Using Nonlinear Filter for Adaptive Blind Channel Equalization

Transcription

1 HAMDRZA BAKHSH Dpt. o ctrca ad Coputr r Shahd Uvrsty Qo Hhway, Thra, RA Us oar Ftr or Adaptv Bd Cha quazato MOHAMMAD POOYA Dpt. o ctrca ad Coputr r Shahd Uvrsty Qo Hhway, Thra, RA Abstract: trsybo trrc S o th rado propaato throuh chas s a aor actor that ts th prorac o ob coucato systs ad ca b copsatd by quazato. O o th basc roups o quazrs s basd o ar aorths. ths papr, w propos th othr thod basd o Harst tr as a oar oryss bd quazr. W hav copard ths two thods by suato ad hav show that th attr thod rsuts hav bttr prorac copard to th orr os;.. th Harst tr troducs owr BR tha ar aorths, so as t a vab atratv to orr quazrs. For a thods studd ths papr, bd quazato s assud. At ast bd Harst quazr aayzd ordr to study ts covrc capabty ad ubasd proprty. Kywords: Bd quazato, Harst Ftr, ast Ma Squar, Zro Forc. troducto May systs sur ro trsybo trrc S; so, th quazato thods shoud b poyd to cobat ths ct. th cas o ar quazrs, two drt crtra ar usd or dtr th vaus o th quazr cocts. O crtro s basd o th pa dstorto at th output o th quazr, ay th zro orc aorths [], ad th othr o s basd o th zato o th a squar rror at th output o th quazr, ad as ast Ma Squar MS []. Ths two aorths ca b prord wthout tra squc whch rsuts bd quazato [, 3]. [4] Harst tr s usd as a oryss tr or at ad cha quazato but t ca ot b usd o at ad cha quazato. o at ad cha cha wth ory ratr tha o HDF quazr [4] s usd or quazato. W hav proposd us oar trs stad o ar os or bd cha quazato. partcuar, w hav usd Harst tr or adaptv bd cha quazato ad hav show that ths tr ca quaz cha wth ory ratr tha o o at ad cha, bdy wth th uch owr copty tha HDF. W hav suatd thr thods wth drt chas ad hav copard th wth rspct to bt rror rat BR. Th suato rsuts cor th astr covrc bd adaptv cas ad aso th bttr bt rror rat prorac o th proposd thod ovr th tradtoa ar quazato tchqus. Th papr s orazd as oows; w propos th adaptv bd quazato tchqu basd o Harst tr scto. Aaytca study o purposd thod show scto 3. scto 4, th suato rsuts ar prstd. ay th ast scto, so cocud rars ar prstd. Bd Harst Adaptv quazato Th boc dara o th proposd quazr s show F., whr s th d, BPSK trasttd data, s th cha pus rspos odd as tapd day s [] ad s th rcvd sa avaab at th rcvr. os at th put o th rcvr s dotd as v ad

2 assud to b Addtv Wht Gaussa os AWG.. Harst Ftr Rrr to F., th output o th Harst tr ˆ has th or o [3, 4]: ˆ or ˆ. Thr ar o day trs, sc w assu o ory or th tr. Th whts hav to b dtrd such that ths poyoa quazs th cha.. Th Harst Ftr as a Bd quazr W usd Harst tr as a cha quazr as show F.. Th quato ca b wrtt atr or as: ˆ ˆ ˆ or X G ˆ. Th output o th cha s: v. 3 Th quato 3 has thr parts; th rst part dcats S, th scod part s os ad th thrd part s dsrd sa. ordr to at S ad os, w shoud z MS by statstca Gradt thod. Th MS cost ucto s: J ˆ 4 Us quato, w hav: J. 5 ordr to z MS, th Gradt vctor shoud b st to zro: J 6 Us quato 6, w ca dtr cocts by th oow tratv quato: ε 7 whr, ε dcats th rror vctor ad s th stp sz. o-bd statos, w ca us tra squc stad o. But bd statos, w ca stat by: s. 8 3 Aaytca Study o Bd Harst quazr W ca td quato 7 to rprst th coct rspct to ta vau, or ths ar ths quato wrts as: ε 9 ε ε ε ε th ta vau s chos zro quato 9, th: ε ˆ ˆ For ar aout o, sa ca b approatd by pctato ad subsstd by 3, Î by so th rwrt as: put data assud to b d wth zro a ad data ar dpdd to os so th rst tr wrts as... w suppos strct statoary o ordr so s qua to th ot o ad ad to: 3 Th scod part o ca b rwrt as:

3 4 ar th covrc, th aouts o ar approaty costat ad aso ow stp ad by strct statoary 4 ca b wrtt as X 5 5 s cobd wth 3 th updat ru or Harst Coct s cacuatd by: 6 t s usu to wrt 6 as a atr or. U M 7 Ths quato s vary portat bcaus dscrb a dscrt stat-spac quato or Harst Coct updat. So covrcs o adaptv syst ad to stabty dscusso o stat-spac syst. Ths stat spac syst s stab ad oy a h suar vau o atr s ot cd o. [ ],, H da V V M ar a a, a < 8 othr to dscuss about stp sz ths prob th a suar o M dd as a th th stp sz ust b owr tha a. For d a usu boud or a cosdrs that a s owr tha th su o th suar vau o M or trac o M so 8 rwrt as:.!! a < M tr 9 Atr succssu covrc by ta vau cos to zro th v cocts bco zros ad Harst or as odd poyoa. Atr covrc th a o stato rror s cacuatd as:,!! So th stator s asyptotcay ubasd. Th rror varac aso ca b cacuatd tratvy as oow: th rst tap o th cha pus rspos s ow, th bco spr by us, t.. 4 Suato Rsuts For vauato o th BR prorac o th rcvr dscussd ths papr, w suatd th quvat bas bad syst show F.. As a purpos o coparso, w hav do th suato procss or th thr bd quazatos

4 studd ths papr ad hav copard th rsuts or drt chas. For th suato, w rat bt stra o uory ro -,. F. shows that th Harst quazr hav bttr BR prorac copard to two othr ar thods th practca ro o b /. W suatd drt ordrs o Harst tr ad obsrvd that th Harst tr o ordr has th bst prorac. F. 3 shows th covrc proprty o Harst quazr ad MMS quazr vrsus ubr o tratos. F. 4 shows BR o thr thods vrsus b / or aothr cha wth dp us ts pus rspos s shows F. 5. Th suato rsuts show that th two ar thods ca ot quaz th cha appropraty; howvr, th Harst quazr has do t wth a outstad prorac. 5 Cocuso ths papr w hav troducd a w approach or bd cha quazato, us Harst tr as quazr at th rcvr. Rard BR prorac o th thr studd thods, w obsrv that Harst tr has th bst prorac copard to othr studd ar quazato thods. W ca cocud that Harst tr as a oar tr ca quaz o at chas or propry tha ar quazrs du to th oar atur o th optu stato. t has aso b obsrvd that by us th proposd thod, th dccy o Harst quazrs ot hav ory ca b sovd wth th uch owr copty tha HDF [4]. Coputrs ad Sa Procss, Vo.,Au., pp [4] Y. Mar, H. Adavar, Harst Dcso Fdbac quazato HDF as a w quazr o GSM Rcvrs, tratoa Syposu o Sa Procss ad ts Appcatos, Vo., Juy 3, pp [5] Y. Mar, A. Mo, H. brahzad, H. Sa, Us Harst Ftr or Mody th Dcso Fucto o Dcso Fdbac quazr, tratoa Corc o orato ad Coucato Tchooy, Apr 4, pp F. : Boc dara o th syst wth Harst typ quazr Rrcs: [] J. G. Proas, Dta Coucatos, 4th dto, w Yor, McGraw H,. [] M. Schtz, Th Votrra ad Wr Thors o oar Systs, w Yor, Joh Wy, 98. [3] X.. Frado, A. B. Ssay, A Harst Typ quazr or th Wr Typ Fbr Wrss Cha, Corc o Coucatos, F. : Bt rror rat vrsus b / db or thr thods o Harst tr o ordr, Zro orc ad MS. 3 Cha: z.89.33z.z.4556z

5 rror Harst quazr MMS quazr Matud db orazd Frqucy π rad/sap ubr o trato Phas drs orazd Frqucy π rad/sap F. 3: Covrc proprty 3 Cha: z.78.8z.8z.693z F. 5: Matud ad Phas o th cha wth pus rspos: 3 z.78.8z.8z.693z F. 4: Bt rror rat vrsus b / db or thr thods o Harst tr o ordr, Zro orc ad MS. 3 Cha: z.78.8z.8z.693z