An Efficient Method for PAPR Reduction of OFDM Signal with Low Complexity

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2 An Effcent Method for PAPR Reducton of OFDM Sgnal wth Low Complety Mahesh Ingle M.E. EXTC MGMCET,Kamothe Nav Mumba Sachn Nkalje M.E. EXTC MGMCET Kamothe Nav Mumba Savta Bhosale H.o.D.(EXTC) MGMCET,Kamothe Nav Mumba Abstract- Owng to the hgh spectral effcency and the mmunty to multpath channels, orthogonal frequency-dvson multpleng (OFDM) s a promsng technque for hgh-rate data transmsson. But the hgh Peak-to-Average Power Rato (PAPR) s one of the man obstacles to lmt wde applcatons. In ths paper, we propose a PAPR reducton method usng Partal Transmt Sequence (PTS) Technque to lower the hgh PAPR of OFDM (orthogonal frequency dvson multpleng) system. The mert of ths proposed method s effcent PAPR reducton performance. In the paper, the PAPR reducton process s made more effcent by Low complety reduced PAPR method usng correlaton property. Keywords PAPR, PTS, OFDM. I. INTRODUCTION Orthogonal Frequency Dvson Multpleng (OFDM) s an attractve multcarrer technque for hgh-bt-rate transmsson. In OFDM system, data s transmtted smultaneously through multple frequency bands. It s robust to frequency selectve fadng and narrow band nterference. So, OFDM has been adopted as wreless communcaton. However t s susceptble to hgh peak-to-average power due to an unstable envelope. Ths, n turn, leads to poor power effcency. Furthermore, when t passes through nonlnear devce such as HPA, hgh peak sgnals may be clpped. The dstortons caused by ths clppng effect wll affect Orthogonalty of subcarrers [1]. In addton to ths, large PAPR also demands ADCs (Analog-to-Dgtal Converters) wth large dynamc range []. In order to reduce the PAPR of an OFDM sgnal, many technques are proposed, whch can be organzed nto three classes: sgnal dstorton, block codng, and sgnal scramblng. The smplest class of technques to reduce the PAPR s sgnal dstorton, ncludng clppng and peak wndows [3]. To clp the sgnal, the peak ampltude s lmted to some desred mamum level. It can gve a good PAPR. But the BER performance becomes very worse due to many defected sgnals [4].Another method for PAPR reducton s based on the use of codng schemes, where the orgnal data sequence s mapped onto a longer sequence wth a lower PAPR n the correspondng OFDM sgnal. Bascally, a codng scheme would nvolve a large look-up table and s more sutable for those OFDM systems wth a small number of sub carrers [5]. Sgnal scramblng ncludes SLM, DSI and PTS technques. SLM [6] may be classfed nto the phase control scheme to escape the hgh peak. One sgnal of the lowest PAPR s selected n a set of several sgnals contanng the same nformaton data. Both technques requre much system complety and computatonal burden by usng of many IFFT block. However, ths s very fleble scheme and has an effectve performance of the PAPR reducton wthout any sgnal dstorton [8]. In DSI, each dfferent dummy sequences are added nto the same nput data, and, after IFFT, the sgnal has a mnmum PAPR s selected for output sgnal [7]. In PTS, an nput data sequence s dvded nto a number of dsjont sub blocks, whch are then weghted by a set of phase factors to create a set of canddate sgnals. Fnally, the canddate wth the lowest PAPR s chosen for transmsson. Ths PTS scheme has a major drawback that t requres a very large number of computatons to dentfy and select the optmum canddate sgnal that has a low PAPR from all the avalable combnatons of canddate sgnals. Ths computatonal complety has been reduced by mplementng several modfed technques lke teratve flppng, but all these technques are mplemented by reducng & elmnatng the some of the canddate sgnals whch has caused n the nformaton loss. Ths paper proposes a new PTS scheme to reduce the PAPR n OFDM systems wth low & much reduced computatonal complety. In ths paper, we reduce the Computatonal Complety n PTS scheme, by usng the correlaton property between the avalable canddate sgnals, nstead of reducng the number of canddate sgnals and thus no 3683

3 PrPAR (n)>clppng level nformaton s beng lost. Ths scheme acheves the PAPR reducton same as the conventonal PTS scheme and reduces the computatonal complety to a large etent. In secton II, we ntroduce the concept of OFDM sgnal and overvew of the PAPR problem. The conventonal PTS scheme has been eplaned n the secton III. The new PTS scheme to reduce the computatonal complety has been mplemented n secton IV. Secton V gves the computatonal analyss and focuses on the smulaton results. The last secton.e. secton VI concludes our paper plot of PAPR of (n)for varous values of N N=16 N=18 N=56 N=104 II. OFDM AND DISTRIBUTION OF THE PAPR clppng level n db Fg 1. Plot of CCDF of PAPR for varous values of N Let us denote the collecton of all data symbols X[k], k = 0, 1,, N 1, as a vector X = [X 0, X 1,..., X N-1 ] T that wll be termed a data block. The comple base band representaton of a multcarrer sgnal consstng of N sub carrers s gven by ( t) 1 N N 1 k0 X[ k] e jfkt / T, t [0, T] (1) Where j 1 Δf s the sub carrer spacng, and NT denotes the useful data block perod. In OFDM the sub carrers are chosen to be orthogonal (.e. Δf = 1/NT). The PAPR of the transmt sgnal s defned as ma PAPR () In partcular, a base band OFDM sgnal wth N sub channels has PAPR ma =10log 10 N. From the central lmt theorem, t follows that for large values of N, the real and magnary values of (t) become Gaussan dstrbuted. Therefore the ampltude of the OFDM sgnal has a Raylegh dstrbuton, wth a cumulatve dstrbuton gven by F(z)= (1 e -z ).The probablty that the PAPR s below some threshold level can be wrtten as P(PAPR z) =(1 e -z ) N. In fact, the complementary cumulatve dstrbuton functon of PAPR of an OFDM s usually used, and can be epressed as P (PAPR > z) = 1 (1 e -z ) N. The CCDFs are usually compared n a graph such as Fg. 1, whch shows the CCDFs of the PAPR of an OFDM sgnal wth 56 and 104 sub carrers (N =16,18, 56,104) for quaternary phase shft keyng (QPSK) modulaton. The horzontal and vertcal aes represent the threshold for the PAPR and the probablty that the PAPR of a data block eceeds the threshold, respectvely. It s shown that the unmodfed OFDM sgnal has a PAPR that eceeds 10 db for less than 1 percent of the data blocks for N = 56. Wth a certan PAPR value, the occurrence probablty of OFDM sgnals whch eceed ths value augment, as the number N ncreases. III. A CONVENTIONAL PTS In the PTS technque, an nput data block of N symbols s parttoned nto dsjont sub blocks. The sub carrers n each sub block are weghted by a phase factor for that sub block. The phase factors are selected such that the PAPR of the sgnal s mnmzed. Fgure shows the block dagram of the PTS technque. In the PTS technque [9,10] nput data block X s parttoned nto V dsjont sub blocks Xv = [Xv, 0, Xv, 1,, Xv, N-1 ], v = 1,,, V. Fg. A block dagram of the PTS technque 3684

4 The sub blocks are combned to mnmze the PAPR n the tme doman. The set of phase factors s denoted as a vector b = [b 1, b,, b v ]. The tme doman sgnal after combnng s gven b (b)= b(v).(v) 0 v V (3) (b) = [ 0 (b), 1 (b). N-1 (b)] (4) The objectve s to fnd the set of phase factors that mnmzes the PAPR. Mnmzaton of PAPR s related to the mnmzaton of ma [ (b)]. In general, the selecton of the phase factors s lmted to a set wth a fnte number of elements to reduce the search complety. The set of allowed phase factors s wrtten as P = {0, 1,, W 1}, where W s the number of allowed phase factors. So, we should perform an ehaustve search for V phase factors. Hence, W V sets of phase factors are searched to fnd the optmum set of phase factors. The search complety ncreases eponentally wth the number of sub blocks V. PTS needs V IDFT operatons for each data block. The amount of PAPR reducton depends on the number of sub blocks V and the number of allowed phase factors W. Thus, ths conventonal PTS scheme requres a large computatons to get an optmal canddates sgnal wth low PAPR. IV. A PROPOSED REDUCED COMPLEXITY PTS SCHEME Here, we propose a new PTS scheme whch reduces the computatonal complety wthout reducng the number of canddate sgnals. In all avalable combnatons there may be certan pars whch may have the same relatons. Thus, we use the correlaton property among these phase factors n each subset, such that the computatonal complety s reduced. To start wth our proposed method, let us frst defne the phase factors n a phase set. Let us denote the number of phase factors as W. If we take W=, then t ndcates that there are two phase factors, one s n-phase & other s out-of-phase factor wth phase factor set as {1,-1}. In same way, f we take W=4, then the phase factors set conssts of {1,- 1,j,-j} whch ndcates real & magnary, n-phase & out-of-phase factors. Now, knowng these phase factors, we can create a fundamental combnaton known as Prototype Vectors. We derve all the other vectors from ths prototype vector. For eample, f W= & M=, then the prototype vectors are {1,1} & {1, j). Because of usng the correlaton property, all the vectors derved from same prototype vector dffer each other by a sgn change only. Based on these phase factor, number of subblocks of the PTS, by knowng all the vectors, we can wrte the canddate sgnals. Hence by usng the correlaton property and knowng all the vectors, we can wrte the frst canddate sgnal derved from frst prototype vector as Now, we can derve the second canddate sgnal from frst canddate sgnal by usng the sgn change property as Where b,k,m represents the kth phase weghtng vector based on the th prototype vector and s appled to the mth subblock of the PTS OFDM transmtted sgnal and ndcates the sgn of A. Smlarly, we can wrte the +1 th canddate sgnal derved from ths frst prototype vector as Now, we can derve the frst canddate sgnal that of the nd prototype vector denoted by s,1 from s 1,prev as gven by Where ndcates the prevous prototype vector, and s the value whch denote the change of the real & magnary phase factors n the varous prototype vectors. So n general, we can wrte the +1 th canddate sgnal derved from the second prototype vector as Combnng all the above equatons from 5 to 9, we can summarze the general equatons to get the canddate sgnals as gven below And... 1,1 1 M 1, 1,1 sgn( b1,1, m 1, 1 1, sgn( b1,, m (5) (6) (7),1 1, prev b1, prev, m( A, m 1) m, 1, sgn( b,, m 1,1, prev b, prev, m( A 1, m 1) m b k1, 1 k1, k1,, m m (8) (9) (10) (11) Wth all the above equatons, we get the all possble canddate sgnals wth reduced computatonal complety. From these canddate sgnals, we choose 3685

5 the one wth mnmum PAPR for transmsson. Now, let us see the above reduced computatonal complety PTS algorthm consderng an eample. Let us do the partal transmsson of sequences by takng 3 sub blocks.e. M=3 and let us consder 4 phase factors set.e. W=4. Rewrtng the equatons 10 & 11 usng M=3 & W=4 to get the canddate sgnals, we can wrte 1, 1 1, sgn( b1,, m,1 1,4 sgn( b1,4,3 )( A,3 1) 3, 1, sgn( b,, m 3,1,4 sgn( b,4, )( A3, 1) (1) (13) (14) (15) and smlarly we can wrte the equatons so on tll we get the last canddate sgnal.e. X 4,4. So, by usng the equatons from 16 to 19, we can wrte the canddate sgnals as follows 1, , 1 3 1, ,4 1 3,1 1 j3,3 1 j3,4 1 j3 (15) (16) (17) (18) (19) (0) (1) property the computatonal complety has been reduced to a large etant. Now, from these avalable canddate sgnals, we transmt the one wth mnmum PAPR. V. Computatonal Complety Analyss In the prevous secton, we have seen how we had reduced the computatonal complety of the proposed system. Here n ths secton, we analyze the computatonal complety reducton by defnng the term Computatonal Complety Reducton Rato (CCRR) of the proposed PTS scheme comparng wth that of the conventonal PTS scheme. The CCRR s gven by Proposed PTS complety CCRR Conventonal PTS Complety (30) From equaton 6 t s clear that the number of multplcatons requred by the proposed PTS s gven by mul W N [( ) M 1 (31) And the number of multplcatons requred by the conventonal PTS s gven by 1] 3,1 1 j j3 3, 1 j j3 3,3 1 j j3 3,4 1 j j3 4,1 1 j 3 4, 1 j 3 4,3 1 j 3 4,4 1 j 3 () (3) (4) (5) (6) (7) (8) (9) mul N.[ C ( M 1) C M 1 M 1 1 M 1 W 1 C W 1 M 1 ] M 1 M 1 W 1 (3) Smlarly, From equaton 11, we can say that the number of addtons requred by the proposed PTS scheme has reduced to N because t s only necessary to calculate the m Hence, the rato of the addton complety of proposed scheme to that of conventonal PTS scheme s.... Here, note that, due to the correlaton Now, f we take, M=6, then we get Addton CCRR as 80% and Multplcaton 3686

6 CCRR as 98% wth the proposed PTS scheme compared to the conventonal PTS scheme. Wth ths, we can say that the proposed PTS scheme can reduce the computatonal complety to a very etant when compared to the conventonal PTS scheme. VI. Smulaton Results In ths proposed PTS scheme, we have not reduced the number of canddate sgnals as n other cases, but we have used the correlaton property n order to reduce the computatonal complety. In ths regard we can prove ths by observng the Complementary Cumulatve Dstrbuton Functon CCDF. Here, as we have used the correlaton property nstead of reducng the number of canddate sgnals, we acheve the PAPR reducton as same as n the case of conventonal PTS scheme. The results have been smulated n the MATLAB. VIII. ACKNOWLEDGMENT I would lke to thank Ms. Savta Bhosale, who had been gudng through out to complete the work successfully, and would also lke to thank Mr.T.Chalapath who help me through hs paper A Low Complety Algorthm for PTS based PAPR Reducton Scheme n OFDM Systems n IJERT 01. REFERENCES [1] R. W. Chang and R. A. Gbby, "A Theoretcal Study of Performance of an Orthogonal Multpleng Data Transmsson Scheme," IEEE Trans. On Commun., vol. 16, no. 4, pp , Aug [] MULLER, s., BAUML, R., FISCHER, R., and HUBER. J.: 'OFDM wth reduced peak-to-average power rato by multple sgnal representaton'. To appear n Annuls of Telecommuncatons, Specal ssue on multrate dgtal sgnal processng n telecommuncaton applcatons [3] Xaodong L and Leonard J. Cmn. Effects of clppng and Flterng on the Performance of OFDM. IEEE,1997, pp [4] X. L and L. J. Cmn, Jr., "Effect of Clppng and flterng on the Performance of OFDM," Elect. Letter, vol., no. 5, pp , May [5] J. A. Davs and J. Jedwab, Peak-to-mean power control n OFDM, Golay complementary sequences and Reed-Muller codes, IEEE Trans. Inform. Theory, vol. 45, no. 11, pp , Nov [6] P. Van Eetvelt, G. Wade, and M. Tomlnson, "Peak to Average Power Reducton for OFDM Schemes by Selectve Scramblng," Elect. Letter, vol. 3, no. 1, pp ,Oct Fg. CCDF of PAPR VII.CONCLUSION Hence our Proposed PTS scheme not only reduces the computatonal complety but also acheves the same PAPR reducton as that of the conventonal system. [7] Heung-Gyoon Ryu, Jae-Eun Lee, and Jn-Soo Park, "Dummy sequence nserton (DSI) for PAPR reducton n the OFDM communcaton system," IEEE Transactons on Consumer Electroncs, vol. 50, pp.89-94, Feb [8] R.W. Bauml, et al., Reducng the Peak-to-average Power Rato of Multcarrer Modulaton by Selected Mappng, Electroncs Letters, Vol.3, No.,1996,pp [9] T.Chalapath and Madhu Babu, A Low Complety Algorthm for PTS based PAPR Reducton Scheme n OFDM Systems, IJERT,Vol. 1,No 3,May 013. [10] S. H. Müller and J. B. Huber, A Novel Peak Power Reducton Scheme for OFDM, Proc. IEEE PIMRC '97, Helsnk, Fnland, Sept. 1997, pp