltary Communcatons Conference, Oct. 1993, pp. 52 56. [8] Q. Chen, E. Sousa, and S. Pasupathy, Performance of coded multcarrer ds-cdma system n multpath fadng channels, Wreless Personnal Communcatons, no. 2, pp. 167 183, 1995. [9] S. Hara and R. Prasad, Overvew of multcarrer cdma, IEEE Communcatons Magazne, vol. 35, no. 12, pp. 126 133, Dec. 1997. [1] M. Hélard, R. L. Gouable, J.-F. Hélard, and J.-Y. Baudas, Multcarrer cdma for future wdeband wreless networks, Annales des télécommuncatons, vol. 56, no. 5/6, pp. 26 274, May/June 21. [11] M. Crussère, J.-Y. Baudas, and J.-F. Hélard, Adaptve spread spectrum multcarrer multple access over wrelnes, to be publshed n IEEE Journal on Selected Area n Communcatons J-SAC, specal ssue powerlne communcatons, July 26. + 147