A Low Complexity VCS Method for PAPR Reduction in Multicarrier Code Division Multiple Access

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1 0 JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 5, NO., JUNE 007 A Low Compexity VCS Method for PAPR Reduction in Muticarrier Code Division Mutipe Access Si-Si Liu, Yue iao, Qing-Song Wen, and Shao-Qian Li Abstract This paper investigates a peak to average power ratio (PAPR reduction method in muticarrier code division mutipe access (MC-CDMA system. Variabe code sets (VCS, a spreading codes seection scheme, can improve the PAPR property of the MC-CDMA signas, but this technique requires an exhaustive search over the combinations of spreading code sets. It is observed that when the number of active users increases, the search compexity wi increase exponentiay. Based on this fact, we propose a ow compexity VCS (LC-VCS method to reduce the computationa compexity. The basic idea of LC-VCS is to derive new signas using the reationship between candidature signas. Simuation resuts show that the proposed approach can reduce PAPR with ower computationa compexity. In addition, it can be bindy received without any side information. Index Terms Low compexity variabe code sets, muticarrier code division mutipe access (MC-CDMA, peak to average power ratio, variabe code sets.. Introduction In wireess communication systems, muticarrier code division mutipe access (MC-CDMA has attracted more and more attentions as a very promising moduation technique. The main idea behinc-cdma is to spread and convert input signas into parae data streams, which are then transmitted over mutipe carriers. MC-CDMA can reaize the high bite rate and arge capacity transmission. The intersymbo interference (ISI and the infuence of deayed waves are amost competey eiminated by introducing a guard time in MC-CDMA symbos. However, one of the major disadvantages of MC-CDMA is its high peak to average power ratio (PAPR which eads to a arge noninear distortion at a high power ampifier (HPA, a significant power efficiency penaty, and the degradation of the bit error rate (BER. To overcome this probem, many methods have been proposed [], such as Manuscript received August 9, 006; revised October 0, 006. S.-S. Liu, Y. iao, Q.-S. Wen, and S.-Q. Li are with Nationa Key Lab of Communications, University of Eectronic Science and Technoogy of China (UESTC, Chengdu, 60054, China (the first author s e-mai: sakura_min@sina.com. cipping [], mutipe signa representation (MSR which mainy incudes partia transmit sequences (PTS [3] and seected mapping (SLM [4], and bock coding [5]. Cipping is a conventiona method to imit the PAPR at the end of the transmitter. However, it reduces signa power, degrades BER performance and causes out of band radiation. A ot of researches were done in the bock coding agorithm, which is a method that reduces the PAPR by coding the input words into the code word with ow PAPR. In the PTS method, the information data are divided into disjoint subbocks and then phase rotated before combination to minimize the PAPR. In the SLM technique, the transmitter generates a set of sufficienty different candidate data bocks, a representing the same information as the origina data bock, and mutipies them with phase factors to choose the sequence with the owest PAPR. Compared with other techniques for PAPR reduction, the main advantage of MSR method is that it is a distortioness technique that does not arise in-band distortion nor out-of-band emission, but it aso increases the compexity of the system and oss of transmission efficiency by using side information. Aso some approaches emphasizing on the aocation strategies of the spreading and despreading sequences in MC-CDMA system have been proposed in [6]-[8]. In our work, a PAPR reduction scheme caed ow compexity variabe code sets (LC-VCS is proposed. The scheme needs itte computationa compexity comparing with variabe code sets (VCS [9]. VCS can reduce PAPR without sending side information; however, it needs arge numbers of computations. The basic idea of LC-VCS is to use the reationship between signas to reduce the amount of computation; in addition, it can aso be bindy received without any side information. This paper is organized as foows. Section introduces the conventiona MC-CDMA system mode and the definition of PAPR. In Section 3, we present the derivation and detaied agorithm of our proposed LC-VCS method. We give the simuation resuts in Section 4 and draw some concusions in Section 5.. MC-CDMA System Mode The conventiona MC-CDMA system mode is shown in Fig..

2 LIU et a.: A Low Compexity VCS Method for PAPR Reduction in Muticarrier Code Division Mutipe Access 03 as :M User d ( User K d (k Assume user k has M data symbos which are presented ( k d ( d ( ( d (k d (k (k Spreading :L ( Fig.. Conventiona MC-CDMA system mode d r = ( d, d, L, d, k =,, L, K ( k M where K is the number of active users. After seria-to-parae ( conversion, each symbo is spread by the orthogona spreading code ( k ( ( ( k = ( c, c, K, c L and L is the ength of the spreading sequence. Each user must seect unique code to guarantee the accurate reception. After the spreading process, a users symbos are added together. Taking another conversion, these M L parae data are sent into the inverse fast Fourier transform (IFFT moduation, whose size is aso M L. The baseband representation of the MC-CDMA signa is give by j { M( ( m } t/ Ts ( = π + m, 0 s m= = k= s t d c e t T ( where T s is the symbo period of a MC-CDMA symbo. In the foowing of the paper, ony discrete-time representation of MC-CDMA signa wi be used, which is expressed as IFFT Size ML muticarrier signas is to utiize the probabiity characteristic that the PAPR is arger than a certain eve, we ca it the compementary cumuative distribution function (CCDF, which is expressed as CCDF( PAPR( s( i = Pr( PAPR( s( i > ς (4 The reason for using CCDF ies in the fact that when the amount of subcarriers grows arge, the signa ampitude can be approximatey thought as Rayeigh distribution, so the high peaks actuay happen rarey. Therefore the statistica distribution property of PAPR aways becomes more meaningfu comparing with the absoute vaue of PAPR. 3. Proposed Technoogy In this section, we first introduce the conventiona VCS method, then emphasis on our proposed LC-VCS scheme and its detaied agorithm. 3. Conventiona VCS Method In [9], the authors proposed a scheme caed VCS, the bock diagram of downink MC-CDMA system using VCS is shown in Fig.. The main idea of VCS is to try to aocate more than one spreading codes to each user, whie in the conventiona MC-CDMA system the spreading code per user is one. After cacuating a the corresponding PAPR of the signas, we choose the code set which has the smaest PAPR and transmit the correspond signa. User d ( :M d ( ( Spreading :L ( ( ( ( Feedback if PAPR>Threshod Peak detection and threshod contro ( m j { M( ( m } i/ NTs m= = k= si = d c e π + ( For the MC-CDMA downink transmitter, the cycic prefix (CP is inserted in the symbos for avoiding ISI which is caused by mutipath fading. Since MC-CDMA is a muticarrier moduaton technique containing many subcarriers as can be seen from the above equation, it can give a high PAPR when a subcarriers added up coherenty. Using the discrete-time definition, the corresponding PAPR is defined as max s( i 0 i N PAPR = E[ s( i ] (3 where E[ s(t ] denotes the average power and max s( i the peak power. 0 i N The more convenient way to express the PAPR of User K d (K d (K (K Fig.. VCS system mode. ( ( ( ( IFFT Size ML In the VCS scheme, every time when computing PAPR, we need to do IFFT whose size is M L after spreading; assume each user has D different spreading codes for choosing, we have to do D K times of IFFT. If the number of active users increases, the computationa compexity increases exponentiay. This wi cost a arge amount of computations to achieve the aim of reducing PAPR.

3 04 Therefore, finding a method to decrease the computationa compexity of VCS is very necessary and significant. 3. The Basic Idea of LC-VC rk rk rk Here we define user k has the code sets of c, c, L, c D, k ( k ( k ( k x = ( cx,, cx,, L cx, L, x =,, L, D. The data after spreading is m x, m= = k= ( ( ( ( dm cx, dm cx, dm cx, m= = m= = m= = x = d c = + + L + (5 ( We assume each user uses the first code ( for user, ( ( ( for user, and so on, we choose,, K, c r as first code set randomy to generate x = m x, m= = k= ( ( ( ( = dm c, + dm c, + + dm c, m= = m= = m= = x d c When user chooses the same, the new data is JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 5, NO., JUNE 007 L (6 ( and other user s codes remain = m x, m= = k= ( ( ( ( = dm c, + dm c, + + dm c, m= = m= = m= = x d c L (7 We can make use of the reationship between x and x to get x from x without cacuating x, the reationship is ( ( ( ( = m, + m, + L + m, m= = m= = m= = x d c d c d c ( ( ( ( ( ( = K dm c, + dm c, + L + dm c, m= = m= = m= = ( ( ( ( + dm c, dm c, m= = m= = ( ( ( = x dm ( c, c, m= = (8 Because IFFT is a inear transform, equation (8 can be adapted to = IFFT ( x ( ( ( = IFFT dm c, c, m= = ( ( (9 ( By the same way, when user chooses and user ( chooses, other user s codes don not change, the data is = IFFT ( x = IFFT d c ( ( ( m, m= = ( ( ( K ( K dm c, L dm c, m= = m= = ( ( ( ( m (,, m= = = IFFT d c c (0 We can use this method to compute a the D K code sets. As for the ast haf part in (9 and (0, we can cacuate and store them in a tabe beforehand. When they are in need, we wi find them by the indices of the tabe. In a word, once we have the signas of a certain code set, we can use the equations above to derive a the other signas. This wi greaty reduce the computationa compexity. The VCS scheme needs to compute D K times to search a the possibe combinations, it means to do D K times of IFFT; but using our method, we need ony to search one set of combination and generate the other D K - sets recursivey. Let and Y denote two different signas, their ony differences are the ith user s spreading code, so the recursive equation can be generay defined as = ( i ( i ( i m x, y, m= = Y IFFT ( d ( c c ( 3.3 Agorithm and Compexity Comparison Firsty, we compute which uses the first code set ( ( (,, L, c r, we choose them as first code set randomy as spreading codes; then we set Stage= and derive, 3, L, D (whose ony differences with are the first user s spreading code from using (9. By the same token, we set Stage= and generate, 3, L, D from, 3, 33, L, 3D from 3, and D, D3, L, DD from D respectivey. Whie i, i 3, L, id distinguish from i by the second user s spreading code, i =,,L, D. In the same way, we compute a the candidature signas unti Stage=K. By this manner, a the D K sets can be searched. Here we wi summarize the agorithm of LC-VCS For each user, choose one spreading code from the D candidature codes randomy and generate by (6. Compute and store the ast haf part of (. Set Stage =0. Set Stage = Stage +. From each signa currenty in storage, generate new signas by changing the Stage-th user s spreading code. Compute the PAPR of the new signas and store them. 3 If Stage<K, go to Step ; ese transmit the signa with the owest PAPR. Tabe gives the comparison of VCS and our LC-VCS method in the aspect of computationa compexity. Tabe The computationa compexity of the two methods Compexity VCS LC-VCS Addition D K (K ML+D K v [K (D +]v+l(d K+(D K +K ML Mutipication D K v/+d K MLK [K (D +] v/+mld K 4. Simuation Resuts The simuation parameters used in the MC-CDMA system are set as foows: QPSK moduation, the number of

4 LIU et a.: A Low Compexity VCS Method for PAPR Reduction in Muticarrier Code Division Mutipe Access 05 data symbos per user M is 8, Wash code is used as spreading code with ength L=6 and L=64; the number of active users is 4, and the number of candidature spreading codes per user D is, 3 and 4 respectivey. The IFFT size is M L=8 in Fig. 3 and 5 in Fig. 4. Pr(PAPR>PAPRo Pr(Papr>Papr 0 Fig. 3. CCDF of MC-CDMA signas using LC-VCS with L=6 and different D. Pr(Papr>Papr 0 Pr(PAPR>PAPRo k=4, origina k=4,d= k=4,d=3 k=4,d= PAPR(dB Fig. 4. CCDF of MC-CDMA signas using LC-VCS with L=64 and different D. Pr(PAPR>PAPRo Pr(Papr>Papr k=4, origina K=4, D= K=4, D=3 K=4, D= PAPR(dB VCS, L=6,D=3 Because our LC-VCS can reduce the computationa compexity of VCS without degrading its PAPR reduction performance, the CCDF of these two kinds of methods are exacty the same. As can be seen in Fig. 5, which shows the CCDF of MC-CDMA signas using LC-VCS and VCS respectivey in the case of L=6 and D=3, the two kinds of ines superpose. Fig. 3 is the CCDF of our approach comparing with that of origina MC-CDMA signas in the case of L=6 and D=, 3, 4 respectivey. For instance, when CCDF is 0-3, the PAPR of our proposed scheme with D=4 can be about 4 db smaer than that of the conventiona MC-CDMA system. In this case, VCS needs to do times of addition and times of mutipication. Whie the computationa compexity of our method is ony times of addition and times of mutipication respectivey. Fig. 4 is the CCDF with the ength of Wash code is 64 3 and different D. When CCDF= 0, the PAPR of our method with D=4 can be approximatey reduced by 5.5 db comparing with the origina MC-CDMA signas. 5. Concusions In this paper, we propose an efficient PAPR reduction and ow compexity method caed LC-VCS. The basic idea is to aocate each user with more than one spreading code and choose the code set which resuts in the east PAPR for transmission. But unike VCS, we do not compute a the combinations of code sets, instead, we ony need to compute one combination of code sets and derive a the other candidature signas from it recursivey. The computationa compexity reduces exponentiay with the decrease of the number of active users. The simuation resut shows LC-VCS can aso reduce PAPR efficienty. Furthermore, it can aso be bindy received without any side information due to the orthogonaity of spreading codes. The proposed scheme can substantiay reduce PAPR and simpify the computations of MC-CDMA system considering the tradeoff between computationa feasibiity and system performance. Furthermore, we can constrain the number of searched signas at each stage; that means the signas with the arge PAPR wi be discarded when the number of currenty stored signas equas the defined number. Using this method combined with the threshod controing, the compexity of the method is rapidy reduced with ony sight performance degradation. LC-VCS, L=6, D= PAPR(dB Fig. 5. Comparison of the CCDF of MC-CDMA signas using LC-VCS and VCS with L=6. References [] S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for muticarrier transmission, IEEE Wire. Commun., vo, no., pp , Apr. 005.

5 06 [] R. O'Nei and L. B. Lopes, Enveope variations and spectra spatter in cipped muticarrier signas, in Proc. IEEE PIMRC '95, Toronto, Canada, 995, pp [3] L. Yang, R. S. Chen, Y. M. Siu, et a., PAPR reduction of an OFDM signa by use of PTS with ow computationa compexity, IEEE Transactions on Broadcasting, vo. 5, no., pp , 006. [4] R. W. Bäum, R. F. H. Fisher, and J. B. Huber, Reducing the peak-to-average power ratio of muticarrier moduation by seected mapping, IEEE Eectronics Letters, vo. 3, no., pp , Oct [5] A. E. Jones, T. A. Wikinson, and S. K. Barton, Bock Coding Scheme for Reduction of Peak to Mean Enveope Power Ratio of Muticarrier Transmission Scheme, Eectronics Letters, vo. 30, no., pp , Dec [6] N. Hathi, I. Darwazeh, and J. O'reiy, Peak-to-average power ratio performance comparison of different spreading code aocation strategies for MC-CDMA anc-ds-cdma, IEEE Eectronics Letters, vo. 38, no. 0, pp. 9-0, Sep. 00. [7] E. Pogossova, K. Egiazarian, and J. Astoa, Spreading sequences for downink MC-CDMA transmission, in Proc. IEEE Vehicuar Technoogy Conf., 004, Mian, Itay, 004, vo. 7, pp [8] H. Ochiai, and H. Imai, OFDM-CDMA with peak power reduction based on the spreading sequences, in Proc. Int. Conf. on Communications, Atanta, USA, 998, vo. 3, pp [9] M. H. Cho, S. J. Lee, J. Y. Jin, et a., A study on the PAPR JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 5, NO., JUNE 007 using variabe code sets (VCS in muti-user mc-cdma system, in Proc. IEEE Vehicuar Technoogy Conf., 004, Mian, Itay, 004, vo. 5, pp Si-Si Liu was born in Sichuan, China, in 98. She received her B.S. degree in eectrica engineering from University of Eectronic Science and Technoogy of China (UESTC in 004. She is currenty pursuing the M.S. degree with Nationa Key Lab of Communications in UESTC. Her research interests incude PAPR probem and spreading codes in MC-CDMA, OFDM, and MIMO-OFDM system. Yue iao was born in Jiangsu, China, in 979. He received his B.S. an.s. degrees from UESTC in 00 and 004, respectivey, both in eectrica engineering. He is currenty pursuing the Ph.D. degree with Nationa Key Lab of Communications in UESTC. His research interests incude PAPR probem in wireess communication system. Qing-Song Wen was born in Sichuan, China, in 98. He received his B.S. degree in eectrica engineering from UESTC in 006. He is currenty pursuing the M.S. degree with Nationa Key Lab of Communications in UESTC. His research interests incude PAPR reduction method (such as PTS and SLM in wireess communication system. Shao-Qian Li was born in Sichuan, China, in 957. He received his B.S. degree from idian University of China, in 98 an.s. degree from UESTC in 984. Now he is the director of Nationa Key Lab of Communications in UESTC. His research interests incude digita communication, wireess communication, spread spectrum anaysis, ceuar and future generation communications.

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