Reducing the jitter noise power by oversampling in High speed of dm system

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1 Itratioa Joura of Egirig Scic Ivtio Voum Iu 3 ǁ arch. 3 Rducig th jittr oi por by ovrampig i High pd of dm ytm B. Vami Kriha, P.Nagarjua, J. SAYANARAYANA 3 (At.Profor, Dpartmt of ECE, IS adaapa, A.P, INDIA) (At.Profor, Dpartmt of ECE, GPREC Kuroo, A.P, INDIA) 3 (At.Profor, Dpartmt of ECE, INELL ENGG COLLEGE,AP, A.P, INDIA ABSRAC: h OFD ytm ha muti ub carrir to d th high pd data. At high data rat thr i b chac of timig jittr i OFD ytm du to mimatch of th ampig coc at th rcivr ith th tramiio pd. h ffct caud by timig jittr i a igificat imitig factor i th prformac of vry high data rat OFD ytm. Ovrampig ca rduc th oi caud by timig jittr. Both fractioa ovrampig achivd by avig om bad-dg OFD ubcarrir uud ad itgra ovrampig ar coidrd. Ovrampig rut i a 3 db rductio i jittr oi por for vry doubig of th ampig rat. Kyord: imig jittr, ovr ampig, jittr oi por, OFD I. INRODUCION Orthogoa frqucy diviio mutipxig(ofd) i bcomig idy appid i ir commuicatio ytm du to it high rat tramiio capabiity ith high badidth fficicy ad it robut ith rgard to muti-path fadig ad day. It ha b ud i digita audio broadcatig (DAB) ytm, digita vido broadcatig (DVB) ytm, digita ubcribr i (DSL) tadard, ad ir LAN. OFD i ud i may ir broadbad commuicatio ytm bcau it i a imp ad caab outio to itr ymbo itrfrc caud by a mutipath cha. Data rat i optica fibr ytm ar typicay much highr tha i RF ir ytm. At th vry high data rat, timig jittr i mrgig a a importat imitatio to th prformac of OFD ytm. A major ourc of jittr i th ampig coc i th vry high pd aaog-to-digita covrtr (ADC) hich ar rquird i th ytm. imig jittr i ao mrgig a a probm i high frqucy bad pa ampig OFD radio. I OFD, fractioa ovrampig ca b achivd by avig om bad-dg ubcarrir uud. Vry high pd ADC typicay u a para pipi architctur ot a PLL for thi mod. II. OVERVIEW OF OFD SYSE A OFD iga i a uprpoitio of N iuoida carrir ith frqucy paratio F N, ach ubcarrir i moduatd by compx ymbo ith priod N qua to th ivr of th frqucy paratio, i.. N =/F N. h moduatd carrir ovrap pctray but, ic thy ar orthogoa ithi a ymbo duratio (th th carrir frqucy i f = f o + F N hr f o i om rfrc frqucy ad < < N ), th iga aociatd ith ach iuoid ca b rcovrd a og a th cha do ot dtroy th orthogoaity. I practic, th amp of th OFD iga ar gratd by taig th ivr dicrt Fourir traform (IDF) of a dicrt-tim iput quc ad paig th traform amp through a pu hapig fitr. At th rcivr dua traformatio ar impmtd. o priodic iga ar orthogoa h th itgra of thir product, ovr o priod, i qua to zro. Dfiitio of Orthogoa: Cotiuou im: co( f t) co( mf t) dt ( m) Dicrtim: N- co N m co N ( m)

2 Rducig th jittr oi por by ovrampig i high pd ofdm ytm h carrir of a OFD ytm ar iuoid that mt thi rquirmt bcau ach o i a mutip of a fudamta frqucy. Each o ha a itgr umbr of cyc i th fudamta priod. III. SYSE ODEL Coidr th high-pd OFD ytm.h OFD ymbo priod, ot icudig th cycic prfix, i. At th tramittr, i ach ymbo priod, up to N compx vau rprtig th cotatio poit ar ud to moduat up to N ubcarrir. imig jittr ca b itroducd at a umbr of poit i a practica OFD ytm but i thi ttr coidr oy jittr itroducd at th ampr boc of th rcivr ADC. Iday th rcivd OFD iga ampd at uiform itrva of /N. h ffct of timig jittr i to cau dviatio τ bt th actua ampig tim ad th uiform ampig itrva. I OFD ytm hi timig jittr dgrad ytm prformac, a cotat tim offt from th ida ampig itat i automaticay corrctd ithout paty by th quaizr i th rcivr. Fig: OFD boc diagram I OFD ytm thr i o chac for itr carrir itrfrc(ici) bcau of th ub carrir ar orthogoa to ach othr. hr a CDA ad GS tchoogi ar ig carrir ytm.at high data rat thr i b chac of timig jittr i OFD ytm du to mimatch of th ampig coc at th rcivr ith th tramiio pd. IV.IING JIER IN OFD: imig jittr i τ oft modd a a id tatioary (WSS) Gauia proc ith zro-ma ad variac. Fig: Dfiitio of timig jittr h ffct of timig jittr ca b dcribd by a timig jittr matrix. h compact matrix form for OFD ytm ith timig jittr i Y = WH +N () hr, Y ad N ar th tramittd, rcivd ad additiv hit Gauia oi (AWGN) vctor rpctivy, H i th cha rpo matrix ad W i th timig jittr matrix. hr Y =[Y N/+. Y Y N/ ] H = diag(h N/+..H. H N/ )

3 Rducig th jittr oi por by ovrampig i high pd ofdm ytm =[ N/+.. N/ ] imig jittr cau a addd oi i compot i th rcivd iga. Y = H + (W I)H +N () hr I i th N N idtity matrix. h firt trm i () i th atd compot hi th cod trm giv th jittr oi.h mt of th timig jittr matrix W ar giv by, N / j j ( ) N N N / hr i th tim idx, i th idx of th tramittd ubcarrir ad i th idx of th rcivd ubcarrir. h timig jittr matrix i giv by (3) (4) V. OVERSAPLING YPES h ffct of both fractioa ad itgra ovrampig i OFD ca b ud to rduc th dgradatio caud by timig jittr. o achiv itgra ovrampig, th rcivd iga i ampd at a rat of N/, hr i a itgr. For fractioa ovrampig om bad-dg ubcarrir ar uud i th tramittd iga. Wh a N ubcarrir ar moduatd, th badidth of th babad OFD iga i N/, o ampig at itrva of /N i Nyquit rat ampig. If itad, oy th ubcarrir ith idic bt N L ad +N U ar o zro, th badidth of th iga i (N L +N U)/. i thi ca ampig at itrva of /N i abov th Nyquit rat. h dgr of ovrampig i giv by (N L + N U)/N. VI. EFFC OF OVERSAPLING ON JIER NOISE POWER: I th gra ca, hr both itgra ad fractioa ovrampig ar appid, th iga amp aftr th ADC i th rcivr ar giv by y y N N N u N H L j N N hr i th ovrampd dicrt tim idx ad η i th AWGN. With itgra ovrampig, th N-poit FF i th rcivr i rpacd by a ovrizd N-poit FF. h output of thi FF i a vctor of gth N ith mt. j N N / Y y (6) N N / hr i th idx at th output of th N poit FF. h modifid ightig cofficit for th ovrampig ca,, N N / N / j j ( ) N By uig th approximatio jθ = +jθ for ma θ, a i(5) ad (7), N / N N / j j( ) / N So for th variac of th ightig cofficit i giv by, p j d N { { (8) N (5) (7)

4 Rducig th jittr oi por by ovrampig i high pd ofdm ytm Whr -p =d. Wh th timig jittr i hit, th {ττ d = for d o, { { N From (9) it ca b that hit timig jittr E{, i ivry proportioa to o icraig th itgr ovrampig factor rduc th itr carrir itrfrc (ICI) du to timig jittr. It i ao that E{, dpd o but ot o, o highr frqucy ubcarrir cau mor ICI, but th ICI affct a ubcarrir quay. AVERAGE JIER NOISE POWER FOR EACH SUBCARRIER Y H NU, I, H N( ) N L hr th cod trm rprt th jittr oi. coidr a fat cha ith,h = ad aum that th tramittd iga por i ditributd quay acro th ud ubcarrir o that for ach ud ubcarrir E{ = σ. h th avrag jittr oi por, Pj () to rcivd iga por of th ubcarrir i giv by (9) () Pj { Nv I,, Nu ( ) N { I,, NL () Rarragig th trm i ()quatio Pj( ) N v N { 3 N () Pj( ) N If thr i o itgra ovrampig or fractioa ovrampig, = ad Nv = N, { (3) 3 N Comparig () ad (3) it ca b that th combiatio of itgra ovrampig ad fractioa ovrampig rduc th jittr oi por by a factor of Nv/N. VII. SIULAION RESULS: By uig mat ab oftar, th imuatio rut ar ho bo. Figur : h graph i dra bt th ovrampig factor ad jittr oi por. Rut: du to ovrampig, hvr icra th ampig Factor by to, thr a th dcra i jittr oi por by 3db.

5 Rducig th jittr oi por by ovrampig i high pd ofdm ytm Figur: h graph i ho bo for th fractioa ovrampig ho to rduc th timig jittr. Rut. h variac of th oi du to jittr a a fuctio of rcivd ubcarrir idx h baddg ubcarrir ar uud. It ho that th por of th jittr oi i ot a fuctio of ubcarrir idx ad that rmovig th bad-dg ubcarrir rduc th oi quay acro a ubcarrir. Avrag jittr oi por a a fuctio of th ovrampig factor. hr i co agrmt bt thory ad imuatio. VIII. CONCLUSIONS It ha b ho both thorticay ad by imuatio that ovrampig ca rduc th dgradatio caud by timig jittr i OFD ytm. o mthod of ovrampig r ud: fractioa ovrampig achivd by avig om of th bad-dg ubcarrir uud, ad itgra ovrampig impmtd by icraig th ampig rat at th rcivr. h jittr variac i ot chagd h ovrampig i appid, o th jittr rprt a argr fractio of th ampig priod for th ovrampd ytm For th ca of hit timig jittr both tchiqu rut i a iar rductio i jittr oi por a a fuctio of ovrampig rat. hu ovrampig giv a 3 db rductio i jittr oi por for vry doubig of ampig rat. Avrag jittr oi por a a fuctio of th ovrampig factor. hr i co agrmt bt thory ad imuatio. It a ao ho that i th prc of timig jittr, high frqucy ubcarrir cau mor ICI tha or frqucy ubcarrir, but that th rutig ICI i prad quay acro a ubcarrir. REFERENCES []. J. Armtrog, OFD for optica commuicatio, J. Lightav cho., vo. 7, o., pp. 89-4, Fb. 9. []. V. Syrjaa ad. Vaama, Jittr mitigatio i high-frqucy bad pa ampig OFD radio, i Proc. WCNC 9, pp. -6. [3]. K. N. aoj ad G. hiagaraja, h ffct of ampig jittr i OFD ytm, i Proc. IEEE It. Cof. Commu., vo. 3, pp. 6-65, ay 3. [4]. U. Ouo, Y. Li, ad A. Sami, Effct of timig jittr o OFD bad UWB ytm, IEEE J. S. Ara Commu., vo. 4, pp ,6. [5]. L. Yag, P. Fitzpatric, ad J. Armtrog, h Effct of timig jittr o high-pd OFD ytm, i Proc. AuCW 9, pp. -6. [6]. L. Suma,. Watari, ad K. A. I. Hao, A -bit -S/ COS para pipi A/D covrtr, IEEE J. Soid-Stat Circuit,vo. 36, pp ,.