Performance Improvement for PAPR Reduction in OFDM with Frequency Domain Technique


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1 Prformanc Improvmnt for PAPR Rduction in OFDM with Frquncy Domain chniqu Pawan Gupta, Vivk kanwar Dpartmnt of Ectronics and Communication Enginring Shooini Univrsity Soan, Mch Studnt Ectronics and Communication Enginring Asst. Profssor Ectronics and Communication Enginring Emai: Abstract OFDM is a most dmocratic procdur of data transmission for high spd communication systm. ransmission tchniqu of OFDM is mutipcarrir whr sing richy data rat stram is sub dividd into many ow data rat stram and transmittd ovr a numbr of subcarrirs. h basic thm of OFDM is disunitd th ovra transmission bandwidth into a figur of orthogona subcarrirs this phnomnon rducs th ISI, Powr consumption and gain th capacity and fficincy of th systm, Fading ffct is rducd by mutipath propagation this is th mrit of OFDM.But in OFDM systm probm occur in tim domain, it consist growth of PAPR, th major imitation of OFDM is PAPR which dgrad th systm fficincy and incras th cost of RF powr ampifir which caus ISI, noninar distortion and out of band radiation. o da with this probm various tchniqu dvopd but in this papr, w wi trim th PAPR prformancs with two diffrnt frquncy domain tchniqu SLM &PS and aso, w compar ths twofrquncy domain tchniqus with ach othr. In this papr QPSK moduation tchniqu is usd. Indx rms OFDM, PAPR, FF, IFF, AWG, BER, CCDF, PS, SLM, IDF. IRODUCIO In today ra communication is on of th important panorama of if and its maturing day by day. On nw moduation schm which is a form of mutipcarrir moduation bcom mor popuar ovr a ast fw yars is cad OFDM. h first OFDM schm was suggstd by CHAG in966[][3]. OFDM is usd mutipcarrir moduation mthod and mutipxing schm is frquncy division, whr th compx data symbo is transmittd in para mod aftr moduating thm ovr orthogona subcarrir. In para transmission compx data is channiz ovr sub carrir whr as in sing carrir(sc)on compx data is channiz using on carrir[].ofdm has most popuar now day and concpt of OFDM has bn around for svra yar. OFDM has many wird and wirss appication such as(bra)broad cast Radio Accss twork, (DAB)Digita Audio Broadcast, (DVB)Digita Vido Broadcast, (ADSL)Audio Digita Subscribr Lin, Wirssmax and LE. ow ths days OFDM considr as significant assts of 4G mobi communication [3]. OFDM is mutipcarrir systm, In mutipcarrir systm avaiab bandwidth is dividd by many subcarrirs, whras sing carrir(sc)systm, it occupis ntir bandwidth, So mutipcarrir(mc) has smar bandwidth as compar to sing carrir (SC)systm. OFDM hand high data rat. h owst v data rat for 4G is anticipat to b mbps and in moving vhic at ast mbps [4].h basic dsign of OFDM is it disunitd th ntir transmission bandwidth into a figur of orthogona subcarrirs. his phnomnon rducs th ISI, Powr consumption, and gain th capacity and fficincy of th systm. h abiity of OFDM is fight mutipath fading chann by using Cycic prfix and Guard intrva, Fading ffct is rducd by mutipath propagation this is th advantags of OFDM.As comparing with sing carrir(sc)systm it provid high data rat and high spctra fficincy[5].howvr OFDM suffr from srious probm of fuctuation of ampitud in arg amount is cad PAPR.o channiz th signa with such high PAPR, it ncssitat vry high powr scop for powr ampifir and rduc th (HPA)High Powr Ampifir fficincy. hs typ of ampifir is vry xpnsiv and hav ow fficincy cost. PAPR occur at th output of IFF in transmittr sction. If th ampitud fuctuation is too giant thn it coud b out of th rang of inar powr ampifir thn occur noninar distortion which dgrad th systm prformanc, to minimiz this probm various tchniqu dvopd. Som of thm Ampitud cipping, Fitring, Coding, on rsrvation, on 69
2 injction, (PS)Partia transmit squnc, (SLM)Sctiv Mapping. [6]. Hr w can b going to invstigat rduction prformanc of PAPR two diffrnt Frquncy Domain chniqu (Signa Scrambing chniqu) such as PS (Partia ransmit Squnc, SLM (Sctiv Mapping). W simuat a rsut in MALAB nvironmnt and thn w wi compar rsut basd on rduction in PAPR ratio.. BASIC OF OFDM SYSEM.. Princip of Orthogonaity As w know that muticarrir systm occupis smar bandwidth chann. his smar bandwidth chann rducs th frquncy spac btwn carrir is obtaind ony whn thy ar orthogona to ach othr. Whn tim avrag intgra product of two signas shoud b zro thn it is orthogona. [] Mathmaticay xprssion of orthogonaity of two signas t f t k Whr (t) ( t) f ( t) dt, if k (.) f k and (t) f ar any two signas ovr th tim intrva [ t, t + ], is a signa tim priod. Whn product of tim avrag intgra of two signas shoud b on thn it is orthonorma. Mathmaticay, orthonorma xprssion of two signas can b xprssd as [] t f t k ( t) f ( t) dt, if k (.) For quation (.) & (.) orthogonaity of OFDM systm is xprssd [] jfkt jkt j ( k) t jft dt jt dt dt Sov quation (.3) w gt [] dt jfk t jft, k, k (.3) (.4) jk jk ns ns j( k) n, k, k (.5) h abiity of OFDM systm, it fficint utiiz th frquncy spctrum through ovrsamping subcarrirs []... OFDM Systm Mod h diagram of discrt tim basband OFDM systm is shown in figur.it consist ransmittr, Chann & Rcivr bock.. ransmittr In this diagram input bit stram ar passd to th moduator bock. In this transmittr sction diffrnt typ of moduator usd dpnding upon systm rquirmnt (.g. M PSK, M QAM tc.).aftr moduation such symbo ar transfrrd by sria to para convrtr(s/p) [7].By using moduation tchniqu compx para data symbo ar obtaind and givn to point IFF bock as shown in figur.compx nvop of basband transmittd OFDM signa can b xprssd [] x(t) ( jfkt) X k, t (.) k ota no. Of subcarrir, X k, k (,,... ) bock of input bits (symbos). f k k f, whr f / ( ), is origina symbo priod. Gnray, th compx data ar uncorratd as shown bow E [ X X k ], k, k (.) ( X ) rprsnt compx conjugat of X ) ( aking discrt samp with th samping instancs at t n S n /, whr n (,,,... ) quation (.4) can b writtn in discrt tim domain as [] Figur.: Bock Diagram of OFDM Systm 7
3 Discrt tim of OFDM signa x(n) is xprssd as x(n) k jkn X ( k),for n,,.. (.3) Equation (.3) can b obtaind by taking th (IDF) Invrs Discrt Fourir ransform & IDF can b comfortaby & thoroughy obtaind by IFF [] Addition Of Guard BandIn OFDM systm, ISI(Intr Symbo Intrfrnc) occur, ISI is introducd btwn squntiay OFDM symbo. o rmov ISI w us guard band intrva [8].Guard band intrva can b usd two ways.zro padding (ZP).Cycic xtnsion. Cycic xtnsion can b xtndd in two ways.cycic prfix (CP).Cycic suffix (CS)[]... Chann Mod In chann mod, th phnomnon of nois & mutipath nvironmnt can b prfigurd. ois can b caus by attach fw random data to th OFDM symbo& gnration of mutipath nvironmnt can b don by adding dayd copis and attnuatd of th OFDM signas. For wirss channs, impus rspons h( t) is givn by [9] L h( t) ( t h ( ) δ(tг) (.4) t Whr h ) and Г ar th tap cofficint or compx ampitud & propagation day. h tap cofficint h ( t),(,,,..., L ) ar mod as zro mans compx Gaussian random variab having varianc.propr nvironmnt of wirss signa provid a Rayigh fading mod.[9].ampitud of wirss signa foowd th Rayigh distribution bcaus of mutipath nvironmnt & its(pdf)probabiity Dnsity Function is givn as[] r r f (r) xp,r (.5) Whr r is nvop of rcivd signa & σ is varianc of nvop of rcivd signa. Aftr mutipath fading h(, t),h rcivd signa y (t) is xprssd as L y (t) h (t) ( t ) n( t) (.6) x xt Whr, n (t) is Additiv Whit Gaussian ois...3 Rcivr At th rcivr sid, th procss is don by th invrs of transmittr. Firsty th guard intrva is rmovd, thn unguardd OFDM symbos is passd to(s/p) sria to para convrtr & thn is passd through FF bock and FF convrt ths para data stram into a frquncy domain[].output of FF is xprssd as[] X ( k) F( k) x( k) w( k),for k  (.7) Whr w(k) is AWG componnt in frquncy domain& F(k) is dnots th FF which is xprssd as[] F (k) L h jkn, k,,...  (.8) Sing tap frquncy domain quaizr ar rcovrd x(k) compx data rcivd symbos and xprssd as G (k) ( F k) (.9) tap cofficint of fitr ar cacuatd basd on chann information []. Finay rcovrd data is passd to P/S convrtr. P/S convrtr convrt th data into sria stram and thn dmoduatd th stram by using schm ik(m PSK,MQAM) to bas band.  Advantags Of OFDM.saving bandwidth.easy to impmnt moduation and dmoduation 3.Easy quaization 4.Suscptib to frquncy sctiv fading 6.Protction against ISI[]  Appication Appication of OFDM divd by two catgoriswir in and wirss appication. h wir in appication.adsl (Asymmtric Digita Subscribr Lin) broad band accss through (POS) Pain Od phon Srvic coppr wiring [3]. MOCA (Mutimdia Ovr Coax aianc) hom ntworking.[4]. h wirss appication such as. IEEE8.a/g/n. IEEE 8.5.3a 3. IEEE 8.6d 4. IEEE 8. 5.DAB (Digita Audio Broadcast) 6.DVB (Digita Vido Broadcast) trrstria V systms 7. HIPERLA/[].  Major Drawback Of OFDM Systm OFDM systm has major probm ik.papr (Pak Avrag Powr Ratio).Synchronization(iming and Frquncy)at rcivr. his papr mainy focusd on PAPR probm in OFDM. 3. PAPR 3. Impact of PAPR On th Systm In transmittr sid, to obtain maximum output powr fficincy (HPA) High Powr Ampifir us th radio systm. HPA ar normay oprat in saturation in rgion. HPA noninar charactristics is vry snsitiv to th diffrnc of th signa ampitud. 7
4 OFDM ampifir diffrnc is vry arg with high PAPR. In HPA, high PAPR wi introduc intrfrnc into th systm &intrmoduation btwn diffrnt subcarrirs. Intrfrnc rduc BER prformanc. PAPR forcs th ampifir having for having high Backoff powr for inar ampifir of th signas. his typ of ampifir has poor powr fficincy[5]. Major impact of high PAPR ar.incras compxity in th ADC&DAC..Efficincy rducd of RF ampifir. 3. Dfinition Of PAPR PAPR is dfin as, Continuous tim basband OFDM transmittd signa x(t) is th ratio of th maximum instantanous powr and th Avrag powr []. max[ x( t)] PAPR,for t (3.) E{ x( t) } Whr, E{.} dnots xpctation oprator and E { x( t) } is avrag powr of x (t) and is symbo priod. x (t) k X f t j k ( k), t (3.) For discrt OFDM signa x (n),papr is cacuat from L tim Ovr samp OFDM signa as[6]. max[ x( n)] PAPR,for n L  (3.3) E{ x( n) } x ( n) } is avrag powr of ) E { x (n.in OFDM signa, ovrsamping is rquird to prvnt aiasing. x(n) is th discrt form of OFDM signa and x (n) can b rprsntd as x (n) k jkn 3.3. Paramtr Infuncing PAPR h numbr of subcarrir () Moduation schm Ovrsamping rat 3.4. Distribution Of PAPR X ( k),for n,,, (3.4) o cacuat th fficincy of PAPR tchniqu most systmaticay usd framwork is (CDF) Cumuativ Distribution Function. ormay (CCDF) Compmntary Cumuativ Distribution Function is usd rathr thn CDF to masur th probabiity[]. CDF of th ampitud of signa samp is givn by [7] z F( Z) ( ) (3.5) Z is a magnitud of compx samps. h CCDF of PAPR for nonovr samping data bock is givn as [][7] P ( PAPR > z ) F ( Z) ( z ) (3.6) is numbr of sub carrir, For ovrsamping data bock CCDF of PAPR is obtain by mutipy this quation with and som constant α, which is xprssd as [][7] z CCDF P ( PAPR > z ) ( ) (3.7) CCDF is gnray usd to stimat th boundary of PAPR. Why PAPR Rduction in OFDM Systm? PPAR is on of th major imitation of th OFDM systm. signa of OFDM consist arg amount of indpndnt moduatd subcarrirs which crat issu of PAPR.it has not workab to convy high pak ampitud signa to transmittr.hrfor w rduc pak in transmittr sid. So w hav to dcras PAPR bfor transmitting []. 4. PAPR Rduction Mthod High PAPR is th major disadvantags of OFDM Systm. o ovrcom this probm various tchniqu dvopd. A th tchniqu ar diffrnt to ach othr in compxity & prformanc [][7].PAPR rduction can dividd in two domain mthod.frquncy domain. im domain [8].In signa scrambing tchniqu, bfor IDF bock it grow th crossconnction of th input mssag& dcras th IDF pak vau at th output. Frquncy domain schm arsctiv Mapping(SLM),Partia ransmit Squnc(PS), prcoding tc., and basic concpt of im domain mthod is rduc PAPR by disfigur th signa bfor ampification addd of xtra signas. im domain schm ar Cipping, Fitring, Pak windowing tc.. im domain mthod is vry simp mthod but it introducs distortion &incras outof  band radiation and dgrad BER prformanc. Whn w compar ths two mthod Frquncy domain mthod is vry fficint, It rduc PAPR without distorting th signa and aso not introduc Inbanddistortion and outofband radiation in OFDM signa. In this papr, w wi invstigat th rduction prformanc of PAPR with two diffrnt Frquncy domain tchniqu such as SLM &PS. Frquncy Domain mthod is mosty usd to rduction of PAPR (i. Signa scrambing & Prcoding) bcaus thy ar distortion ss. 7
5 ab4.comparison Of PAPR Rduction chniqu [9] [9] Mth ods Cipp ing &Fit ring Codin g Avr ag Pow r Incr ass Comp xity Band width Expa nsion BER Dgra dation o Low o Ys o o Low Ys o o Sid Infor mation PS o High Ys o Ys SLM o High Ys o Ys Prcodin g o Low Ys o o Frquncy Domain mthod is mosty usd to rduction of PAPR (i. Signa scrambing & Prcoding) bcaus thy ar distortion ss. 4.. Partia ransmit Squnc(PS) PS agorithm was first proposd by Mur SH, Hubr JB []. In PS, frquncy domain symbos ordr (X) is sparatd into V disjoint subbock X (i) Whr i V,such that  X Sum ( X (i) ); i V (4.) & thn sub bock X(i) ar transformd into V tim domain Partia ransmit Squnc. x (i) IFF ( X (i) ); i V (4.) Aftr that ths sris ar indpndnt rotatd by som phas aspct, b (i) xp( j ) ; i V i (4.3) hn ths ar combind to provid th tim domain OFDM signa packt rvrs. b( i) x( i ); i V (4.4) x Sum ( ) Figur4.: Bock Diagram of PS Sub bock Partitioning can b don by 3 mthod Adjacnt partition, Psudo random Partition and Intravd Partition. [] and ach subbock has quivant siz. PS tchniqu is affctd by not ony th figur of subbock &aso th figur of aowd phas vctor (w) as w as partitiond of sub bocks. 4.. Sctiv Mapping First SLM pan was introduc by Baum, Fischr & Hubr in 996[].h basic ida of this tchniqu is basd on Phas rotation. Figur show th bock diagram of SLM schm [3] Figur4.: Bock Diagram of SLM In SLM, Origina input data X ] [ X, X,..., X mutipid with indpndnt phas squncs. P [ P, P,..., P ] (u,,..., U ),Whr U is numbr of phas squnc. wi b th sam for both input data &phas squnc & is th ngth (u,,..., U ).Aftr mutipication, IFF wi appid on ach sris to transform signa from frquncy dominion to tim dominion. h concusion from mutipication wi produc th data bock of an OFDM signa that has dissimiar tim dominion signa, with ngth of V and dissimiar PAPR vaus, X [ X X... X ].Fina stag is comparing th PAPR among th indpndnt data bocks and th signa with th shortst PAPR wi b pickd for transmission [3]. 5. Simuation In this zon, an vauation of factor which coud impact th PAPR rduction prformanc is xcut by using MALAB simuation. 5.. Simuation of SLM schm Construct on th princip of SLM agorithm, it is vidnty that th potntia of PAPR dption using SLM is infunc by th rout numbr M and subcarrir numbr. hrfor, simuation with diffrnt vau of M and wi b conductd, and th rsut xhibit som dsird proprtis of signa rprsnting th sam information. Comparison of PAPR rduction prformanc with diffrnt vau of M whi is 8, 56, 5, 4.and rotation factor is P m, n ϵ[±,±ϳ]. h agorithm xcuts 3 (,) tims, ovrsamping factor is 8 and QPSK mapping is adoptd as moduation schm in ach subcarrir. Rout numbr M, M4, M8, M6 ar usd. From figur (5.), it can b obsrvd that th SLM mthod dispay bttr 73
6 PAPR rduction prformanc than th origina OFDM signa with diffrnt vau of V and W. h simuation rsut in fig. (5.) shows th varying PAPR rduction with diffrnt W (coction rang of wighting factor W v) whn using PS rduction schm. Simuation spcific paramtr ar: th numbr of subcarrir 8, 56, 5, 4, QPSK constation moduation, ovrsamping factor taks L8, h numbr of sub bock V4. (a) (b) (a) (b) (c) (d) Figur 5.: Comparison of PAPR rduction prformancs of SLM whr diffrnt vau of M &diffrnt numbr of subcarrir (a)8,(b)56,(c)5 &(d)4. h agorithm xcuts 3 (,) tims, ovrsamping factor is 8 and QPSK mapping is adoptd as moduation schm in ach subcarrir. Rout numbr M, M4, M8, M6 ar usd. From figur (5.), it can b obsrvd that th SLM mthod dispay bttr PAPR rduction prformanc than th origina OFDM signa. ab5.: Obsrvation tab for SLM tchniqu: o. of subcarrir() Max symbos 3 () Rout numbr (M) M M M M Simuation of PS schm In PS schm, thr ar varying critrion ffct th PAPR rduction prformanc, ths ar:) h numbr of subbocks V, which infunc th compxity strongy; ) h numbr of possib phas vau W, which ffcts th compxity as w; and 3) h subbock partition schm. Simuation vauats th PAPR rduction prformanc using PS agorithm (c) (d) FIGURE 5.: Comparison of PAPR rduction prformancs of PS whr (Phas vau)w, W4,&(subbock)V4 with diffrnt numbr of subcarrir (a) 8,(b) 56,(c) 5 &(d) 4. ab 5.: Obsrvation tab for PS tchniqu whn (V4): Max Ovrsam umb Phas Phas symbos ping r of vau( vau( 3 factor(l) sub W) W4) carrir () W ngotiat that in a PS  OFDM systm, th argr W vau taks, th suprior PAPR prformanc wi b gt whn th figur of subbock V is fixd. Simiary, in cas of subbock V, arg subbock V wi cacuat in sma rfinmnt of PAPR rduction prformanc, but pay for trmndous hardwar compxity. hrfor practicay, w prfr to choos 74
7 a suitab vau of V to achiv a tradoff in th us of PS Comparison of SLM and PS schm SLM and PS agorithm ar two cassica nondistortion tchniqus for rducing PAPR in OFDM systm. In ordr to hav rrorfr dmoduation in th rciving nd, sid information must b snt to th rcivr, corrcty. PS mthod dmand a highr information rdundancy, compar to SLM agorithm. Figur (5.3) show th simuation rsut of using SLM an PS mthod to an OFDM systm, sparaty. In PS procdur w assign th figur of sub carrir 56, and 5 and appying psudo random partition schm, for ach subcarrir, choosing QPSK constation mapping, wighting factor W v ϵ[±,±ϳ];in SLM mthod, rotation factor P m, n ϵ[±,±ϳ].basd on th thory,w know that th IFF cacuation amount of ths two mthods is sam whn VM, but for PS mthod, it can provid mor signa manifstations, thus, PS mthod shoud provid a suprior prformanc on PAPR rduction. from this figurr5.3 w arnd that with th sam CCDF probabiity %, h PAPR vau qua to 7.6dB &8.dB whn PS is mpoyd, whi th PAPR rais up to9db & 9.4dB whn SLM is mpoyd. (a) (b) FIGURE 5.3: Comparison of PAPR rduction prformancs btwn PS agorithm and SLM agorithm for PS  OFDM systm with no. of subcarrir (a)56, (b)5.it show cary that PS mthod provid a bttr PAPR rduction prformanc compard to SLM mthod. vrthss, cost is aso payd for sacrificing transmission fficincy and rising compxity. thus, in practica appication, a tradoff shoud b mad btwn good prformanc and auxiiary information. from th discussion abov, w can say that SLM schm is mor suitab if systm can torat mor rdundant information, othrwis, PS schm is mor accptab whn compxity bcoms th first considring factor. 6. Concusion his papr provids an ovrviw of OFDM. h focus of papr is that w invstigat on of th bottnck probm that xist in OFDM wirss communication systmhigh Pak Avrag Powr Ratio(PAPR) of OFDM signa, and discuss how to rduc it by diffrnt ffctiv agorithms. In this papr two frquncy domain tchniqu (signa scrambing tchniqu) such as PS & SLM ar invstigatd to rduc PAPR, A of ths two frquncy domain tchniqu hav th potntia to provid substantia rduction in PAPR. Prformanc of PS mthod is bttr th SLM mthod in rducing PAPR. REFERECES [] E. A.Daakta, A. A.Dwik & C. simnidis (),Efficint BER Rduction chniqu for oninar OFDM ransmission Using Distortion Prdiction. IEEE ransactions on Vhicuar chnoogy. Vo. 6, O. 5, pp [] A. R. S. Bahai and B. R. Satzbrg, MutiCarrir Digita Communications: hory and Appications of OFDM, Kuwr Acadmic Pubishrs, w York,. [3] Adarsh B. arasimhamurthy, Mahsh K. Banavar, and Cihan pdnio gu, OFDM Systms for Wirss Communications,, ISB: [4] R.W Chang, Synthsis of BandLimitd Orthogona Signas for Mutichann Data ransmission, B Syst. ch., Vo.45, pp , Dc [5] S. S. irodkar, Y. M. Pati Intrnationa Journa of Advanc Rsarch in Computr Scinc & Managmnt Studis Voum 3, Issu, Fbruary 5 pg [6] Suvrna Sngar, Partha Pratim Bhattacharya Signa & Imag Procssing : An Intrnationa Journa (SIPIJ) Vo.3, o., Apri [7] Arun Kumar,Manisha Gupta/Amrican Journa of Enginring and Appid Scincs 5,8():.9 DOI:.3844/ajassp.5..9 [8] Minakshi Duby * and raj Shrivastava Dpartmnt of Ectronics and Communication, Rustamji Institut of chnoogy, BSF kanpur Gwaior (MP), India Accptd 8 ov 5, Avaiab onin 9 Dc 5, Vo.5, o.6 (Dc 5) [9] H.D. Joshi and R. Saxna, OFDM and its Major Concrns: A Study with Way Out, IEE Journa of Education, vo. 54, Issud., pp. 49, JanJun. 3. []. S. Rappaport, Wirss Communications, Princips and Practic. Prntic Ha, w Jrsy, 996. [] Mamdouh Esayd Gouda, Mohamd Hussin Moharam, Mohamd Rabi Ragab, Ahmd Mahmoud. Anwar, Ahmd Fathi Gouda. USRP Impmntation of PS chniqu for PAPR Rduction in OFDM Using LABVIEW. 75
8 Advancs in Wirss Communication & tworks. Vo., o., 6, pp doi:.648/j.awcn.6. [] Zou, W.Y. and Wu, Y., COFDM: An Ovrviw, IEEE transactions on broadcasting, vo. 4, no., pp. 8, March 995. [3] P. S. Chow, J. C. u and J. M. Cioffi, Prformanc vauation of a mutichann Systm for ADSL and VHDSL srvics, IEEE Sctd Ara, vo., SAC9, no. 6, pp.999, August 99. [4] Anton Monk, Ronad L and Yoav Hbron, h mutimdia ovr Coax Aianc, Procding of th IEEE, pp. 7, 3. [5] S. H. Han and J. H. L, An ovrviw of pak to avrag powr ratio rductions tchniqus muticarrir transmission, IEEE Wirss communication, vo., no., pp.5665, Juy 5. [6] Gama Mabrouk Abd Hamid, Sahar Abd Rahman Intrnationa Journa of Computr Appications ( ) Voum 53 o.8, Sptmbr [7] Mohindr Jankiraman, Muticarrir tchniqus, in Spactim cods and MIMO systms, Artch Hous, 4, pp.. [8] MiinJong Hao and Chiu Hsiung Lai., Prcoding for PAPR Rduction of OFDM Signas With Minimum Error Probabiity, IEEE ransactions on Broadcasting, vo. 56, no., pp. 8, ovmbr. [9] Sung H Han and Ja Hong L, An Ovrviw of Pak to Avrag Powr ratio rduction tchniqus for Muticarrir transmission, IEEE Wirss Communication, vo., no., pp , Apri 5. [] H. Mur, J. B. Hubr, A nov pak powr rduction schm for OFDM, h 8th IEEE Intrnationa Symposium on Prsona, Indoor and Mobi Radio Communications, Fb 997, pp [] Sog Gun Kang, Jong Goo Kim and Eon Kyong, A nov subbock schm for Partia ransmit Squnc OFDM, IEEE ransactions on Broadcasting, vo.45, no. 3, pp , March 999. [] Baum, R., Fischr, R., and Hubr, J, R Guangyu Lu, Ping Wu and Catharina Carmam Logothtis, Rducing th paktoavrag powr ratio of muticarrir moduation by sctd mapping" IEE Ectronics Lttrs, vo. 3,pp , 996. [3]  Pankaj Kumar Sharma, Powr Efficincy Improvmnt in OFDM Systm using SLM with Adaptiv oninar Estimator Word Appid Scincs Journa 7 (Spcia Issu of Computr & I): 455, 9, ISS
CH 7. Synchronization Techniques for OFDM Systems
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