# Performance Improvement for PAPR Reduction in OFDM with Frequency Domain Technique

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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 sub-carrirs []... OFDM Systm Mod h diagram of discrt tim bas-band 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 bas-band transmittd OFDM signa can b xprssd [] x(t) ( jfkt) X k, t (.) k ota no. Of sub-carrir, 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

4 OFDM ampifir diffrnc is vry arg with high PAPR. In HPA, high PAPR wi introduc intrfrnc into th systm &intr-moduation btwn diffrnt sub-carrirs. Intrfrnc rduc BER prformanc. PAPR forcs th ampifir having for having high Back-off 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 bas-band 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 non-ovr 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 sub-carrirs 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 cross-connction of th input mssag& dcras th IDF pak vau at th output. Frquncy domain schm ar-sctiv Mapping(SLM),Partia ransmit Squnc(PS), pr-coding 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 out-of - 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 In-banddistortion and out-of-band 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 & Pr-coding) bcaus thy ar distortion ss. 7

5 ab-4.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 & Pr-coding) 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 sub-bock 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 ( ) Figur-4.: Bock Diagram of PS Sub bock Partitioning can b don by 3 mthod- Adjacnt partition, Psudo random Partition and Intravd Partition. [] and ach sub-bock has quivant siz. PS tchniqu is affctd by not ony th figur of sub-bock &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]- Figur-4.: 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 sub-carrir. 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 sub-carrir 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 sub-carrir. 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 sub-bocks V, which infunc th compxity strongy; ) h numbr of possib phas vau W, which ffcts th compxity as w; and 3) h sub-bock 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,&(sub-bock)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 sub-bock V is fixd. Simiary, in cas of sub-bock V, arg sub-bock 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 trad-off 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 rror-fr 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 sub-carrir, 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 trad-off 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 systm-high 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, Muti-Carrir 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 Band-Limitd Orthogona Signas for Muti-chann 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, Jan-Jun. 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

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