2th Europan Signal Procssg Confrnc (EUSIPCO 212 Bucharst, Romania, August 27-31, 212 PAPR REDUCTIO OF OFDM SIGALS USIG SELECTIVE MAPPIG AD CLIPPIG HYBRID SCHEME Victor Cutanu, Alandru Isar Polithnica Univrsity, Faculty of Elctronics and Tlcommunications, Communication Dpartmnt, Timisoara, Romania, victor.cutanu@gmail.com, alandru.isar@tc.upt.ro ABSTRACT Th Orthogonal Frquncy Division Multiplg is on of th modulation tchniqus widly usd th broadband wirlss tchnology. On of th ma problms of this tchnology is th high pak-to-avrag powr ratio of transmission signal du to th suprposition of many subcarrirs. This papr prsnts a nw hybrid pak-toavrag powr ratio rduction tchniqu, which combs a slctiv mappg mthod with th clippg mthod. Th papr prsnts th prformanc and advantags of th nw tchniqu and compars it with othr istg mthods. Ind Trms OFDM, PAPR, SLM, Clippg 1. ITRODUCTIO Th Orthogonal Frquncy Division Multiplg (OFDM is on of th vry fficint and oftn usd modulation tchniqus usd broadband wirlss communication systms lik WiMAX, DVB-T, or wirl systms lik ADSL. On of th ma issus of th OFDM basd systms is th Pak-to-Avrag Powr Ratio (PAPR of th transmittd signal. Du to th tim-doma suprposition of th many data subcarrirs which composs th OFDM signal, th PAPR may rach high valus. Du to th larg numbr of subcarrirs, th rsultg tim-doma signal hibits Rayligh-lik charactristics and larg timdoma amplitud variations. Ths larg signal paks rquirs th high powr amplifirs (HPA to support wid lar dynamic rang. Th crasd signal lvl causs nonlar distortions ladg to an fficint opration of HPA causg trmodulation products rsultg unwantd out-ofband powr. In ordr to rduc th PAPR of OFDM signals, many solutions hav bn proposd and analyzd. Ths mthods can b charactrizd by various paramtrs lik non-larity, amount of procssg and siz of sid formation ndd to b snt to rcivr. Som of th wll known lar mthods ar slctiv mappg (SLM [1], partial transmit squnc (PTS [2], and ton rsrvation (TR [3]. Th SLM mthod prforms svral vctor rotations of th origal frquncy-doma OFDM signal, basd on a st of prdfd vctor arrays. For ach signal variant obtad, its corrspondg PAPR is valuatd. Th on with th lowst PAPR is chosn for th transmission. Th PTS mthod hav a similar approach with th diffrnc that sam rotation angl is applid to mor than on vctor. Th mthod considrs th compl valus rprsntg OFDM signal vctors as bg groupd to K sub-blocks of /K lmnts ach. Aftr calculation of th corrspondg PAPR of ach signal variant, th on with mimal PAPR is bg chosn for th transmission. Th fficincy of th SLM and PTS mthods crass with th numbr of phass from th considrd st. Th fficincy of th PTS mthod also crass whn a highr numbr of blocks ar usd. Th drawback is that a bttr fficincy rquirs an crasd amount of computation at th transmittr s and rcivr s sids. For th rgnration of th origal signal, th rcivr must know thos phass sts and block sizs and displacmnts. Whn ths arrays hav a wll dfd limitd amount of lmnts, thy can b prdfd with th rcivr. Whn ths arrays hav a variabl amount of lmnts, thn additional formation is rquird to b snt to rcivr. Thrfor anothr disadvantag of ths mthods may ris whn this amount of additional formation is comparabl to th amount of ffctiv data formation with th transmittd frams. Optimizations of ths mthods has bn proposd svral paprs [4,5]. Th TR mthod is anothr lar PAPR rduction tchniqu which stad of altrg th data subcarrirs, it uss a st of rsrvd st of subcarrirs (tons to gnrat signals with lowr PAPR lvl. [3] Sc th origal variant, svral drivat tchniqus hav bn proposd: slctiv mappg of partial tons (SMOPT [6], On-Ton On-Pak (OTOP [7] and on-by-on itration [8]. Th class of non-lar mthods is rprsntd by approachs lik activ constllation tnsion (ACE, clippg, partial clippg, and signal comprssion. Th ACE mthod oprats on tons whos bas band modulation symbol is an outr pot of th constllation. EURASIP, 212 - ISS 276-1465 2551
It movs th compl valus of thos tons toward outsid of th origal constllation ordr to rduc th PAPR lvl of th transmittd signal. [9] Th clippg mthod is anothr wll known non-lar PAPR rduction tchniqu, whr th amplitud of th signal is limitd to a givn thrshold. Takg considration th fact that th signal must b trpolatd bfor A/D convrsion, a varity of clippg mthods has bn proposd. Som mthods suggst th clippg bfor trpolation, havg th disadvantag of th paks rgrowth aftr trpolation.. Othr mthods prform th clippg aftr trpolation, havg th disadvantag of out-of-band powr production. In ordr to ovrcom this problm diffrnt filtrg tchniqus hav bn proposd. Filtrg can also caus pak rgrowth, but lss than th clippg bfor trpolation [1]. Th partial clippg mthod is anothr nonlar tchniqu which supposs that only subcarrirs havg th highst phas diffrnc btwn th origal signal and its clippd variant will b changd. [11] For additional PAPR rduction, som paprs proposd µ- law/a-law compandg functions [12], ponntial compandg function [13], picwis-scals [14] or polynomial ratio functions [15] aftr th clippg. Th rst of th papr is organizd as follows. Th scond paragraph dscribs th OFDM signal and som of its proprtis. Th third sction dscribs th proposd hybrid PAPR rduction schm. t, th numrical rsults highlightd by th computr simulation ar prsntd and discussd. Basd on th rsults obtad, som conclusions ar prsntd. 2. THE OFDM SIGAL In an OFDM basd systm, th signal contas a st of basband subcarrirs, {f n, n=,1,,-1}, which ar modulatd by th signal sampls from a block of symbols, {X n, n=,1,,-1}. Ths subcarrirs ar chosn to b orthogonal, that is f n =n f, whr f=1/t, and T is th OFDM symbol priod. Th rsultg signal can b writtn as: 1 ( t = n= 1 X n j2πfnt. (1 In ordr to avoid th trsymbol trfrnc (ISI gnratd by th multipath channls, a rpatd signal squnc from th currnt priod, corrspondg to a guard trval, is addd to th signal. Aftr Digital-to-Analogu (D/A convrsion, th signal is amplitud modulatd to a carrir frquncy and applid to a high-powr amplifir (HPA which drivs th antnna load. At th rcivr, aftr dmodulation, th guard trval will b rmovd, th symbols bg valuatd for a tim trval of [,T]. Tim doma sampls of th low-pass OFDM signals th compl doma ar apprciativly Gaussian distributd du to statistical dpndnc of carrirs. Th wightd sums of random variabls which forms paks th signal, causs th PAPR problm. Th prssion of th PAPR for a givn OFDM signal block is givn by: 2 ( ( t 2 ( t ma PAPR ( =, (2 E [ ] whr E[.] dnots th pctation oprator. This is usually valuatd usg valuats th complmntary cumulativ distribution function (CCDF of th PAPR: CCDF = 1 Pr ( Y = Pr( PAPR > Y ( PAPR < Y whr Y is a givn PAPR thrshold. 3. THE HYBRID TECHIQUE In this paragraph w prsnt th proposd hybrid PAPR rduction tchniqu which has bn obtad by srialization of slctiv mappg mthod and clippg mthod. Th ma ida for combg th two mthods is rlayg on th obsrvation that two diffrnt typs of signal procssg for PAPR rduction will cras th ovrall prformanc. On prforms lar transformation by rotatg th vctors from th frquncy-doma signal, and th othr on prforms a non-lar transformation rprsntd by signal limitation to a givn thrshold. Th SLM mthod consists an itrativ sarch algorithm, whos computation tim dpnds by th amount of variants for phas changs. In cas of th clippg mthod, which has a fid numbr of oprations, th computation tim is constant. Thrfor anothr advantag of th hybrid mthod is that total amount of computation tim may b rducd, du to rducd siz of sarch spac usd by th SLM block. Th prformanc of th proposd PAPR rduction tchniqu is analyzd with a MATLAB simulator as prsntd Figur 1. With this simulator, th uniformly random gnratd sampls ar mappd from bary rprsntation to th M- QAM or M-PSK constllation pots. Th obtad compl valus ar groupd blocks of lmnts ach, formg th OFDM symbols. Th obtad OFDM frams ar applid squntially to th SLM block and thn to th clippg block. For th rsultd signal, th PAPR lvl is valuatd usg th CCDF charactristic. In ordr to valuat th prformanc of a communication systm whn this PAPR rduction tchniqu applid, th BER for th cas of an AWG channl is computd as wll. = (3 2552
Data T M-QAM / M-PSK mappr OFDM Modulation PAPR IFFT Slctiv Mappg Clippg & Filtrg X Vctor Rotation φ n,h X slm BER(SR Clippg & Filtrg CCDF Phass Tabl Figur 2. Th SLM drivat mthod for PAPR rduction. Data R Figur 1. MATLAB modl for th analysis of th hybrid PAPR rduction tchniqu. Th applid SLM mthod is prsntd th diagram from Figur 2. It gnrats a st of signal variants basd on th algorithm consistg th followg stps. 1 Startg with a st of data symbols X, rprsntg an OFDM fram: PSD M-QAM / M-PSK dmappr 1 1 n= ( t = X ( n AWG OFDM Dmodulation j2πf t n, (5 This sid-formation may conta only som labl bits or th phas vctor itslf, dpndg on th availability of th phas st at th rcivr. Th data bits ar usually codd usg a rcursiv convolutional cod which may affct almost all bits from th rspctiv fram if it is non-systmatic. For this cas, th litratur provids th followg CCDF approimation [16]: Pr π Y K Y SLM > 1 3 ( PAPR Y whr K is th numbr of th symbols with a block, and U is th ovrsamplg factor. Th applid clippg tchniqu [1] is prsntd th block diagram from Figur 3. U (8 2 Rotat all constllation vctors from X usg th phas tabl φ n,h, whr n=1 is th d of a vctor, and h=1..r is th d of th signal variant from a st of R possibilitis. Th signal bcoms: a,,a /2-1 (p-1 zros a /2,,a -1 Invrs on-lar procssg (Clippg X ( n, h X ( ϕ( n h =. (6 slm, 3 Apply IFFT to gt th corrspondg tim-doma signal rprsntation slm (t,h. slm 1 1 n= ( t, h = X ( ( n, h j2πfnt ϕ. (7 4 Comput th PAPR for all R variants, and choos th on with lowst PAPR lvl for th transmission. Th signal X slm is drivd from X which has modifid valus for phas of all vctors. Bcaus th rcivr must rconstruct th origal signal by applyg th vrs vctor rotations, it has to know th rotation angl tabl. For this purpos, it is ncssary ithr to considr a prdfd tabl or to transmit additional formation to th rcivr. Forward Signal zro paddg Frquncy doma filtrg Invrs Figur 3. Clippg basd PAPR rduction modl. In this mthod, additionally to th ffctiv clippg, th signal is adaptd and applid to a frquncy doma filtr. Such filtrg tchniqus ar usd and dtaild prsntd som works [1,17]. Considrg an ovrsamplg factor p, th put array of compl valus [a,,a -1 ] is paddd with a squnc of (p-1 zros placd th middl. Thn, th obtad signal is convrtd from frquncy to tim doma usg an ovrsizd IFFT. This rsults a trigonomtric trpolation of th tim doma signal, which fits wll for th signals with tgral frquncis ovr origal FFT wdow, lik is th cas of OFDM. Th trpolatd signal is thn clippd by limitg its amplitud. Th clippg ratio applid this 2553
mthod is dfd as ratio of th clippg lvl A to th rootman-squar powr σ of th unclippd basband signal. = log CR 1 A σ 2. (9 Additional rsarch on th various clippg tchniqus has bn mad svral papr [18,19]. Th proposd hybrid PAPR rduction tchniqu contas both lar and non-lar signal procssg blocks. This fact rprsnts a high flibility from th signal procssg pot of viw. Whn SLM block uss a rducd st of phas arrays, its smallr PAPR rduction can b compnsatd by th clippg block. This cas has th advantag of a rducd amount of computation, but also has th disadvantag of a highr signal distortion. Whn th SLM block uss an tndd st of signal variants, th crasd PAPR rduction allows a dcrasd signal distortion. This cas prsnts a bttr BER prformanc but with th drawback of an crasd amount of computation. 4. UMERICAL RESULTS Th MATLAB simulations hav bn prformd for bas-band signals with =128 and =256 subcarrirs usg M-QAM and M-PSK modulations. Th rsults prsntd this papr ar obtad usg a phas rotation array contag 3 sts of phas valus givn byϕ k = 2kπ / M, whr M={4,5,6} and k= M-1. Th tabl contas phas squncs with th rptitiv pattrns of th forms {φ,φ 1,,φ M-1 }, {φ,φ,φ 1,φ 1,,φ M-1,φ M-1 } and {φ,φ 1,,φ M-1,φ M-1,φ M-2,,φ }, for ach valu of M. Th numrical rsults hav shown that th proposd schm improvs th PAPR rduction comparison with th us of only on of th componnt mthods. BER CCDF (Pr[PAPR>PAPR] 1 BER for OFDM for SLM-Clippg Hybrid Schm 1-4 Origal clippd only with SLM only Hybrid SLm-Clippg 2 4 6 8 1 12 14 16 18 2 SR [db] Figur 5. BER of OFDM signal bfor and aftr PAPR rduction. 1 PAPR Rduction for Hybrid SLM-Clippg Schm. Orignal with Clippg Only with Slct.Mappg only Hybrid SLM-Clippg 2 4 6 8 1 12 PAPR [db] Figur 6. PAPR rduction usg hybrid SLM-Clippg mthod. 1 PAPR Rduction for Hybrid SLM-Clippg Schm. Orignal with Clippg Only with Slct.Mappg only Hybrid SLM-Clippg 1 BER for OFDM with SLM-Clippg hybrid schm Origal clippd only with SLM only Hybrid SLm-Clippg CCDF (Pr[PAPR>PAPR] BER 1-4 2 4 6 8 1 12 PAPR [db] Figur 4. PAPR rduction usg hybrid SLM-Clippg mthod. 2 4 6 8 1 12 14 16 18 2 SR [db] Figur 7. BER of OFDM signal bfor and aftr PAPR rduction. 2554
For th valuation of th prformanc of th proposd tchniqu, two cass ar considrd and prsntd. Th first cas considrs an OFDM signal with =128 subcarrirs with a 16-QAM modulation and a clippg rat of CR=12. Th Figur 4 and Figur 5 dicat th corrspondg PAPR rduction and BER prformanc rspctivly. Th scond cas considrs an OFDM signal with =256 subcarrirs with a 16-PSK modulation usg a clippg rat of CR=9.5. Th corrspondg rsults ar dicatd th Figur 6 and Figur 7. Th two cass show also that a lowr clippg thrshold has an crasd flunc th BER prformanc dgradation. Thrfor ordr to avoid this dgradation, an tndd SLM vctor rotation tabl can b usd. Th computation complity of th hybrid tchniqu is givn by th sum of oprations don by SLM and clippg mthods. Considrg th block structur and paramtrs of ths componnt mthods, prsntd th prvious sction, th computation complity of th SLM bock is O( R ( 1+ log2 (. Considrg th block diagram of th clippg mthod which with contas frquncy doma filtrg block, which prforms Fourir transformations on th zro paddd signal, its computation complity is givn by th sum of oprations rquird by th ffctiv clippg and filtr rlatd blocks. This which is sum of O( p ( 1 + log2 ( p and rspctivly O( ( p 1 + 2 p log2 ( p. Thrfor, for a givn OFDM signal of subcarrirs, th total amount of oprations dpnds by th paramtrs R and p, which can b adjustd ordr to limit th total dlay with th PAPR rduction blocks. 5. COCLUSIOS In this papr w proposd an altrnativ PAPR rduction tchniqu basd on combation of a partial transmit squnc mthod with th clippg mthod. Th papr prsntd th SLM and clippg algorithms usd with th hybrid tchniqu. Th numrical rsults show that th hybrid schm brgs highr PAPR rduction than th componnt mthods. 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