Spatal Multplexng appled to Turbo Coded Mult-Carrer CDMA Vncent Le Nr, Marylne Hélard, Rodolphe Le Gouable To cte ths verson: Vncent Le Nr, Marylne Hélard, Rodolphe Le Gouable. Spatal Multplexng appled to Turbo Coded Mult-Carrer CDMA. 2004, 5 p., 2004. <hal-00005808> HAL Id: hal-00005808 https://hal.archves-ouvertes.fr/hal-00005808 Submtted on 4 Jul 2005 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.
Spatal Multplexng appled to Turbo Coded Mult-Carrer CDMA Vncent Le Nr, Marylne Hélard, Member, IEEE, Rodolphe Le Gouable France Telecom R&D, 4 rue du Clos Courtel BP 91226-35512 Cesson Sévgné Cedex, FRANCE E-mal: vncent.lenr@rd.francetelecom.com Abstract In ths paper, we combne Spatal Multplexng wth a Mult-Carrer Code Dvson Multplex Access (MC-CDMA) system assocated to a Turbo Codng (TC) scheme. MC-CDMA s lkely to be a very promsng access technque for future wreless communcaton systems. In fact, MC-CDMA explots the advantages of both mult-carrer modulaton and Code Dvson Multple Access (CDMA) technque. On the other hand, the capacty of mult-antenna system can lnearly ncrease wth the mnmum of transmt and receve antennas usng Spatal Multplexng. We study the concatenaton of Multple Input Multple Output (MIMO) systems for N t transmt and N r receve antennas and MC-CDMA wth a TC scheme. Smulaton results are provded for dfferent loads n order to demonstrate the effcency of spatal multplexng combned wth turbo channel codng scheme for a mult-user system based on MC-CDMA for both uncorrelated and correlated antenna systems. I. INTRODUCTION On one hand, MC-CDMA s a very promsng technque for the future wreless communcaton systems. Ths technque combnes Orthogonal Frequency Dvson Multplex () mult-carrer modulaton and CDMA access technque dervng benefts from both technques ncreasng the hgh spectral effcency and the robustness aganst mult-path channels. The modulaton conssts n splttng the ntal data rate n lower data rates transmtted over nonselectve frequency subcarrers. Moreover, the mult access flexblty and low multuser nterference are provded by CDMA [1]. On the other hand, multple antenna systems were also demonstrated to sgnfcantly ncrease the capacty of future wreless communcaton systems [2]. In ths paper, we brefly present a MC-CDMA system n a Sngle Input Sngle Output (SISO) antenna system before extendng MC-CDMA to a MIMO system wth N t transmt and N r receve antennas. In [3][4], t was demonstrated that a good tradeoff between complexty and BER performance s acheved by usng a Sngle User (SU) Mnmum Mean Square Error (MMSE) detector wth a Turbo Codng (TC) scheme for a SISO MC- CDMA transmsson. Indeed, t was shown n [3] that more complex Mult User (MU) Successve Interference Canceller (SIC) or Parallel Interference Canceller (PIC) detectors lead to worse performance results than a one when MC-CDMA s assocated to a TC scheme. Moreover, for a MIMO scheme, the Vertcal Bell Labs Advanced Space-Tme (VBLAST) recever uses a SIC detector [5] n order to retreve the nformaton of the mult-antenna transmtted symbols. In ths paper, we assocate a TC scheme and a detector wth the MIMO MC-CDMA system. We compare two types of MIMO recevers whch are the detector adapted to spatal multplexng wth or wthout a mult-antenna SIC detecton. We provde smulaton results over uncorrelated Raylegh flat fadng channels per V-BLAST for dfferent loads for both uncorrelated or correlated antenna systems. II. MC-CDMA, PRESENTATION In ths secton we brefly present the prncple of a MC- CDMA system. Frst, data bt stream of each user s ndvdually turbo coded and converted nto a symbol vector. The multuser turbo coded symbol matrx X ncludng the nformaton of all the users s of sze N u N and denoted X = [ ] x 1... x n... x N where n s the tme ndex and N the number of symbol vectors transmtted durng N symbol duratons. x n = [ ] T x 1n... x jn... x Nun s a vector of length N u, where N u s the number of users and [.] T the transpose operaton. The multuser coded sequence s spread usng a Fast Hadamard Transform (FHT). We consder that the length of the spreadng sequences s equal to L c. Here we assume L c N c, where N c s the number of subcarrers of the. In practce, modulaton and demodulaton are easly carred out n the dgtal doman by performng Inverse Fast Fourer Transform (IFFT) and FFT operatons. Furthermore the nserton of a guard nterval between adjacent symbols guarantees the absence of Inter Symbol Interference (ISI). In ths paper, uncorrelated frequency nonselectve Raylegh fadng per subcarrer s consdered. The theoretcal channel response of the kth subcarrer can be estmated by h k = ρ k e θ k due to perfect orthogonalty n synchronous transmsson [4]. In the SISO case, the receved
sgnals for the L c subcarrers can be expressed by: R = HCX + N (1) where R = [ ] r 1... r n... r N s a matrx of sze Lc N, wth r n = [ ] T r 1n... r kn... r Lcn the receved vector of length L c on the dfferent subcarrers. H s a L c L c tme varyng dagonal matrx, each element of the dagonal standng for the frequency channel response of each subcarrer, C = [ ] c 1... c j... c Nu s the Lc N u matrx of user s spreadng codes, c j = [ ] T c 1j... c kj... c Lcj s the vector of length L c of user j, and N s the Addtve Whte Gaussan Nose (AWGN) matrx of sze L c N. At the recever sde, the orthogonalty between users has to be restored by applyng an equalzaton process before despreadng. In ths paper, we only consder a detector. In fact, for a SISO MC-CDMA transmsson wth TC, a detector was demonstrated to be a good tradeoff between complexty and performance, avodng the use of more complex MU detectors lke SIC or PIC detectors [3]. Hence, at the recever n case of SU detector, an equalzer g k corrects the L c ampltude and phase varatons of each subcarrer k. G s a dagonal matrx contanng the equalzaton coeffcents g k. We can consder that H H G = H H H + 1 γ I (2) correspondng to the MMSE SU equalzaton matrx where [.] H denotes the transpose conjugate and γ the nput Sgnal to Nose Rato (SNR) at the receve antenna. Thus, the equalzaton coeffcent can be wrtten as follows: g k = h k 2 + 1 (3) γ After equalzaton, the resultng sgnal s: Y = GHCX + GN (4) where Y =[y 1...y n...y N ] s the L c N matrx of the equalzed sgnals, wth y n = [ ] T y 1n... y kn...y Lcn the L c length vector of the receved symbol n. The fnal step conssts n executng the despreadng by applyng the IFHT to the vector Y n order to detect the N coded symbols x jn transmtted by the user j. Fnally soft demappng and turbo decodng are carred out. III. COMBINING MC-CDMA AND SPATIAL MULTIPLEXING The MIMO MC-CDMA transmsson and recepton schemes are presented n Fgure 1 and Fgure 2 respectvely. h k User 1 User Nu Nr Nu Demodulaton (FFT) Demodulaton (FFT) Turbo Codng Turbo Codng Nr Fg. 2. Fg. 1. Symbol Mappng Symbol Mappng Nu Spreadng FHT MC-CDMA MIMO Transmtter Lnear Equalzer G or SIC detector Despreadng User j FHTj 1 Symbol Demappng MC-CDMA MIMO Transmtter and Recever Nt Modulaton (IFFT) Modulaton (IFFT) Turbo Decodng A. Transcever Frst, data bt stream of each user s turbo coded ndvdually and converted nto a symbol vector. The multuser turbo coded symbol matrx X ncludng the nformaton of all the users s send over N t transmt antenna. Then, the multuser coded sequence s spread usng a FHT coded symbol as for classcal MC-CDMA. The transmtted matrx S of sze N t L c N s therefore gven by: S = C.X (5) where the spreadng sequences are gven by the followng equaton C = I Nt C of sze N t L c N t N u and where X s the N t N u N matrx of multuser coded sequences. Uncorrelated frequency non-selectve Raylegh fadng per subcarrer s assumed as well as perfect channel estmaton. The theoretcal channel response, for the k th subcarrer, from transmt antenna t to receve antenna r can be estmated by h rt,k = ρ rt,k e θ rt,k. In the MIMO case, consderng that the columns of the receved matrx R of sze N r L c N are gven by the vector r of length N r L c 1, [1...N] durng N adjacent symbols, we obtan the followng matrx representaton: r = H.s + n [1...N] (6) where the AWGN vector n s a vector of length N r L c 1 and where the channel matrx H s a N r L c N t L c tme varyng matrx H = H 11 H 12... H 1Nt H 21 H 22... H 2Nt. H Nr1..... H Nr2... H NrNt Nt User j (7)
where H rt s the L c L c tme varyng dagonal matrx wth h rt,k the k th element at tme. B. Decodng and MC-CDMA Equalzaton As for SISO, n order to restore the orthogonalty between users, an equalzaton process s done before despreadng. Ths equalzaton process has to take nto account the Co- Antenna Interference (CAI) caused by the spatal multplexng scheme. In ths secton, we present two types of MIMO MC- CDMA detectors, whch are the detector adapted to a spatal multplexng transmsson and the SU SIC-MMSE detector wthout orderng. The SIC s carred out only on the mult-antenna receved symbols whch have CAI and not for the mult-user detecton whch s a SU detecton. 1) detector adapted to spatal multplexng: The equalzaton process conssts of applyng an equalzaton matrx G to the receved vector r. If we choose a equalzer, the equalzaton matrx s : H H G = H HH + 1 γ I (8) where γ s the Sgnal to Nose Rato at the receve antenna. After the decodng process we have: ŝ = G r = G H s + G n [1...N] (9) In order to retreve the nformaton, a despreadng on the dfferent layers of the resultng symbols s needed. The layer l corresponds to a sgnal transmtted by one of the N t transmt antenna. For the despreadng, the estmated soft symbols of user j are gven by the followng vector of length N t L c 1: ˆx l j = C H j ŝ l (10) wth Cj H the transconjugate of user j s matrx spreadng code over N t transmt antennas of sze N t N t L c. Ths leads to the followng detector: detector adapted to spatal multplexng forl=1ton T for=1ton G = H + ŝ = G r end for ˆx l j = CH j ŝl end for where [.] + s the Moore-Penrose pseudo-nverse operaton. Ths detector adapted to spatal multplexng s later called detector. 2) SU SIC-MMSE detector: However, one can take advantage of the detectons of the dfferent layers by a SIC detector as descrbed n [5]. We use a SIC detector wthout orderng. The orderng polcy s not mplemented because t does not mprove the performance of spatal multplexed MC-CDMA wthout orderng. In fact, the optmum orderng polcy cannot be appled to spatal multplexed MC-CDMA because the SIC algorthm cancels spreaded symbols due to CAI nterference whle the decsons has to be made on despreaded symbols. Therefore, these despreaded symbols don t take advantage of the MIMO channel snce the despreadng operaton s performed over L c spreaded symbols affected by dfferent subchannels. Frst, a despreadng on the frst layer of the resultng symbols s needed leadng to the soft estmated symbols of the dfferent users gven by the followng vector of length N t L c 1: ˆx 1 = C H ŝ 1 (11) wth C H the transconjugate of users matrx spreadng code over N t transmt antennas of sze N t N t L c. It s possble to make a hard decson on the estmated symbols of the dfferent users accordng to the chosen modulaton x 1 = Q(ˆx 1 ). When the soft or hard decsons of the frst layer for the dfferent users are made, t s needed to estmate the spreadng symbols by the followng formula s 1 = C x 1. From the V-BLAST detector [5], the estmated symbols from the dfferent users need to be wthdrawn from the receved vectors r : r r D 1. s1 [1...N] (12) wth D 1 = [ H 11 H 21... H Nr1 ] T [1...L] (13) The equvalent channel matrx H becomes: H = H 12... H 1Nt H 22... H 2Nt..... H Nr2... H NrNt (14) wth H rt the dagonal matrx channel of sze L c L c between transmt antenna t and receve antenna r for the tme. Then a new equalzaton matrx G s calculated. The precedent step s carred out teratvely untl all layers are detected. We summarze all these steps by the followng detector for the dfferent users:
10 1 10 2 AWGN Dv4 SU SIC MMSE 18 17 16 15 14 SIC SIC MMSE BER 13 12 10 3 11 10 9 10 4 0 5 10 15 20 8 7 10 20 30 40 50 60 Nb users Fg. 3. Bt error rate performance of a 8 bps/hz MIMO MC-CDMA system wthout channel codng Fg. 4. Requred Eb/N0 for a BER of 10 3 of a 8 bps/hz MIMO MC- CDMA system wthout channel codng SU SIC-MMSE detector forl=1ton T for=1ton G = H + ŝ = G r end for ˆx l = C H ŝ l optonal : x l = Q(ˆx l ) s l = C x l for=1ton r r D 1. s1 H H \l end for end for IV. SIMULATION RESULTS In order to compare these two detectors, we carred out smulatons n uncorrelated Raylegh flat fadng channels subcarrers frst for uncorrelated antennas, then for dfferent correlaton between antennas. We use QPSK modulaton wth N t =4and N r =4leadng to a 8 bps/hz system wthout channel codng. We compare smulatons for dfferent load cases. For full load system, the number of actve users N u s equal to the length of the spreadng code L c =64and the number of subcarrers N c =64. Fgure 3 shows the BER performance of the detector and the SU SIC-MMSE detector wthout channel codng at full load. Fgure 4 shows the performance of these two detectors at a BER 10 3 for dfferent loads. The curve Dv4 s the theoretcal curve of a system wth four antennas leadng to a4dversty order. One can see that the full load curve s parallel to the theoretcal curve due to the same exploted dversty order. The MIMO capacty s expressed by: C = n log 2 (1+ γ ) χ 2 2m (15) N t wth n = mn(n t,n r ) and m = max(n t,n r ) and γ the SNR at the receve antenna. For the full load curve n the 4 4 system, n = m = 4therefore full capacty and dversty are reached. In the lower load cases, the performance curve s obvously better due to less Mult Access Interference (MAI). We observe that the performance of the SU SIC- MMSE detector s better than the detector. Ths can be explaned by the degrees of freedom ntroduced by the SIC detector whch reduces the nose plus CAI and then ncreases the relablty of the decsons. Fgure 5 shows the BER performance of the same systems ncludng a duo-bnary Convolutonal Turbo Code of rate 1 2 at full load [6]. The encodng turbo code block sze s equal to 432 (54 bytes) [7] and we carry out 6 teratons of turbo decodng. Fgure 6 shows the performance of these two detectors at a BER 10 3 for dfferent loads. Thus, we compare the systems at spectral effcences of η = 4 bps/hz for both detectors. We observe that the performance of the SU SIC- MMSE detector leads to worse results than the one. In fact, compared to the detector that doesn t take any decsons the SU SIC-MMSE one can provde bad decsons harmful for channel decodng. Moreover, the BER performance wth TC manly depends on performance at low SNR before decodng, slghtly better for detector. Therefore, the combnaton of a detector for a
10 1 AWGN SU SIC MMSE 10 1 wthout corr. corr 20% TC wthout corr. TC corr 20% 10 2 10 2 BER BER 10 3 10 3 10 4 0 5 10 15 Fg. 5. Bt error rate performance of a 4 bps/hz turbo coded MIMO MC- CDMA system wth channel codng 10 4 0 5 10 15 20 Fg. 7. Influence of the correlaton on the detector wth and wthout channel codng E 10 9 8 7 6 5 4 3 2 1 SU SIC MMSE 10 20 30 40 50 60 Nb users Fg. 6. Requred Eb/N0 for a BER of 10 3 of a 4 bps/hz turbo coded MIMO MC-CDMA system wth channel codng turbo coded MC-CDMA system s a low complexty effcent soluton wthout usng any SIC detectors to remove CAI. Fgure 7 shows the nfluence of the correlaton between antennas for the detector wth and wthout channel codng. We compare ths detector wthout correlaton and wth a correlaton matrx of 20 % over the adjacent antennas, consderng that the correlaton s neglgble between other antennas [8]. The chosen correlaton matrx s: 1.0 0.2 0.0 0.0 0.2 1.0 0.2 0.0 0.0 0.2 1.0 0.2 0.0 0.0 0.2 1.0 (16) We observe that the performance loss between correlated and non correlated curves dmnshes when channel codng s used,.e 0.7 db wth channel codng nstead of 3dB at BER 10 4 owng to the BER before decodng as prevously mentoned. V. CONCLUSION In ths paper, we have frst extended SISO MC-CDMA to MIMO MC-CDMA systems. We have tested two types of mult-antenna recevers, both based on detector and the second one ncludng mult-antenna SIC detecton. Wthout channel codng, the SU SIC-MMSE detector gves the best results compared to the detector. However, wth channel codng, the detector gves better results than the SU SIC-MMSE detector. Therefore, the combnaton of a detector for a turbo coded MIMO MC-CDMA system s a low complexty effcent soluton wthout usng any SIC detectors. Future work wll focus on systems ncludng more realstc MIMO channels. REFERENCES [1] N. Yee, J. P. Lnnartz, G. Fettwes, Multcarrer CDMA n Indoor Wreless Rado Networks, IEEE PIMRC 93, pp. 109-113, Yokohama, Japan, 1993. [2] G. J. Foschn, Layered space-tme archtecture for wreless communcaton n a fadng envronment when usng mult-element antennas, Bell Labs Techncal Journal, Vol. 1, No. 2, 1996, pp. 41-59. [3] M. Hélard, R. Le Gouable, J.-F. Hélard, J.-Y Baudas, Multcarrer CDMA Technques for Future Wdeband Wreless Networks, Annales des Telecoms, Specal ssue on UMTS, May 2001. [4] V. Le Nr, M. Hélard, R. Legouable Space-Tme Block Codng Appled to Turbo Coded Multcarrer CDMA, Vehcular Technology Conference, Jeju, South Korea, 22-25 Aprl 2003. [5] P. W. Wolnansky, G. J. Foschn, G. D. Golden, R. A. Valenzuela V-BLAST: An archtecture for realzng very hgh data rates over the rch-scatterng wreless channel, Proc. IEEE ISSSE-98, Psa, Italy, 30 September 1998 [6] C. Berrou, M. Jézéquel, Non bnary convolutonal codes for turbo-codng, Electronc Letters, vol. 35, N. 1, January 1999, pp. 39-45. [7] ETSI EN 301 958 V1.1.1 Dgtal Vdeo Broadcastng (DVB); Interacton channel for Dgtal Terrestral Televson (RCT) ncorporatng Multple Access, march 2002. [8] S. Loyka Channel Capacty of MIMO Archtecture Usng the Exponental Correlaton Matrx IEEE Communcaton Letters, Vol. 5, No. 9, September 2001.