Adaptive Coding in MC-CDMA/FDMA Systems with Adaptive Sub-Band Allocation

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1 Adaptive Coding in MC-CDMA/FDMA Sytem with Adaptive Sub-Band Allocation PETER TRIFONOV 1, ELENA COSTA, ALESSIO FILIPPI AND EGON SCHULZ Siemen AG, ICM N PG SP RC FR, Germany, ptrifonov@ieee.org,{elena.cota,aleio.filippi,egon.schulz}@iemen.com February 2, 24 Abtract. The MC-CDMA/FDMA cheme i a candidate for the air-interface of beyond 3G mobile communication. An efficient adaptive ub-band allocation (ASBA) approach ha been recently hown to provide a coniderable gain in the uncoded ytem performance. In thi paper, adaptive coding i propoed for application in conjunction with ASBA. Thi i proved to yield a ignificant performance improvement, epecially if a uer-ervice prioritiation i conidered in the ASBA. 1 INTRODUCTION The orthogonal frequency diviion multiplexing (OFDM) multi-carrier (MC) tranmiion technique ha gained a high popularity in the lat few year and i currently regarded a the leading candidate for a new air interface for 4 th generation (4G) mobile radio ytem [1]. Thi mainly owe to the high robutne of OFDM tranmiion to the radio channel timediperion. However, in thi repect, ome ingle carrier olution employing frequency domain equaliation have been recently hown to repreent valid alternative to OFDM [2]. Indeed, major advantage of OFDM are alo the adaptability to the propagation condition and the granularity and flexibility offered in the frequency reource aignment in multiple uer environment. Thee characteritic allow for increaed data throughput while providing a wide range of quality of ervice (QoS) requirement [3]. Lately, OFDM-baed frequency and code diviion multiple acce cheme uch a OFDMA and MC-CDMA have been widely invetigated, epecially for ynchronou downlink application [4]. Thi paper conider the highly flexible MC-CDMA/FDMA hybrid cheme [5]. The tranmiion bandwidth i ubdivided into a number of ub-band, not necearily coniting of adjacent ub-carrier, and each ub-band i allocated to a group of uer (FDMA) tranmitting in a MC-CDMA fahion [6]. MC-CDMA relie on MC-pread pectrum (SS) modulation, according to which, within one MC ymbol period, the ingle uer pread it data ymbol in the frequency domain over the whole aigned tranmiion bandwidth, o exploiting the diverity gain provided by the typically frequency-elective radio channel. In MC-CDMA ytem, different uer imultaneouly pread their information over the ame et of ub-carrier, only eparated by orthogonal preading code. For long time it ha been argued in the literature that the inherent frequency diverity gain of the MC-CDMA cheme make the reort to any adaptive tranmiion technique unneceary. While many adaptive ub-carrier allocation, bit and power loading olution have been propoed for OFDMA ytem [7]-[1], the topic link adaptation for MC-CDMA ytem i till quite unexplored. Due to the additional granularity given by the CDMA component, a greater potential can be actually expected from MC-CDMA/FDMA ytem with repect to OFDMA in dynamical multi-uer cenario. In 4G wirele mobile communication, the tranmiion of a large variety of uer ervice i expected to be accommodated over broadband channel, which, given the enviaged high data-rate and uer-mobility, will be een in general a frequency-elective and timevarying by the mobile uer. In order to ae the potential of MC-CDMA/FDMA ytem in uch application, the gain in term of power/pectral efficiency enabled by adaptive ub-carrier allocation trategie and tranmiion mode election need to be invetigated. An efficient adaptive frequency mapping for the downlink of MC-CDMA/FDMA, referred to a adaptive ub-band allocation (ASBA), ha been propoed by the author in [11]. Perfect channel tate information (CSI) i aumed to be 1 Mr. Trifonov i on leave from St. Peterburg State Polytechnic Univerity, Ruia Submiion 1

2 P. Trifonov at al. uer group 1 group Q uer u 1 u u 1 u K 1 K Q a p (1,1) (K,1) 1 a p (1, Q) a p (K, Q) Q a p pread pread pread K MC K MC pread K MC KMC S/P 1:P K MC S/P 1:P K MC (1) 1,1 (1) 2,1 (1) K,P MC (Q) 1,1 (Q) 2,1 (Q) K,P MC Interleaving M = P K b MC Interleaving M = P K b MC MC M=QPK Frequency mapping on OFDM Figure 1: MC-CDMA/FDMA Tranmiion Scheme. available at the bae tation tranmitter for each uer over the whole bandwidth, e.g. through the uplink received ignal in a time diviion duplex (TDD) ytem. On the bai of the CSI, an optimiation algorithm produce a combination of uer-grouping and ub-carrier grouping that maximie the overall link capacity. The ASBA ha been hown to provide a ignificant gain in the uncoded average Bit Error Rate (BER) performance a compared to the uual fixed frequency mapping, baed on the interleaving of the ub-carrier aigned to different uer-group [11]. Starting point of thi work ha been the obervation that the ASBA yield indeed a coniderable performance gain alo in a coded ytem. Hence, the main goal i that of finding a proper channel coding cheme for MC-CDMA/FDMA employing ASBA. It ha to be oberved that, ince the conidered ASBA optimie the overall link capacity, it i likely to produce a combination of uer-grouping and ub-carrier grouping for which the ignal-to-noie-plu-interference ratio (SNIR) experienced by the different uer differ ignificantly. A a conequence, if a too low coding rate i choen according to the performance of the uer with the lowet SNIR, a wate in pectral efficiency may occur. We propoe here to ue adaptive coding in conjunction with ASBA. By adaptive coding we mean the adjutment of the coding rate for each uer according to the actual SNIR een by that uer, with the aim of maximiing the overall ytem throughput. We conider two adaptive coding cheme. The firt i given by the concatenation of a Reed-Solomon and a convolutional code, while the econd i a turbo code [12], [13]. We invetigate the downlink throughput performance of a MC-CDMA/FDMA ytem in a ingle cell environment, when adaptive coding i adopted with and without ASBA. Simulation reult how that the two adaptive tranmiion trategie yield a ignificant gain, both eparately and jointly applied. Moreover, baed on the obervation that ome ervice may need to be guaranteed a certain throughput, while other may have very low throughput demand, we alo introduce a prioritiation among clae of uer ervice baed on their throughput requirement. We then reort to a light modification of the ASBA algorithm propoed in [11] to cope with the conidered prioritiation. More pecifically, higher priority uer are favoured in the aignment of the ub-carrier on which they experience the highet SNIR, o allowing them to tranmit with higher modulation format and/or coding rate, while till achieving given BER performance. Different but fixed coding rate can be ued for uer with different priority. We will how, however, that adaptive coding enable a coniderable performance gain over a much larger ignal-to-noie ratio (SNR) range. The remainder of the paper i organied a follow. In Section 2, the MC-CDMA/FDMA ytem model and the principle of ASBA are briefly reviewed. In Section 3, we explain how adaptive coding can be applied in conjunction with ASBA. In Section 4, the imulation et up i decribed and the throughput reult of MC-CDMA/FDMA with joint adaptive coding and ASBA are reported and dicued. Finally, ome concluding remark are given in Section 5. 2 ADAPTIVE SUB-BAND ALLOCATION IN MC-CDMA/FDMA 2.1 MC-CDMA/FDMA SYSTEM MODEL The MC-CDMA/FDMA tranmiion cheme i depicted in the block diagram of Fig. 1. The whole et of active uer i ub-divided into Q uer-group repreenting Q conventional MC-CDMA ub-ytem [6]. In the q th ub-ytem, q = 1... Q, K q uer pread P data tream each, a (k,q) p, k = 1... K q, p = 1... P, by mean of K q orthogonal code of length K MC, 2 ETT

3 Adaptive Coding in MC-CDMA/FDM Sytem with Adaptive Sub-Band Allocation [ c (k) = c (k) 1... c (k) K MC ], over the ame et of M b = K MC P ub-carrier. In principle, in a perfectly ynchronou ituation, K q K MC uer can be imultaneouly active without multi-uer interference (MUI). In practice, even in the ynchronou downlink, MUI may arie due to the lo of uer code orthogonality caued by tranmiion over frequencyelective channel [5]. In a fully loaded ytem, the total number of active uer i K = QK MC. In the q-th ub-ytem, q = 1... Q, after the preading in the frequency domain, we obtain M b = K MC P data chip given by Kq (q) i,p = c (k) i a (k,q) p i = 1... K MC, p = 1... P. (1) k=1 A frequency interleaving over M b ub-carrier i then applied in the ingle ub-ytem to enure that the frequency eparation between ub-carrier conveying chip of the ame data ymbol i maximied, o gaining in term of frequency diverity. Before undergoing the OFDM modulation over the complete et of M = QM b ub-carrier, the reulting vector of M data chip enter a frequency mapping block, where the chip of different uer-group are aigned dijoint et of ub-carrier. In the literature, an interleaving of the ub-carrier aigned to the different uer-group i uually carried out to further increae the frequency diverity gain [5], [14]. In thi paper, the frequency mapping block accomplihe the ASBA approach propoed in [11], hereafter reviewed for convenience. 2.2 ADAPTIVE SUB-BAND ALLOCATION Let B = {B 1, B 2... B Q } be a partition of the whole et of M ub-carrier within the tranmiion bandwidth. The q th ub-band B q, q = 1... Q, conit of M b not necearily adjacent ub-carrier. Let then U = {U 1, U 2... U Q } be a partition of the et of up to K active uer. The q th uer-group U q conit of K q uer. Without lo of generality, the uer-group U q i aigned the ub-band B q. The normalied capacity of uer k, k = 1... K, over ub-carrier m, m = 1... M, can be expreed a ( C k,m = log H k,m 2 ) bit//hz, (2) where H k,m i the channel tranfer factor experienced by uer k over ub-carrier m and ση 2 i the variance of an additive white Gauian noie (AWGN) including both the AWG channel noie and the MUI [11]. Under the hypothei of normalied channel and ignal power equal to 1, SNIR = H k,m 2 σ. Thu, the capacity of uer k over the ub-band B η 2 q, hereafter referred to a uer-capacity per ub-band, i given by C k,bq σ 2 η = m B q C k,m, (3) from which the capacity of the uer-group U q over the ub-band B q can be derived a C Uq,B q = k U q m B q C k,m. The overall link capacity read then a C TOT = Q q=1 C U q,b q. The optimiation addreed by the ASBA conit in electing the pair of partition B and U which maximie C TOT for a given channel etimate. For detail on the optimiation algorithm the reader i referred to [11] and [15]. In order to let the ASBA take a given prioritiation among uer into account, the uer-capacity per ub-carrier C k,m can be multiplied by a proper weighting factor F > 1. Let u aume that the et of active uer i ub-divided into P c priority clae, in uch a way that the uer in cla P c 1 have the highet priority and the uer in cla have the lowet priority. Then, in order to guarantee that highly-prioritied uer are allocated the ub-band where they experience the highet SNIR, we aign to their uer-capacity higher weight than for other, lower priority, uer. That i, the ASBA optimiation algorithm i fed with the modified uer-capacity per ub-carrier C k,m = F i k C k,m, where i k i the priority of uer k and F i the choen weighting factor. 3 ADAPTIVE CODING By adaptive coding we mean the adjutment of the coding rate for each uer according to it SNIR, while keeping the codeword length and the decoding parameter fixed. A block diagram of the tranmiion cheme with adaptive coding in conjunction with ASBA i depicted in Fig. 2 for the general cae in which the code i given by the concatenation of an outer and an inner code. When adaptive coding i jointly applied with the ASBA, the ingle uer-capacity per ub-band (cf. (3)) provided by the ASBA, hereafter referred to a optimied uer-capacity, can be ued a an indicator of the SNIR. Submiion 3

4 P. Trifonov at al. Outer encoder Interleaver (optional) Inner encoder Bit mapping and preading Frequency mapping OFDM modulation multipath channel OFDM demodulation Selection of coding rate Adaptive ubband allocation Frequency demapping Channel etimation and equalization Outer decoder Deinterleaver (optional) Inner MAP decoder Depreading and de-bit mapping Figure 2: Tranmiion cheme with adaptive coding and ASBA. According to it value, the coding rate of the ingle uer i elected in order to optimie the ytem performance with repect to a given criterion. We oberve that the BER i not appropriate performance meaure, ince, if decoding error occur, typically burt of data bit are corrupted. Hence, bit error after decoding are ditributed trongly non-uniformly in the data packet. In thi repect, the Frame Error Rate (FER) would be a more proper performance meaure. However, in order to obtain a meaningful optimiation problem, the minimiation of the FER hould be ubject to ome contraint, e.g. fixed data rate or fixed tranmit power. Indeed, the probability of decoding error can be minimized by electing the lowet poible coding rate, but at the cot of introducing very high redundancy. In order to take into account the trade-off between powerful error correction and high data rate, we conider here a a performance meaure the uer throughput and we aim at maximiing it by mean of adaptive coding. We define the uer throughput a the average number of received data ymbol per codeword. For a code of dimenion and codeword length n over the Galoi Field GF(2 r ), the throughput can be expreed a R(n, r,, C) = (1 P e (n, r,, C)), (4) where denote alo the number of received data ymbol in cae of ucceful decoding and P e (n, r,, C) i the probability of incorrect decoding for a given uer-capacity per ub-band C (cf. (3)). Given a fixed codeword length n, in order to maximie the average uer throughput an optimiation proce i carried out that reult in a lit of interval of uer-capacity per ub-band, [T i ; T i+1 ), i = 1... L, with each interval aociated to a code dimenion i. That i, a code with parameter (n, i ) i ued whenever the optimied uer-capacity i C [T i, T i+1 ). The value T i are the witching threhold for which the uer throughput i maximied for the conidered operational environment. Thi include the channel propagation condition, e.g. the noie level and the channel power delay profile, a well a the ASBA etting, e.g. the initial aumption and the number of iteration of the optimiation algorithm [11], which are choen accordingly. Since both the propagation condition and the uer-capacity C k,n of (2) are random variable, the reulting uer-capacity per ub-band C i alo a random variable with ome probability denity function p(c), both before and after the ASBA optimization algorithm. A a conequence, by defining the et {T} of all poible lit of witching threhold T = (T 1,..., T L ), with T i < T i+1, i = 1... L, the optimiation problem can be tated a finding T = arg max R(n, r, C, T)p(C)dC, (5) T where R(n, r, C, T) i the uer throughput achieved by the adaptive ytem for given witching threhold T and uercapacity per ub-band C, that i R(n, r, C, T) = R(n, r, i, C), i : C [T i ; T i+1 ). (6) We note that thi optimiation proce doe not need to be performed very often at the bae tation of the conidered ytem, ince the operational environment may be expected to vary very lowly, e.g. in outdoor, when new buiding are 4 ETT

5 Adaptive Coding in MC-CDMA/FDM Sytem with Adaptive Sub-Band Allocation R ( n,r,c, T ) R( n, r, 1, C) R ( n, r, 2, C ) R( n, r, 3, C) R( n, r, 4, C) T 1 T 2 T 3 T 4 C Figure 3: Approximation of the average uer-throughput a a function of the uer-capacity per ub-band and of the et of witching threhold. built or the tree hadowing change with the eaon or, in indoor, when a wall i removed or erected. Therefore, the witching threhold can be derived off-line and aved into look-up table. The only additional operation to be carried out after the ASBA conit, thu, in earching into the table the optimum code dimenion correponding to the obtained value of optimied uer-capacity. It can be inferred that the additional complexity effort due to the propoed adaptive coding doe not repreent an iue. Let u now explain more in detail how the optimiation proce i carried out. Since it i difficult to find an analytical expreion for the function in (4), we can approximate it by mean of imulation. More pecifically, the optimiation in (5) can be performed a follow: 1. Simulation are run for a number of value of the code dimenion and for different value of SNR = E /N, where E i the average received energy per ymbol and N i the one-ided power pectral denity of the channel noie. 2. For each value of SNR, we record the uer-capacity per ub-band provided by the ASBA and the correponding throughput value obtained for different value of. 3. For each ufficiently mall capacity interval [C i ; C i + ], the bet code, i.e. the (n, i ) code yielding the highet average throughput for thi capacity range, can be found a roughly illutrated in Fig An approximate function (C) can then be contructed by leat quare fitting of the data {(C i, i )} obtained in Step 3. Thi function provide an approximate value of the code dimenion yielding the highet throughput for a given optimied uer-capacity C. For a ufficiently large code family, i.e., when ufficiently many code with different rate are available, (C) can be well approximated by the igmoid function (C) max, (7) 1 + ea bc where max i the maximal available code dimenion. By determining a and b through leat-quare fitting of the imulation data, (7) can be ued to compute the bet code dimenion for a given optimized uer-capacity C a well a to derive the witching threhold T i. Fig. 4 how imulated and approximated curve of bet code dimenion and achieved throughput veru optimized uer-capacity. From thee curve, it can be inferred that the igmoid function provide very cloe approximation of the optimal code dimenion. It ha to be oberved, however, that thi approximation i valid only for ufficiently large code familie. If thi i not the cae, more ophiticated approximation function hould be found or the witching threhold hould be derived directly from imulation reult a illutrated in Fig. 3. Two adaptive coding cheme have been conidered in thi work. The firt i contructed through the concatenation of a Reed-Solomon (RS) code and a convolutional code (CC) and it i referred to a ARSCC in the equel. The econd i given by an adaptive turbo code (ATC). We note that the rate of the ARSCC cheme can be changed either by changing the dimenion of the RS code or by changing the rate of the CC. The latter tak i uually accomplihed by puncturing Submiion 5

6 P. Trifonov at al. 3 Simulated bet code dimenion Approximated bet code dimenion Achieved throughput 25 2 Code dimenion Optimized uer capacity Figure 4: Optimization of the adaptive ytem baed on RS code concatenated with convolutional code. and/or by changing the number of generator polynomial. However, to achieve a ufficient number of different coding rate, it might be neceary to ue very long puncturing pattern and/or very high number of generator polynomial, which may repreent deign and implementation iue. In thi work, we retrict ourelve to changing the rate of the RS code. Neverthele a good granularity in the choice of the coding rate i provided, which guarantee a cloe match of the imulated and approximated curve of bet code dimenion veru optimied uer capacity. A the choen turbo code (TC) are given by the parallel concatenation of CC [12], their rate can be changed a for the CC. A a conequence, the ATC exhibit a lower granularity than the ARSCC cheme, a proved by the imulation reult reported in Section 4. In thi cae, the witching threhold are derived from the imulated reult. 4 SIMULATION RESULTS In the imulation, a bandwidth B = 2 MHz and a carrier frequency f c = 5.5 GHz are aumed. The channel i choen to be a Rayleigh fading channel with exponentially decaying power delay profile and maximum delay pread τ max = 5 µ. M = 512 ub-carrier and Q = 8 ub-band are conidered within the bandwidth. For the preading, Walh Hadamard code with length K MC = 8 are ued, and minimum mean quare error (MMSE) ingle uer detection (SUD) i implemented at the receiver a in [11]. Moreover, 16 QAM bit mapping i aumed. For a fair comparion of the different coding cheme, the codeword length i fixed to 512 byte. The conidered RS code are RS(255,, 256 ) over GF(2 8 ) [12]. The concatenated CC i the rate 1/2 recurive ytematic CC baed on the generator polynomial 133 and 171 (octal). The TC ha the encoder tructure pecified in [13]. Performance reult are reported in term of average uer throughput, expreed a data per packet in byte, veru the SNR in db. Fig. 5.a illutrate the reult for a MC-CDMA/FDMA ytem with ASBA when only fixed CC with different coding rate i adopted. It can be een that the ytem without coding can achieve the maximum throughput of 512 byte per packet for very high SNR. However, for SNR below 15 db the ytem fail to tranmit any data. On the other hand, the ytem with coding i able to tranmit data at low SNR, but it i efficient only in a narrow SNR range. Moreover, ince the coding rate i fixed, it i not poible to achieve the maximal throughput a in the uncoded ytem. The beneficial effect of adaptive coding can be oberved in Fig. 5.b, which report the reult achieved with the two conidered adaptive coding method. For the ARSCC, the comparion of the reult obtained with and without ASBA prove that ASBA provide a ignificant gain alo in the preence of channel coding. Moreover, the ARSCC yield a coniderable gain a compared to a fixed rate 1/4 code given by the concatenation of the RS(255, 128, 128) code with the rate 1/2 CC. The ATC give even a higher gain. However, a lack of flexibility in the election of the TC parameter lead to a non-mooth behaviour for SNR in the range 4 to 6 db. In thi SNR region, in fact, the ub-carrier aignment yielded by the ASBA i good enough to achieve almot error-free tranmiion uing a rate 1/6 TC, but till too bad to ue a rate 6 ETT

7 Adaptive Coding in MC-CDMA/FDM Sytem with Adaptive Sub-Band Allocation Average received data per packet, byte Convolutional coding, 16-QAM ASBA conv(1/2)+asba conv(1/4)+asba Average received data per packet, byte Adaptive data tranmiion. 16-QAM RS(255,128,128)+conv(1/2) ARSCC RS(255,128,128)+conv(1/2)+ASBA ARSCC+ASBA Turbo(1/4)+ASBA ATC+ASBA E /N, db (a) Fixed CC with ASBA E /N, db (b) ARSCC, with and without ASBA, and ATC with ASBA. Figure 5: Performance of the un-prioritied ytem Adaptive data tranmiion with prioritization, fixed code, 16-QAM 4 uer with priority 3 8 uer with priority 2 4 uer with priority 1 48 uer with priority 3 25 Adaptive data tranmiion with prioritization, 16-QAM Unprioritized 4 uer with priority 3 8 uer with priority 2 4 uer with priority 1 48 uer with priority Average received data per packet, byte 2 15 Average received data per packet, byte E /N, db E /N, db (a) ASBA and fixed RS-CC coding. (b) ASBA and adaptive coding ARSCC. Figure 6: Performance of different priority uer. 1/4 TC. Hence, the lower coding rate ha to be choen, o limiting the throughput. The reult obtained with ASBA in the preence of uer prioritiation are reported in Fig. 6.a and Fig. 6.b, for fixed and adaptive coding, repectively. P c = 4 priority clae are aumed over K = 64 uer, of which 4 with priority 3, 8 with priority 2, 4 with priority 1 and 48 with priority. In cae of fixed coding, the concatenated RS-CC cheme ha been choen, and fixed, but different, coding rate have been elected for uer with different priority. More pecifically, on the bai of the average uer throughput at E /N = 1 db, the dimenion of the RS code equal 241, 17, 85 and 35 for uer with priority 3, 2, 1,, repectively. From Fig. 6.a it can be inferred that fixed average throughput value are achieved depending on the uer priority at high SNR. With fixed coding it i not poible neither to improve the throughput in cae of very good channel (higher E /N ), e.g. when the ASBA provide a favourable allocation, nor to achieve atifactory throughput in bad channel (lower E /N ). By uing adaptive coding, in contrat, a gain in throughput i oberved over a large SNR region in Fig. 6.b. In particular, for lower priority uer a noticeable throughput improvement i achieved at high SNR. Moreover, adaptive coding enable a full exploitation of the prioritiation, i.e. a ignificant difference in the throughput of uer belonging to different priority group can be noticed. Submiion 7

8 P. Trifonov at al. 5 CONCLUSIONS An adaptive coding approach ha been propoed and invetigated for application in MC-CDMA/FDMA ytem jointly with the adaptive frequency mapping known a ASBA, that maximize the overall link capacity. Through adaptive coding, the coding rate of the ingle uer i changed according to the SNIR provided by the ASBA, in uch a way that the average uer throughput i maximied. Simulation reult have hown that adaptive coding yield in general a ignificant improvement of the throughput at higher SNR, while enabling atifactory throughput at low SNR. Moreover, the application of adaptive coding reult to be particularly advantageou when uer prioritiation i conidered in conjunction with ASBA. REFERENCES [1] WWRF/WG4 White Paper Broadband Multi-Carrier Baed Air Interface, October 22. [2] D. Falconer, S.L. Ariyaviitakul, A. Benyamin-Seeyar and B. Eidon, Frequency Domain Equaliation for Single-Carrier Broadband Wirele Sytem, IEEE Commun. Mag., vol. 4, n.4, April 22, pp [3] H. Rohling, T. May, K. Brüninghau and R. Grünheid, Broad-Band OFDM Radio Tranmiion for Multimedia Application, in IEEE Proceeding, vol.87, Oct [4] K. Fazel and S. Kaier, Multi-Carrier Spread-Spectrum and Related Topic, Kluwer Academic Publiher, Boton, 22. [5] S. Kaier, Multi-carrier CDMA Mobile Radio Sytem- Analyi and Optimiation of Detection, Decoding, and Channel Etimation, Number 531 in Fortchrittberichte VDI, Reihe 1. VDI- Verlag, Dueldorf, [6] S. Hara and R. Praad, Deign and Performance of Multicarrier CDMA Sytem in Frequency-Selective Rayleigh Fading Channel, IEEE Tran. on Vehic. Technology, vol. 48, n. 5, Sept [7] R. Grünheid and H. Rohling, Adaptive Modulation and Multiple Acce for the OFDM Tranmiion Technique, Wirele Peronal Communication 13, 2, pp [8] C. Y. Wong, R. S. Cheng, K. B. Letaief and R.D. Murch, Multiuer OFDM with Adaptive Sub-carrier, Bit and Power Allocation, IEEE J. Select. Area Commun., vol. 17, Oct. 1999, pp [9] D. Kivanc, Guoqing Li and Hui Liu, Computationally Efficient Bandwidth Allocation and Power Control for OFDMA, IEEE Tran. on Wirele Commun., vol. 2, n.6, Nov. 23. [1] T. Keller, T. H. Liew and L. Hanzo, Adaptive Redundant Reidue Number Sytem Coded Multicarrier Modulation, IEEE J. on Select. Area in Commun., vol. 18, n. 11, Nov. 2. [11] E. Cota, H. Haa, E. Schulz and A. Filippi, Capacity Optimiation in MC-CDMA Sytem, ETT Eur. Tran. on Telecomm., vol. 13, Sept./Oct. 22. [12] M. Boert, Channel Coding for Telecommunication, Wiley and Son, [13] C. Berrou, A. Glavieux and P. Thitimajhima, Near Shannon-limit Error-Correcting Coding and Decoding: Turbo Code, in Proceed. of International Commun. Conference ICC, 1993, Geneva, Switzerland, 1993, pp [14] R. Grünheid Vielfachzugriffverfahren fuer die Multitraeger-Uebertragungtechnik, Number 636 in Fortchrittberichte VDI, Reihe 1. VDI- Verlag, Dueldorf, 2. [15] E. Cota, A. Filippi, H. Haa, S. Ometto and E. Schulz, Adaptive Sub-Band Allocation in MC-CDMA/FDM Sytem, in Proceed. 7 th International OFDM-Workhop (InOWo) 22, Hamburg, Sept ETT