Adaptive Code Allocation for Interference Exploitation on the Downlink of MC-CDMA Systems

Adaptive Code Allocation for Interference Exploitation on the Downlink of MC-CDMA Sytem E. Alua and C. Maouro School of Electrical and Electronic Engineering, The Univerity of Mancheter, PO. Box 88, email: E.Alua@mancheter.ac.uk, Chri.Maouro@potgrad.mancheter.ac.uk, Abtract Thi paper preent a new technique baed on adaptive code-to-uer allocation for interference management on the downlink of BPSK baed MC-CDMA ytem. The principle of the propoed technique i to exploit the dependency of multiple acce interference on the intantaneou ymbol value of the active uer. The objective i to adaptively allocate the available preading equence to uer on a ymbol-by-ymbol bai to optimize the deciion variable at the downlink receiver. The reulting SINR improvement happen by making ue of the energy that i already in the ytem o the performance benefit i attained with no additional power-per-uer invetment. The preented imulation how a ignificant performance improvement with the propoed technique while the adaptation overhead i kept le than 10% of the available bandwidth. I. INTRODUCTION The ue of orthogonal Walh-Hadamard preading equence provide excellent performance for the downlink of multiple carrier code diviion multiple acce (MC-CDMA) ytem [1] in additive white Gauian noie (AWGN) channel. However, the hotile nature of the wirele channel can everely degrade the orthogonality of uch equence and unle compenated for at the receiver it will reult in ignificant multiple acce interference (MAI). Optimizing the ignature waveform for tranmiion in MC-CDMA can greatly benefit a wirele communication ytem. Many reearcher have propoed optimization of the preading code toward orthogonalizing the uer in multipath cenario which involved waveform deign of the code ued taking into account the characteritic of the channel encountered (ee e.g. [3], [4] & [5]). Thi paper propoe a different approach to code optimization in which, intead of performing code waveform deign, the preading equence available in the ytem are ued unmodified but are adaptively allocated to the uer on a ymbol-by-ymbol bai. Secondly, the optimization i not done according to the channel encountered, but rather to the data to be tranmitted. In addition, intead of total interference rejection, a adopted in conventional technique, the primary objective of the adaptive code-to-uer allocation i to influence and exploit the contructive interference inherent in the ytem to deliver an enhanced ignal to interference-plu-noie ratio (SINR) at the receiver. More pecifically, the MAI experienced by the different uer depend on the cro-correlation of the uer code a well a the intantaneou value of the uer data ymbol to be tranmitted. Hence, by appropriately reditributing the code and conequently the cro-correlation value amongt the uer taking into account the value of the data ymbol to be tranmitted at each ymbol period, MAI can be manipulated. The reallocation i done in uch way that the detructive component of MAI i minimized while the contructive component i enhanced to provide optimized deciion variable at the mobile unite (MU ) receiver toward making detection more reliable. Thi i the objective here and contitute the adaptation criteria of the propoed method. It hould be noted that with thi method the improvement in the received SINR i attained without the need for additional per-uer-power invetment at the tranmitter, a energy inherent in the ytem i exploited. It may be clear by now that the propoed technique entail ome overhead in the form of tranmitting ide information (SI) in order to inform the MU receiver of their code allocation at each ymbol period to achieve correct depreading. It will be demontrated in the reult ection that the bandwidth efficiency reduction due to the SI tranmiion can be maintained at le than 10% of the bandwidth. Thi i worthwhile a the achieved bit error rate () improvement are ignificant compared to the non-adaptive cae. II. SYSTEM DESCRIPTION Conider the downlink tranmiion in a dicrete-time ynchronou frequency elective MC-CDMA ytem of K equal power uer, where all code and channel are aumed normalized to unit energy and the preading gain i equal to L. For implicity we aume that the number of OFDM ubcarrier M = L. The ue of cyclic prefix i preuppoed o that the ISI i completely uppreed. Auming preequalization at the tranmitter the received ignal at the u-th MU can be expreed in matrix form a: r iu = [x i A (C E)] H u + N u (1) where x i =[ x 1i x 2i... x Ki ] i the 1 K matrix containing all uer data for the i-th ymbol period, A=diag([ a 1 a 2... a K ]) i the K K diagonal matrix of amplitude, C=[C 1 C 2... C K ] T and E=[E 1 E 2... E K ] T are the K L matrice containing the uer code and equalization coefficient for each ubcarrier while H u and N u are the u-th MU channel and noie matrix of ize 1 L. In (1) the notation i ued to denote element-byelement matrix multiplication. To attain initial reference reult, three imple ingle uer pre-equalization cheme are conidered in thi paper, namely, Maximum Ratio Combining (MRC), Equal Gain Combining () and Minimum Mean

Square Error (MMSE) pre-equalization [2] given by E u =H u *, E u =H u * / H u, E u =H u * /((K-1) H u 2 /L+σ n 2 ) repectively. The above are not optimal for the downlink tranmiion, a, due to the knowledge of all uer data at the bae tation (BS), more ophiticated precoding technique can be applied. It can be proved however that the propoed method can offer performance gain with more complex MC-CDMA preequalization cheme. Following (1), at the receiver the data i extracted a where K H = = x + x + n iu iu u uu iu ku ik iu k= 1, k u d r C ρ ρ (2) ρ pq =(C p E p H p ).C q H In (2) ρ x i the deired uer ignal, uu iu (3) K ρ x =MAI ku ik iu k= 1, k u i the Multiple Acce Interference caued by the other K-1 uer and n iu i the noie component. A regard the uer crocorrelation, it i evident from (3) that even if orthogonal code are ued where C C H =I, the reulting crocorreltation of the code viewed at the receiver i non-zero due to the channel ditortion. It can be een in (2) that given the channel tate information (CSI) and data knowledge readily available at the BS the deciion variable at the receiver can be pre-etimated. By electing the appropriate code allocation for tranmiion at each ymbol period the factor ρ ku can be influenced and hence the ditribution of the d iu value in (2) for all uer can be improved to offer enhanced reliability in the detection. To clarify thi we preent a imple example of K=5 uer a hown in Table 1. Here the ditribution of the deciion variable for eight different code allocation pattern are depicted, for two different tranmitted ymbol combination (a,b). It can be een that by changing the code-to-uer allocation and hence the uer cro-correlation, the deciion variable are dramatically affected. It can alo be viewed that ome code allocation, e.g. =3, =6 for (a), deliver better deciion variable ditribution than other, e.g. =2, =8. A mentioned above thi i a derivative of the difference in the reulting interference for different code allocation. Conequently the detection can be made more reliable by optimizing the code-to-uer allocation to be employed at each ymbol period. Additionally, it i apparent that for (b), with a different ymbol combination, different code allocation (e.g. =4, =7) provide improved deciion variable ditribution. Thi i why in the propoed method the code allocation to be ued i dynamically adjuted to the ymbol x ik to be tranmitted at the period i of interet. Thi i a way of fine tuning the uer ymbol and code o that the energy in the channel be ued contructively intead of being wated becaue of data mialignment a in conventional method. A a reult the effective received SINR can be increaed and improved deciion variable can be delivered at the MU receiver without the need to increae the tranmitted per-uer-power. III. CODE TO USER ALLOCATION METHOD (CUA) In order to limit the amount of SI needed, the adaptive codeuer allocation i performed by electing the code-to-uer allocation for every ymbol period from a limited number, p c, of allocation pattern, which are known at both the tranmitter and the receiver. By doing o, only the index of the allocation pattern need to be conveyed to the receiver. The elected allocation pattern i choen at the tranmitter according to a certain optimization criterion which i explained in the ubection below. A) Method Analyi For reaon of implicity, the analyi preented aume Matched Fliter (MF) detection but the proce for the cae of Multiuer Detection (MUD) i eaily deduced by analogy. Firtly, a number p c of allocation pattern i formed for an initial et of N c K code by randomly huffling them amongt the uer. In order to chooe the appropriate code allocation pattern prior to tranmiion the expected deciion variable at the MU for all the available code-to-uer allocation combination need to be determined at the tranmitter uing the intantaneou ymbol value for the active uer. Hence, in the propoed method, the etimated effective crocorrelation matrix R ˆ of dimenion K K i formed for each allocation pattern at the BS from the etimated ˆ ρ ku given by (3) in which the etimated channel coefficient H ˆ are ued: p ˆ R ˆ ρ ˆ ρ ˆ ρ 11 12 1K ˆ ˆ ˆ ρ ρ ρ 21 22 2 K = ˆ ρ ˆ ρ ˆ ρ K1 K 2 KK The deciion variable at the MU output for the i-th ymbol period for the -th code-to-uer allocation pattern can then be pre-etimated a: [ d ˆ d ˆ d ˆ i1, i2, ik, ] (4) dˆ = = xarˆ = d + e (5) i, i i, i, where e i i the deciion variable pre-etimation error due to inaccurate channel etimation. The propoed algorithm work a hown in the diagram in Fig. 1. Auming N c =K, at each ymbol period and uing the intantaneou value of x i, the deciion variable ditribution for each of the p c allocation pattern i evaluated uing (5) and the optimal pattern i choen according to a election criteria that will be preented below. Since the receiver ha knowledge of all the p c available pattern it only need to be informed about the index () of which pecific pattern i ued at each ymbol-period by a control ignal of log ( p ) 2 c bit tranmitted at a different frequency/time lot a SI. By recognizing the correct pattern each MU can find the new code aigned to it for the current ymbol detection a well a the remaining code of the ret of the uer to utilize for mutliuer detection (MUD).

x 1 x 2 x 3 x 4 x 5 1-1 1 1-1 allocation pattern No. d 1 d 2 d 3 d 4 d 5 =1 0.75-1 0.5 0.75-1 =2 0.5-1.75-0.5 1.25-2 Rˆ ˆR 1 d ˆi, d ˆi,1 dˆi,2 dˆ ipc, arg max min ( ( d, )) ˆi =3 2.5-2.75 2.25 3-0.5 =4 0.5-1 0.75 0.75-1 =5 0.75-0.5-0.25 0-1 Hˆ p =6 2.25-0.5 3.25 2.5-2.5 =7-0.25-0.5 0.75 0-1 =8 1.25-2 0.5-0.5-1.75 a x 1 x 2 x 3 x 4 x 5-1 -1 1-1 1 allocation pattern No. d 1 d 2 d 3 d 4 d 5 =1-0.25 0 0.5-0.25-1 =2-1 -1.25 1-0.25-0.5 =3-0.5 0.25 0.25 0-0.5 =4-3 -1.75 3.25-2.75-2.25 =5 0.25 0 0.25-0.5-0.5 =6-0.25-1 0.5 0-0.25 =7-2.75-3 3.25-2.5-1.5 =8 0.75-1.5 1-1 -1.25 b Table 1: Noiele deciion variable ditribution for different allocation pattern of a ytem of K=5 uer with random code of L=16 for p c =8 An alternative route toward performance improvement, alo conidered here for the ake of comparion, i uing a larger number of code (N c >K) to attain a greater variety of interference ditribution, but thi would lead to the requirement for increaed ytem reource, i.e. more available ignature waveform. A will be hown the performance enhancement attained by thi i inignificant. It i noteworthy to highlight that the SI bit do not need to be pread a the information they convey i common to all uer and furthermore thi would be more bandwidth efficient. If the number of SI bit i not a power of two or if the SI i to be forward error correction encoded, then a frame baed approach can be adopted a depicted in Fig. 2. Here the allocation procedure i run for all the ymbol in the frame prior to tranmiion and the control bit for all ymbol are tranmitted in the beginning of the frame. Each ymbol in the frame i a CDMA-multiplexed ymbol for K uer. B) Allocation criteria It i intuitive from equation (5) and Table 1 that a number of criteria can be extracted for the election of the optimum available code allocation pattern baed on the intantaneou interference amongt uer and the ditribution of the reulting value of d ˆi. Since the performance of the wort uer cˆopt Fig. 1. Flow diagram of code allocation technique Fig. 2. Frame-baed tranmiion tructure for the code allocation technique catalytically affect the overall ytem, the following code pattern election criteria i propoed and examined here: In more detail, min ( ˆ i, ) d iu ( ( ˆ i, )) arg max min d (6) d determine the MU output that i the mot prone to deciion error for each code allocation. From the p c available ditribution of d ˆi according to the p c available code allocation pattern, the optimum i choen a the one that maximize the minimum of d ˆi which denote the deciion variable of the wort uer at each ymbol period for each ditribution of d ˆi. Hence, the code allocation elected (c opt ) i the one that deliver the highet deciion variable for the wort uer. In the cae where two different allocation pattern offer the ame minimum, the econd minimum i conidered and o on. For the example depicted in Table 1 thi criteria would indicate allocation pattern =3 for (a) and pattern =4 for (b). Evidently, thi i one bit error rate () optimization approach that favor the uer that are more uceptible to error. By inpection of thi criteria and Table 1, the comparion to other available code allocation pattern how that by thi optimization a favorable contructive to detructive MAI ratio i choen which evidently deliver a higher SINR and boot performance. Contructive interference i enhanced while detructive interference i minimized.

IV. NUMERICAL AND SIMULATION RESULTS Monte Carlo imulation for variou combination of the propoed technique with conventional method have been performed for frequency elective fading channel with AWGN. Walh-Hadamard code of variable length have been ued. The multipath channel conidered here i a chippaced 4-path Rayleigh frequency elective fading with unity gain and equal average power per channel path (uniform channel power-profile). The channel i implemented in the form of a 4-tap delay line with an independent complexnumber Gauian ditributed coefficient per tap to repreent each path phae and amplitude. In order to provide a good average performance a new et of the tap coefficient are generated at every ymbol period. The channel characteritic are aumed to be perfectly known. A in the mathematical analyi preented above, the ue of cyclic prefix i preuppoed o that the ISI i completely uppreed. In all imulation it i aumed that the number of OFDM ubcarrier M = L. For reaon of efficiency the SI bit are QPSK encoded. Performance of MRC, and MMSE preequalization cheme for MC-CDMA with and without adaptive code-uer allocation (CUA) are compared. Reult for ytem utilizing ucceive interference cancellation (SIC) detector [6] are alo preented. In Fig. 3 the performance of the propoed method with p c =16 allocation pattern for N c =K i depicted for all three pre-equalization cheme and compared to the ytem without CUA. The number of uer i K=20 and the preading gain L=32. The channel i Rayleigh fading with P=4 path. It can be een in the figure that for low SNR value the propoed method perform wore due to unreliable SI detection. However, for higher SNR all three type of pre-equalization benefit from a ignificant performance improvement when combined with the propoed technique. Thi i due to the enhanced effective SINR that i attained with the adaptive allocation election. For it can be een that the performance enhancement reache an order of magnitude. A regard the SI overhead, the SI bit in thi cae are log ( p ) 2 = 4 equivalent to 2 QPSK ymbol. Thi yield a c ymbol tranmiion rate efficiency of 20/22=91%. Although a 9% efficiency reduction i not inignificant it i obviou from thi figure that thi method produce a ignificant improvement. Uing a larger number of uer or higher order modulation would further reduce the efficiency lo (e.g. in the cae of 40 uer or uing 16PSK modulation the efficiency lo would be ~5%). Fig. 4 how the comparion of both MF and SIC receiver cheme with and without CUA for the ame ytem a in Fig. 3 uing pre-equalization. The cae of N c >K and pecifically N c =32 i alo included to invetigate any potential performance improvement. Simulation reult with perfect SI detection for the propoed technique are alo preented to how how the reliability of SI detection affect the overall performance. Perfect SI detection refer to a genie-type detection of the SI bit. It can be een that the reult with imperfect SI detection converge to the cae of perfect SI for high SNR a the SI detection become much more reliable. In both receiver cae ignificant performance improvement i attained. A for the cae of N c =32 it can be een that a mall performance benefit i gained for a pecific SNR area. Fig. 5 depict the comparion for the cae of the ame channel for a fully loaded ytem of K=16, L=16 and p c =16 pattern. Performance for pre-equalization for MF and SIC detection i depicted to how the propoed method uperiority. In all cae the propoed technique offer a ignificant performance enhancement. In Fig. 6 the for different value of p c at SNR=7dB i depicted for MRC and pre-equalization for K=16, L=16 in the ame multipath to how the performance improvement a a function different value for p c. For both ytem increaing p c further than a pecific value yield limited benefit. For the cae depicted on the figure, value of p c >16 would provide no ignificant performance improvement while an unneceary SI overhead increae would be required. V. CONCLUSION In conventional cheme the uer code mialignment lead to wait of critical ueful energy inherent in the tranmiion medium. By fine tuning the uer code o that contructive interference be exploited, we have hown that the adaptive code allocation technique can improve performance for both MF and MUD in MC-CDMA by up to an order of magnitude. Thi come with no need for additional per-uer-power invetment a exitent energy i exploited. The trade-off i the need for tranmiion of ide information which impoe an overhead on the detection proceing. Further work can be focued on improving the ditribution of code between uer intead of randomly huffling. Moreover the election criteria could be invetigated toward further optimization. Though the contructive MAI analyi applie only to PSK modulation, further work can be done toward applying code huffling to PAM and QAM modulation with the ue of adaptive deciion threhold. REFERENCES [1] Stefan Kaier, Multi-Carrier CDMA Mobile Radio Sytem -Analyi and Optimization of Detection, Decoding, and Channel Etimation, VDI-Verlag, Dueldorf, Germany, 1998. [2] I. Coovic, Uplink Multi-Carrier CDMA Mobile Radio Sytem, Belgrade: Mediagraf, 2005 [3] M. Brandt-Pearce and A. Dharap, Tranmitter-baed multiuer interference rejection for the down-link of a wirele CDMA ytem in a multipath environment, IEEE Journal on Selected Area in Communication, vol. 18, no. 3, pp. 407 417, Mar. 2000. [4] G. W. Wornell, Spread-ignature CDMA: Efficient multiuer communication in the preence of fading, IEEE Tran. Inform. Theory, vol. 41, pp. 1418 1438, Sept. 1995. [5] W. H. Mow, Minimizing the wort-cae interuer interference experienced by any uer in CDMA ytem: A metric approach, in Proc. Int. Symp. Spread-Spectrum Technique and Application, vol. 2, Mainz, Germany, Sept. 1996, pp. 561 565. [6] P. Patel and I. Holtzman, Analyi of a DS/CDMA ucceive interference cancellation cheme uing correlation, Proc. GLOBECOM Houton, TX, 1993.

MRC MRC SIC SIC MRC MMSE MRC - CUA - CUA MMSE - CUA Tranmitted Eb/No per uer (db) Fig. 3. for conventional and code allocation uing MRC,, MMSE pre-equalization with N c =K, p c =16, K=20, L=32 in an Rayleigh channel of P=4 5 10 15 20 25 30 pc Fig. 6. v. p c performance for the cae of MRC and preequalization with MF and SIC detection for K=16, L=16 in Rayleigh P=3 channel employing code allocation for SNR=7dB - CUA Nc=K - CUA Nc=32 - SIC - SIC - CUA - SIC - CUA perfect SI detection Tranmitted Eb/No per uer (db) Fig. 4. performance of conventional pre-equalizing and -SIC method and the method uing the code allocation technique with N c =K and N c =32 for p c =16 in an Rayleigh multipath channel of P=4 with K=20, L=32 - CUA - SIC - SIC - CUA - SIC - CUA perfect SI detection Tranmitted Eb/No per uer (db) Fig. 5. performance of conventional pre-equalizing and -SIC method and the method uing the code allocation technique with N c =K, p c =16 in an Rayleigh multipath channel of P=4 with K=16, L=16