THRESHOLD EXTENDING RECEIVER STRUCTURES FOR CE-OFDM

Transcription

1 THRESHOLD EXTEDIG RECEIVER STRUCTURES FOR CE-OFDM hen U. hmed, Seve C. Thompon*, and Jame R. Zeidler Univeriy of California, San Diego (UCSD) alo wih SPWR Syem Cener (SSC), San Diego *alo wih corn Technologie, San Diego brac -- Conan Envelope OFDM (CE-OFDM) alleviae he high pea-o-average power raio (PPR) problem in OFDM. However, ince CE-OFDM i baed on angle modulaion, i i ucepible o he well nown hrehold effec. Thi paper conider everal hrehold exending receiver rucure for CE-OFDM. The imple arcangen receiver [4] i compared o he convenional limier-dicriminaor ype FM receiver and a econd-order phae loced loop rucure. novel cycle lip eliminaor (CSE) i alo developed o deec and cancel cycle lip and i hown o provide ignifican hrehold exenion. I i oberved ha he opimum receiver deign depend on he CE-OFDM modulaion index. The variou cheme are compared in erm of hrehold exenion capabiliy and complexiy for a wide range of modulaion indexe. I. ITRODUCTIO OFDM i widely ued in boh commercial and miliary applicaion. One of he major iue wih OFDM i he high pea-o-average power raio (PPR) [, pp. 9-9] which reul in inermodulaion diorion a well a ou of band pecral growh in he preence of yem non-lineariie. Therefore, i i cuomary o employ a ignifican bacoff a he ranmi amplifier for OFDM reuling no only in reduced ranmi power bu alo low power efficiency [, chap. ] which i epecially derimenal o mobile device operaing on baerie. Furhermore, he hea diipaion due o inefficien operaion reul in addiional deign requiremen. Conan Envelope OFDM (CE-OFDM) provide one oluion o he high PPR iue in OFDM []-[4]. I ranform he high PPR OFDM ignal o a conan envelope ignal uing phae modulaion, hereby removing no only he need for a bacoff a he amplifier, bu alo permiing he ue of highly efficien and non-linear amplifier which are no compaible wih OFDM []. The pecrum, ignal pace properie and performance of CE- OFDM were preened in [4] and [6]. The CE-OFDM bandwidh and performance have alo been udied in [7] and [8]. In [9], he uiabiliy of CE-OFDM for a Gbp wirele lin a 6 GHz wa udied and he applicaion of convoluional coding o CE- OFDM wa conidered in []. pracical CE-OFDM receiver i baed on a phae demodulaor, o exrac he OFDM ignal from he phae, followed by a convenional OFDM receiver [4]. Since CE- OFDM i baed on angle modulaion, i uffer from he well nown hrehold effec [] whereby he demodulaed ignal o noie raio (SR) fall off much more rapidly han he inpu carrier o noie raio (CR). The hrehold effec i encounered a low CR and i accompanied by he appearance of phae cycle lip (clic noie in FM). Variou receiver rucure have been developed over he year o provide hrehold exenion. Thi i accomplihed mainly hrough eiher a feedbac rucure uch a in a phae loced loop (PLL) or frequency modulaion wih feedbac (FMFB) receiver [], or hrough ome form of clic noie (cycle lip) eliminaion [3]. In hi paper, we udy he hrehold performance of variou receiver rucure for CE- OFDM. We conider he imple arcangen baed receiver [4] wih and wihou a phae unwrapper along wih a cycle lip eliminaor o deec and compenae for phae cycle lip. We alo conider convenional FM baed receiver uch a a limier dicriminaor (LD) ype receiver and a digial phae loced loop (PLL). We how ha he arcangen receiver wihou he phae unwrapper perform well for mall modulaion indice when he correc phae reference ha been eablihed. We furher how ha for all oher cae, he cycle lip eliminaor ued in conjuncion wih he arcangen receiver provide hrehold exenion of everal db. II. SIGL DESCRIPTIO The CE-OFDM ignal i obained hrough a imple ranformaion of OFDM. The OFDM ignal i phae modulaed ono a carrier ignal o obain a conan envelope ignal wih db PPR. Thi i implemened hrough a raighforward modificaion of a andard OFDM yem a hown in Fig.. DT GEERTE OFDM High PPR Fig.. The modificaion of an OFDM yem o obain CE-OFDM. The baeband CE-OFDM ignal i given a j () () = e φ, () where i he ignal ampliude. The phae ignal φ() wih he embedded OFDM ignal i given a PHSE MODULTOR db PPR POWER MPLIFIER Sandard OFDM Modificaion φ() = πhc diq( it) + θi, it ( i+ ) T. = () The real daa ymbol d i ± modulae he orhogonal OFDM ubcarrier q () defined below. T i he CE-OFDM ymbol (bloc) period. The normalizing conan C = σ I enure ha he phae variance i independen of he number of OFDM ubcarrier and σ I i he daa variance wih σ I = for binary daa [, p. 47]. The modulaion index h i he ey parameer ha conrol he performance (ignal pace properie) and he pecral properie of CE-OFDM [4]. I deermine he radeoff beween power and bandwidh. In hi paper, he caled modulaion index (πh) i alo imply referred o a he modulaion index. The phae memory may be ued θ i ()

2 o enure phae coninuiy acro he CE-OFDM ymbol boundarie for improved pecral conainmen [6], [7]. Wihou lo of generaliy, full ine and coine ubcarrier (DFT) eparaed by /T, q () co,in π π for = = T T o /, are ued o fulfill he ubcarrier orhogonaliy requiremen []. The ubcarrier energy E q for hee ubcarrier i T E = q () d = T. q III. GEERL RECEIVER The general receiver rucure for CE-OFDM coni of a phae demodulaor, o undo he ranformaion (phae modulaion), followed by a andard OFDM demodulaor a hown in Fig.. lhough hi reul in a ub-opimum receiver [4], i provide for a pracical receiver implemenaion. φ ˆ( ) exenion would permi a larger CR range over which channel coding would be able o provide error correcion, which would be epecially ueful in a fading channel wih inerleaving. The hrehold effec i accompanied by a change in he characeriic of he noie a he oupu of he phae demodulaor. The noie n() a he inpu of he receiver from (3) can be repreened in polar form a [, p. 36] n ( ) j arcan nc ( ) j n ( ) c n n() = n () + n () e = V () e φ, () where V n () and φn () are he envelope and phae of he noie proce repecively. Uing hi repreenaion, he phaor diagram of he ignal and noie in (3) i hown in Fig. 3 [] below. r() PHSE DEMODULTOR OFDM DEMODULTOR DETECTOR RECEIVED DT Fig.. The modificaion of an OFDM receiver o obain a CE-OFDM receiver. The baeband received CE-OFDM ignal i given a jφ ( ) r () = e + n (), (3) where n( ) nc ( ) + jn ( ) i he baeband Gauian noie wih power pecral deniy [4, p. 8], / f Bbp Φ n( f ) =,, f Bbp / (4) where B bp i he yem fron-end bandwidh which i aen o equal he yqui ampling rae (F =/T ) reuling in independen Gauian noie ample [, p. 3].. Predeecion Filer The noie ha ener he phae demodulaor i he primary caue of cycle lip (clic noie in FM) and herefore uing a predeecion filer a he inpu of he phae demodulaor can reduce he rae of cycle lip. narrow bandwidh predeecion filer ha rejec he ou of band noie while reuling in negligible ignal diorion can improve he hrehold performance. In hi paper, we how reul boh wih and wihou a linear phae FIR predeecion filer of lengh 3 deigned uing he Par-McClellan opimal filer deign algorihm (firpm in MTLB). IV. THRESHOLD EFFECT The hrehold effec i inheren in angle modulaion and herefore alo affec CE-OFDM. In he hrehold region, a low carrier o noie raio (CR), he demodulaed SR fall off much more rapidly for a decreae in CR. Thi reul in poor performance below hrehold. One propery of angle modulaed waveform i he poible radeoff beween bandwidh and power wih an increae in he modulaion index. However, hi radeoff i limied by he hrehold which appear a even higher CR for larger modulaion indice [, p. 3]. Threhold exenion provide an increae in he range of CR over which hi radeoff i poible. ddiionally, for CE-OFDM, hrehold Fig. 3. Phaor diagram of he phae of an angle modulaed ignal wih noie [, p. 37] I i eviden from he phaor diagram ha he received phae i given a Vn()in ( φn() φ() ) φr ( ) = φ( ) + arcan. (6) + Vn()co ( φn() φ() ) Uing hi and auming high CR, he oupu of he phae demodulaor can be approximaed a [, p. 37] Vn () φr() φ() + in ( φn() φ() ) = φ() + Zn(). (7) Z n () provide a good approximaion for he noie componen a high CR. ddiionally, i can be well approximaed a Gauian diribued for high CR [, p. 8]. While hi approximaion hold up well for high CR, he exac diribuion for he noie ha been compued a [6], [7, p. 47] co ( φr φ) π co( ) σ σ φr φ p( φr φ) = e + co( φr φ) e Φ π σ σ CR = e + πcr φ φ e Φ( CR φr φ ) π 4 CRco ( φr φ) co( r ) co( ), (8) where σ i he variance of bandpa noie a he receiver inpu x y and Φ ( x) = e dy π. The carrier o noie raio (CR) i given a CR = =, (9) σ B where B m =/T i he meage ignal (OFDM) bandwidh. The diribuion in (8) approache Gauian for high CR [8] agreeing wih he Gauian approximaion menioned above. Furhermore, he power pecral deniy of he noie componen for a phae modulaed ignal can be approximaed a SZ ( f) W/Hz when he modulaed ignal bandwidh i much larger han he meage bandwidh. Therefore, in order o m

3 deermine he relaionhip beween he CR and he demodulaed SR [6] a high CR, he noie a he oupu of he phae demodulaor can be characerized a Gauian noie wih a fla power pecral deniy of W/Hz over he meage bandwidh. The phae demodulaor i followed by a convenional OFDM demodulaor a hown in Fig.. Conidering he ih CE-OFDM ymbol wihou lo of generaliy, he oupu of he h mached filer of he OFDM demodulaor i given a it Y = φ () q ( it ) d = S +, () where and r ( i) T it = φ() ( ) = π q ± π q ( i) T S q it d d hc E hc E it = n ( i) T Z () q ( it ) d. () () Since he noie proce Z n () i well approximaed a Gauian for high CR and {q ()} are an orhogonal e panning an - dimenional pace, he are independen zero mean Gauian random variable wih variance E q σ =. The demodulaed SR i herefore given a [6] S ( πhce ) q ( πh) T (3) SRou = = = = ( πh) CR. σ E q Equaion (3) repreen he linear relaionhip beween he CR and he demodulaed SR ha hold above hrehold. I alo ignifie he radeoff whereby he demodulaed SR increae wih an increae in he modulaion index a he expene of bandwidh [, p. ]. When he CR drop below hrehold, he noie phaor in Fig. 3 i large enough o occaionally encircle he origin reuling in a π phae hif (roaion) in he reulan phae []. Thi new ype of noie i nown a clic noie (in FM) reuling in pie in he demodulaed FM ignal or cycle lip in he demodulaed PM ignal. Each pie i of area π, while each cycle lip reul in a π phae hif. The pie and cycle lip conribue a ignifican amoun of noie power for low CR reuling in a rapid decline in demodulaed SR a he CR fall below hrehold. Exac analyi of noie effec below hrehold i ediou if no inracable in mo cae due o he inheren nonlineariie. pracical approach of an approximae noie model wa preened by Rice in [9] in which he modeled he noie a having a coninuou Gauian componen ha i occaionally inerruped by clic. Wih hi model, he noie i compried of wo componen: a coninuou Gauian componen added o a equence of randomly occurring clic. The rae of clic, which depend on he CR, deermine he noie power conribued by he clic componen. Rice noie model ha been found o be quie accurae down o CR a low a db [], []. The realizaion, baed on Rice model, ha clic noie i primarily reponible for he one of hrehold uppor he developmen of receiver rucure ha provide hrehold exenion by ome form of reducion in clic noie. Thi i accomplihed by eiher uing a feedbac loop mechanim uch a in PLL and FMFB baed receiver [] for clic noie uppreion or by employing clic deecion and eliminaion cheme [3] wih a convenional receiver uch a he limier dicriminaor (LD). V. RECEIVER STRUCTURES The general receiver rucure for CE-OFDM i hown in Fig.. I coni of a phae demodulaor followed by a convenional OFDM demodulaor. We conider hree ype of phae demodulaor for he CE-OFDM receiver: he limier dicriminaor ype demodulaor, he arcangen baed demodulaor, and he phae loced loop. We udy heir implemenaion and compare he relaive performance.. Cro-Correlaor Receiver (CCR) The convenional limier dicriminaor (LD) receiver i a common pracical embodimen of an ideal FM deecor [, p. ]. I coni of a limier followed by a dicriminaor [, chap. 9]. Since he meage ignal in FM i embedded in he frequency, he ampliude variaion of he ignal are due o noie alone and herefore a limier i ued o uppre he noie induced ampliude variaion. The limier i followed by he dicriminaor which ha a ranfer characeriic which increae linearly wih frequency. The dicriminaor i eenially a differeniaor ha perform differeniaion in he ime domain, reuling in a ignal whoe ampliude varie preciely a he inananeou frequency of he ignal. If he received ignal i given a r () = co( ω c+ φ()) + n () = r()co( ωc+ φr()), (4) hen he oupu of he limier dicriminaor i d yld () = L ωc + φr () in( ωc + φr ()), d () where L i he limied ampliude from he limier. For he cae of FM, an envelope deecor can be ued a he oupu of he dicriminaor o recover he meage ignal embedded in he frequency. dding an inegraor a he oupu of he LD reul in a phae demodulaor [, p. 7]. Similar o he limier dicriminaor, anoher receiver baed on he ideal FM deecor [, p. ] i he cro-correlaor receiver (CCR) which wa fir propoed by Par [] who deermined ha he performance of he cro-correlaor receiver wa beer han he LD a low SR for he cae wih no limiing or invere limiing. The overall performance of he CCR ha been udied in [3] and i found o be imilar o ha of he LD. Mo imporanly, he CCR i well uied for a digial implemenaion in a DSP. The baeband received ignal given in (3) may be wrien a r () = co φ() + nc() + j ( in φ() + n()) = I () + jq (), (6) where I() and Q() are he quadraure componen. The phae of he received ignal i ˆ( () ) an Q φ = I () (7) and he oupu of he ideal FM deecor [] i hen given a 3

4 ˆ d ˆ d Q() φ () = φ() = an d d I() I() Q () QI () () =. I () + Q () (8) Thi i nown a he cro-correlaor receiver. I i hown in Fig. 4 and lend ielf well o a digial implemenaion. Since he oupu i he inananeou frequency, adding an inegraor reul in a phae demodulaor a needed for CE-OFDM. I'() d I() d - (.) d φˆ ( ) + d Q() d Q'() I () + Q () Fig. 4. Cro-correlaor receiver (CCR) a phae demodulaor. The cro-correlaor receiver in Fig. 4 can be implemened in dicree ime uing he ampled baeband quadraure componen, I(n) and Q(n). The differeniaor can be implemened in a DSP or FPG environmen for varying degree of fideliy and complexiy [4]. The cenral difference differeniaor (I'(n) = (I(n+) - I(n-))/) provide a very imple differeniaor which i linear for mall frequencie (f <.8F ) and provide good aenuaion a higher frequencie. higher order differeniaor can be deigned o aain greaer accuracy a he co of complexiy. In hi paper, we ue an FIR filer of lengh 9 deigned uing he Par-McClellan opimal filer deign algorihm (firpm in MTLB) wih a frequency repone ha increae linearly up o a normalized frequency of. and a op band from.7 o a hown in Fig. (where he frequencie are normalized by F /). Magniude Magniude Repone ormalized Frequency ( π rad/ample) Fig.. FIR differeniaor of lengh 9 ued in he cro-correlaor receiver. B. rcangen Baed Receiver imple arcangen baed phae demodulaor [4] a hown in Fig. 6 can alo be employed for phae demodulaion. r() Q () an I() PHSE UWRPPER φ r () Fig. 6. rcangen baed phae demodulaor. The phae of he baeband received ignal r() i exraced by aing he invere angen of he quadraure baeband componen. The arcangen provide he inananeou phae which i rericed o he π o +π range. Thi reul in phae wrapping when he phae croe he π/+π phae boundary uch a for high OFDM ignal pea. Phae wrapping i more frequen for higher modulaion indice ha ravere a larger ecion of he uni circle a hown in Fig. 7 or for he cae when random phae hif due o he channel puh he phae reference from o a poin cloer o he π/+π phae boundary. In uch cae, i i neceary o ue a phae unwrapper o reconruc he original unrericed phae. Complex plane πh=. πh=.6 radian reference Fig. 7. CE-OFDM phae deviaion a a funcion of modulaion index. The phae unwrapper (unwrap in MTLB) operae on a ample by ample bai by earching for phae jump larger han π and replacing hem by heir π complemen. The phae unwrapper i prone o maing error due o he preence of noie and perform epecially poorly a low CR when ignifican noie i preen. The phae unwrapper error reul in π phae jump in he demodulaed phae, analogou o cycle lip decribed earlier. For mall modulaion indice where an equalizer correc any phae hif due o he channel reuling in a radian phae reference, he phae wrapping i very infrequen and hence, beer performance i aained by operaing wihou he phae unwrapper. Converely, he phae unwrapper i eenial for higher modulaion indice. The performance of he cro-correlaor receiver (CCR) along wih he arcangen baed receiver boh wih and wihou a phae unwrapper i hown in Fig. 8 for an over ampling facor of R OS =4. Fig. 8 (b) i for he cae wih a predeecion filer while Fig. 8 (a) how he cae where no filer i ued. The arcangen receiver wihou he phae unwrapper require an equalizer o undo he random channel phae hif. The linear demodulaed SR compued for high CR in (3) i alo ploed. expeced, he performance i much beer wih he predeecion filer preen due o he reducion in noie enering he receiver. Boh he CCR and he arcangen receiver wih he unwrapper how he one of hrehold a indicaed by he deviaion of he demodulaed SR from he linear model. However, he arcangen receiver wihou he unwrapper doe no how any ign of he hrehold effec. Thi can be explained from he fac ha hi receiver only provide a ample by ample eimae of he phae and herefore in prone o cycle lip which reul in π phae jump in he demodulaed phae. However, he demodulaed SR for i doe deviae lighly from he linear model for low CR which i due o he reduced accuracy a low CR of he approximaion ued o obain he linear model in (3). For modulaion indice higher han πh=.6, here i ignifican amoun of phae wrapping and hence he arcangen baed receiver wihou a phae unwrapper ha a ignifican lo over he linear model. The arcangen baed receiver wih he phae unwrapper how a lower hrehold (of around. db) compared o he CCR (around db). Thi i mainly becaue of he amplificaion of high frequency noie by he differeniaor in he CCR which alo explain he poor performance of he CCR 4

5 when a predeecion filer i no ued. πh=.6 The hrehold exending capabiliie of phae loced loop (PLL) are well nown [], [] wih hrehold exenion of a much a db obained wih a PLL []. Since he hrehold i primarily he reul of cycle lip (clic noie), he PLL provide hrehold exenion by uppreing he rae of cycle lip compared o a convenional limier dicriminaor receiver. The cycle lip in a PLL are from wo ource [, p. 9]: () Threhold induced cycle lip (TICS) due o noie and () Lo of loc cycle lip (LLCS). The hrehold induced cycle lip are he reul of he PLL racing an encirclemen of he origin by he received ignal phae due o noie. The PLL rejec mo TICS by no racing he origin encirclemen and inead lipping a cycle. PLL wih infinie bandwidh would rac all TICS and reul in noie performance idenical o a LD. Reducing he bandwidh of he PLL reduce he amoun of noie enering he loop and herefore reduce he rae of TICS. Converely, cycle lip due o lo of loc are a reul of he PLL no being able o rac he received ignal phae. Therefore, he rae of LLCS i reduced by increaing he loop bandwidh. The overall goal for hrehold reducion in a PLL i o reduce he oal number of cycle lip o a minimum (le han a LD) by opimizing he loop bandwidh. Wih he adven of high peed DSP, digial implemenaion of he PLL have been udied and implemened over he year [6]. In [7], i wa hown ha he hrehold exenion properie of a econd-order digial PLL are uperior o hoe of he firorder and hird-order PLL. We udy he applicaion of a econdorder, ype, digial PLL [8]-[3], hown in Fig. 9, a a phae demodulaor for CE-OFDM. Oupu SR (db) - - πh=.3 an Cro-Correlaor Rcvr I[n] Q[n] I n + Q n [ ] [ ] in co G LOOP FILTER z - T Oupu SR (db) (a) πh=.6 πh=.3 an Cro-Correlaor Rcvr - 6 Fig. 8. Demodulaed SR a a funcion of CR wih R OS =4 for (a) o predeecion filer, (b) Wih predeecion filer (ft b =.4 for πh=.3 and ft b =.6 for πh=.6). C. Phae Loced Loop (PLL) (b) PHSE DETECTOR π/ φ ˆ( n ) Fig. 9. Second-order digial PLL phae demodulaor. The digial PLL in Fig. 9 coni of hree main componen. The phae deecor provide an error ignal ha i proporional o he phae difference beween he received ignal and he oupu of he volage conrolled ocillaor (VCO). Thi error ignal i hen inpu ino he loop filer which provide a conrol ignal o he VCO o eliminae he error. The oupu of he phae deecor i given a ˆ π in in( ) co co( ˆ π ) co( ˆ π φr φ + + φr φ + = φr φ ) (9) = in( φ ˆ r φ). The loop filer i choen a he perfec inegral filer given a G z ranform G F() = + F(). z + z = () The cloed loop ranfer funcion of he PLL i hen given a KF() H() = + KF() () K + KG ζωn + ωn = =, + K+ KG + ζωn+ ωn where ω n i he naural frequency of he cloed loop and ζ i he damping facor. G, he gain conan of he loop filer, and K, he loop gain, are hen deermined from ω n and ζ a G = ω n /ζ and K = ζω n. The digial PLL require a higher ampling rae o wor correcly. Lindey and Chie noed in [6] ha hi requiremen eem o imply ha he digial PLL mu be deigned o approximae an analog PLL o funcion properly. Fig. how he demodulaed SR ploed again he CR for boh he PLL and he arcangen baed receiver wih a phae unwrapper for modulaion indice of πh=.6 and. The imulaion wa conduced wih an over ampling facor of R OS = and for modulaion indice of πh=.6 and repecively. The predeecion filer wa employed wih ft b =.3 and for he PLL and ft b =.7 and.4 for he arcangen receiver for modulaion indice of πh=.6 and repecively. The naural frequency of he cloed loop wa eleced a f n =ω n /π=./t b afer opimizaion while he damping facor of ζ =.77 wa eleced. The reul in Fig. indicae a ligh reducion in hrehold for πh=.6 compared o he arcangen receiver wih phae T z - K VCO

6 unwrapper (R OS =4) hown earlier in Fig. 8 while he reducion i around. db compared o he cro-correlaor receiver (CCR). Oupu SR (db) πh=.6 πh= PLL - 6 Fig.. Demodulaed SR a a funcion of CR wih R OS = for πh=.6 and R OS = for πh= (For PLL, f n =ω n /π=./t b and ζ =.77). While he PLL doe provide hrehold exenion over he limier dicriminaor ype receiver (cro-correlaor receiver hown in Fig. 8), he hrehold exenion i relaively mall. Thi i due o he relaively low modulaion indice being conidered here. Furher reducing he PLL loop bandwidh o obain a larger hrehold exenion reul in ignal diorion of he embedded OFDM ignal. The arcangen receiver alo perform quie well compared o he PLL. VI. CYCLE SLIP ELIMITOR noher hrehold exenion echnique employed in FM i baed on clic noie eliminaion [3]. The eliminaion of clic noie reduce he effecive oupu noie power hu improving he demodulaed SR. The baic idea i o accuraely deec clic while avoiding deecion of any fale clic. Thi i followed by compenaing for he clic wih he goal of canceling hem ou compleely. Variou clic noie eliminaion echnique have been propoed over he year wih varying degree of ucce [3]. I wa hown in [3] ha a perfec clic deecion cheme can provide hrehold exenion of a lea 6 db for an FM ignal wih a modulaion index of. rnd and Loch propoed a echnique in [3] o deec he clic noie uing ignal correlaion where a delayed verion of he ignal i ubraced from ielf o reveal noie clic a eiher a poiive pea followed by a negaive pea or vice vera. We employ a omewha imilar echnique for he deecion of cycle lip a hown in Fig.. ˆ[ n] φ ˆ φ '[ n ] > γ d d ˆ φ [ n ] CSE ˆ'[ φ n] I i a local maxima or minima? Generae π phae hif of oppoie polariy o cancel cycle lip Fig.. Cycle lip eliminaor. The demodulaed phae i differeniaed uing he novel differeniaor from [4] o reveal large phae jump due o cycle lip. The differeniaed phae ignal i hen compared o a hrehold value (γ ) o pinpoin poenial cycle clip which are alo required o be local maxima or minima. I ha been hown in YES YES Difference of avg ˆ[ φ n ] { } before and afer CS > γ [3] ha only looing a he envelope or phae of he received ignal a a ample poin i no adequae for reliable clic deecion. Therefore, he poenial cycle lip ha exceed he predeermined hrehold are hen verified by requiring he difference beween he average value of he phae before and afer he poenial cycle lip o be greaer han a econd hrehold value γ. Thi average i compued over ample or le if here i anoher poenial cycle lip wihin ample. Each cycle lip ha i deeced wih hi echnique i hen cancelled by adding a π phae hif of polariy oppoie o he cycle lip. The performance of he cycle lip eliminaor (CSE) i hown in Fig. for CE-OFDM modulaion indice of πh=.3 and.6 for an over ampling facor of R OS =4. Fig. (b) i for he cae wih a predeecion filer while Fig. (a) how he cae where no filer i ued. Oupu SR (db) Oupu SR (db) - πh=.6 πh=.3 an +CSE (a) πh=.6 πh=.3 an +CSE - (b) Fig.. Demodulaed SR a a funcion of CR wih R OS =4 for (a) o predeecion filer wih γ =., γ =π/4 for πh=.3 and γ =, γ =π/4 for πh=.6 (b) Wih predeecion filer (ft b =.4 for πh=.3 and ft b =.6 for πh=.6) and γ =., γ =π/4 for πh=.3 and γ =.7, γ =π/4 for πh=.6. In boh cae, he CSE provide coniderable hrehold exenion wihou requiring a large over ampling facor. Wihou he predeecion filer, he CSE provide around db of hrehold exenion while for he cae wih he predeecion filer, hrehold exenion i more han db. Similarly, Fig. 3 how hrehold exenion of 4 db down o a CR of db for CE-OFDM wih a modulaion index of πh= for an over ampling facor of R OS =8. Fig. 3 alo how he large performance lo for he arcangen receiver wihou a phae unwrapper. Thi i due o he phae wrapping which i much more frequen for higher modulaion indice whereby he CE- OFDM phae ravere a larger ecion of he uni circle a hown earlier in Fig. 7 6

7 Oupu SR (db) - πh= an +CSE - 6 Fig. 3. Demodulaed SR a a funcion of CR wih R OS =8 wih predeecion filer (ft b =3) for πh= and γ =., γ =π/4. VII. COCLUSIO Several receiver rucure for CE-OFDM have been udied and heir hrehold exenion capabiliie have been compared. For he cae of modulaion indice maller han πh=.6 where he equalizer compenae for he random channel phae hif, he arcangen baed receiver wihou a phae unwrapper provide he be performance wihou uffering from he hrehold effec. Thi i due o i ample by ample phae eimaion echnique. For all oher cae, he arcangen baed receiver wih an unwrapper provide good performance wih a low complexiy. I hrehold occur around db for an over ampling facor of R OS =4 when ued wih a predeecion filer. n furher increae in he ampling rae doen reul in any ignifican hrehold exenion. The PLL perform lighly beer han he arcangen baed receiver below hrehold a he co of much greaer complexiy. Furher reducing he loop bandwidh of he PLL o aain greaer hrehold reducion reul in ignal diorion novel cycle lip eliminaor (CSE) ha alo been udied and i i hown o provide ignifican hrehold reducion when ued in conjuncion wih he arcangen baed receiver. Mo imporanly, he CSE doe no require a large increae in he ampling rae hereby eeping he complexiy low. The hrehold exenion wih he CSE for πh=.3 and.6 i greaer han db and i around 4 db for πh=. REFERECES [] R. van ee and R. Praad, OFDM for Wirele Mulimedia Communicaion. Boon, M: rech Houe,, pp [] S.C. Thompon, Conan Envelope OFDM Phae Modulaion, Ph.D. dieraion, Univeriy of California, San Diego,. [Online]. vailable: hp://zeidler.ucd.edu/~c/hei/ [3] S.C. Thompon, J.G. Proai, and J.R. Zeidler, Binary OFDM Phae Modulaion, in Proc. of IEEE Milcom 3, Boon, M, Oc. 3. [4] S.C. Thompon,.U. hmed, J.G. Proai, and J.R. 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