æ Ø ã Ý ä â å Channl Tracking in Wirlss OFDM Systms Hiko Schmidt, Volkr Kühn, and Karl-Dirk Kammyr Univrsity of Brmn, FB-1, PO Box 33 04 40, D-28334 Brmn, Grmany, -mail: schmidtcommuni-brmnd and Rinhard Rückrim and Stfan Fchtl Infinon Tchnologis AG, PO Box 80 09 49, D-81609 Munich, Grmany -mail: rinhardruckriminfinoncom Abstract In th prsntd papr, th principl of frquncy domain channl stimation for wirlss OFDM systms will b shown A wll known nois rduction tchniqu will b adaptd to HIPERLAN/2 and IEEE80211a standards, and its positiv ffcts will b dmonstratd by simulation rsults Channl tracking has not bn considrd by th WLAN standards namd abov, although it is wll known that tim-variant indoor radio channls can chang thir charactristics within on PH burst This papr prsnts som tchniqus for dcision dirctd channl tracking, applicabl in wirlss OFDM systms Kywords HIPERLAN, IEEE80211, OFDM, channl stimation, channl tracking, nois rduction I INTRODUCTION Th Amrican IEEE80211a standard and th Europan quivalnt HIPERLAN/2 ar two similar concpts for broadband wirlss LANs (WLAN) in th 5 GHz band Both standards ar basd on th multicarrir modulation tchniqu OFDM (orthogonal frquncy division multiplxing) combind with convolutional channl coding Th basband modulation schms of both standards ar vry similar, which simplifis implmntation considrably Challangs and difficultis considrd in this papr rgard both systms Excpt for slight diffrncs in signal mapping, most discrpancis btwn th standards rgard th highr protocol layrs Sction II prsnts som fundamntals of OFDM and th WLAN standards Hr w focus on th basband modulation in th PH layr and xplain parts of th PH burst structur rlvant to channl stimation Sction III dscribs a frquncy domain channl stimator Assuming channl impuls rsponss bing limitd in tim, corrlations btwn adjacnt subcarrirs can rduc th nois influnc on th stimatd transfr function Hr, a nw mthod for computing th corrlations is shown In cas of tim variant channl cofficints, a dcision dirctd channl tracking algorithm for r-stimating th channl cofficints is prsntd in sction IV Th rmodulation of th dtctd data can b don with or without xploiting channl dcoding as dmonstratd in sction IV II WIRELESS LAN OFDM SSTEMS As mntiond in th introduction, th nw WLAN standards HIPERLAN/2 and IEEE80211a ar basd on th multi-carrir (MC) tchniqu OFDM [1], [2], [3] Primarily, OFDM can b dscribd as an analog discrt multiton tchniqu with rctangular (orthogonal) puls shaping filtrs for ach subcarrir A guard intrval protcts th rcivd data against intr-symbol- (ISI) or intr-carririntrfrnc (ICI) Practically, discrt transmittr and rcivr filtr banks ar usd and computd by vry fficint FFT algorithms Concrning th considrd standards, th total OFDM sym- bol duration is s including a s guard intrval and th s cor symbol Th activ subcarrirs ar placd symmtrically (no DC!" componnt) With a subcarrir distanc of khz th total occupid &%' OFDM bandwidth is about 165 MHz Using an $# point FFT algorithm (ovrsampling rat ( )*+*,' ), th rquird tim domain sampl rat is xactly MHz ƒ8 { $ =ˆQ 4Š ]Œ Q ª«± ² ³ µ Ÿ 4 6+787:9 ;=<?> A BCEDF G?>+H Z []\*^UZ _E`Qa=\Q \ `QbScQdUdS\XU[]fU^U\X OQPSRQTUTSVXW Ž SX QS U X 4 Sš Uœ+ ž S UŽ Eš K LEM?N Fig 1 Tim discrt OFDM systm wx8y{z$ =}~X}X S}Q gih l jk ¾  ÀÁ Ô Õ Ö Ã Ä min q op Ç ÅÆ Ù Ú ÛÜ È É ÊË r s v tu Ì Þ ß àá I8I:J ¹º»4¼ ½ -/ 243 5 01 ÍÎ Ñ4Ò Ó ÏÐ Du to ISI- and ICI-fr rcivd symbols, th channl influnc can b rducd to on complx Rayligh fading factor (channl cofficint) on ach subcarrir ç è{iêxëuì îí iêëïìñòè{ êëïì] whr è êëïì dnots th data symbol of th ô õxö subcarrir and th ë õxö OFDM symbol (ô : frquncy indx, ë : tim indx) Assuming a slow fading channl, th transfr function is narly constant for th duration of on OFDM symbol In cas of a tim invariant channl transfr function, (1)
d Z ø ç ç [ ÿ Ò ô Ö z Ž { è Ëç í í iêxëïì dscribs th blonging cofficints Sinc all subcarrirs ar orthogonal, OFDM nds only on qualizr cofficint for ach subcarrir, according to figur 1 è êxëuì úù êëïìñ èç êxëuìû ù êxëuì ü*íý êxëuì normally computd by This zro forcing solution is viabl if th channl stat information will b considrd in th Vitrbi channl dcodr In combination with variabl cod rats (puncturd convolutional cods) and diffrnt symbol mapping schms (BPSK 64-QAM), th nw WLAN standards provid data rats from 6 up to 54 Mbit/s In th PH layr of HIPERLAN/2 and IEEE80211a, diffrnt burst typs with qual training symbols ar dfind Th prambl contains a synchronisation squnc of 8 s (xcpt th downlink è{þ êëïì burst) followd by 2 idntical training symbols (ach 32 s) and protctd by on long guard intrval Th payload contains usr data packts of 432 bit/packt Figur 2 shows an xampl PH burst (27 Mbit/s mod) Each data OFDM symbol consists of 48 data and 4 pilot carrirs Th pilot carrirs can b usd for fin frquncy tuning =>?BAC4DE+? )+*-,/(01 0243657489;:<3!"$#&%!'( \]^_]`]Ba bc ^ (2) W X F4GIHKJMLON6P;Q4RKS$T<N U V Fig 2 Tim domain burst structur (27 Mbit/s mod) III CHANNEL ESTIMATION Th prsntd standards includ cohrnt data dmodulation so that th channl has to b stimatd As mntiond in sction II, OFDM nds only on cofficint pr subcarrir With th givn burst structur, th systm prmits an stimation using two subcarrirs cofficints at th bginning of ach burst, th division in (3) can b practically r- Assuming tim invariant channls, th avragd cofficints ar í ç êëïì è{þ êëïì è þ With d è{þ êëïì ê èþ ìb placd by a multiplication with ç í {ê ç í ê ì!f ç í ê ì4ì Figur 3 shows th block diagram of th channl stimator In cas of AWGN th stimatd cofficints ar givn by th íý tru channl transfr cofficints and additiv nois hgji í,í kf gji (3) (4) (5) l$mn o(prq ˆ / / 1 ª -«( /«< $ ± 6²³ È1É B} ~ 1 6ƒ1 uv+w s uv+x œž uv(y t œžÿ tt 6 1 ŠŒ / / œ š šš v(y v+x œ v+w œžÿ œž µ1 $ ¹ º+»½¼¾ž ¾( K ÁÀ-ÂÃÅÄÆ ÇÀ Fig 3 Initial Channl stimation in frquncy domain whr th avragd powr of hgji is 3 db blow th data symbol distortion (du to avraging ovr 2 pilot symbols) As simulation rsults will show, th prsntd channl stimation mthod rsults in an Ê loss of about 2 db compard to simulations with prfctly known channls By xploiting th corrlations btwn adjacnt subcarrirs cofficints, th stimator nois in (5) can b rducd substantially Th so-calld nois rduction algorithm (NRA) is placd btwn IFFT and FFT as shown in figur 4 êëªì<írîïrîñò;ôõ+ì(ëê&ö (øªëï6ì õ(ù$úüû(ýmþ ÿ ÌÎÍ Ï Ó_ÔÔÕ ÐÐÑ Ø ÙÚBÛÜ ÝÞßÜ Þ-àáâ ã!ü Ø ÙäØ â(å-â Ø æà Fig 4 Nois rduction algorithm (NRA) In ordr to fulfill th condition of ISI and ICI fr dmodulation, th channl impuls rspons has to match th guard intrval In particular, th maximum channl dlay must not xcd th guard tim With th numbr of guard sampls (hr: 16), th channl impuls rspons vctor of on FFT block with lngth # satisfis ê ì, # Th stimatd channl impuls rspons can b computd by an invrs fourir transformation of th stimatd channl transfr function vctor with th IDFT matrix ê ] IDFT (6) (7) IDFT containing all twiddl factors ì # ù! #"$&% (*)' Th basic ida of nois rduction is th limitation of th impuls rspons according to ø ê ì ç ê ì + -, $# (8) (9)
t Aftr r-transformation into frquncy domain / IDFT021 (10) í ø th avragd nois powr in has bn rducd by th factor (not: if IDFT and DFT ar usd for nois rduction, th numbr of subcarrirs must b qual to th DFT lngth # Anothr possibility will b prsntd in th following txt) Th problm of this wll known tchniqu is th computation of th IDFT (7) and th DFT (10) in cas of incompltly stimatd channl transfr functions Som of th subcarrirs cannot b stimatd sinc thy ar not usd (guard band, DC componnt) In ordr to ovrcom ths -4 problms, w can split th vctor into subvctor, containing all known or assssabl cofficints and subvctor 65 with all unknown channl cofficints A similar split can also b don in tim domain 8 ç ê ì ç ê ì: E? ç ê 9 ì;: =< 8 ç ê ì:*ç ê f ì: E? 'ç ê ì;: $# whr contains th tru channl impuls rspons and?< by 7C7-4?<BA DCDGA 5 A whr th IDFT submatrics 7E7,, DC7, and DCD 3 (11) (12) includs zros (6) or pur nois Th IDFT can b computd (13) includ all # twiddl factors (8) in a rarrangd ordr Du to a switchd ranking within th frquncy domain vctor, th rows of 4 hav to b r-organizd in th sam way With quation (9),?< can b substitutd in ê < DC7 4 f DED 5 H I4 DCD ê DCD DED fgl D CMòìN 7 O PRQ DED S TGU VWV With a modifid psudo invrs KJ DCD DED 65 ì] M th unknown transfr factors can b computd by 65 XHKJ DED 4 (14) (15) (16) (17) KJ Z L [ DED from numrical instability, a small factor # has bn introducd Th complt computation of 7 is ]\ 7C7 ^ J DED F_ I4 whr M dscribs th idntity matrix In ordr to prvnt Considring (9) < ` and with th parts of th rsortd DFT matrix I4 65 A 7C7 DCD A <aa with *: transposd conjugat (18) (19) (20) (21) it is possibl to comput th nois rducd subcarrir cofficints 4 bc d\ 7C7 7C7 4&4 I4 ^ J DED _ 4= (22) 4&4 Th nois rduction matrix can b pr-computd offlin Thus, th nois rduction algorithm rquirs only on run-tim matrix multiplication (22) Figur 5 dpicts som simulation rsults of th 27 Mbit/s mod For Mont-Carlo simulations, a typical Rayligh fading mobil indoor channl modl with a dlay sprad 6f =100 ns has bn chosn As a rfrnc, th rsults with prfctly known channl cofficints ar givn, too i!jrs ikj n>r ikjcn=q ikjcn=p CE without NRA CE and NRA prfct ikjcn3o g h ikj i!l iwm i!g i!h uvwwx s Fig 5 Simulatd bit rror rats () with channl stimation (CE) and nois rduction algorithm (NRA) With raw channl stimation ovr 2 training symbols (CE without NRA), th y9z I{ loss is about 2 db, compard to prfctly known channls Aftr r-calculating th subcarrir cofficints by multiplying th nois rduction matrix (22), th y z { loss is rducd to 07 db For othr HIPER- LAN/2 or IEEE80211a mods, similar rsults hav bn obtaind IV CHANNEL TRACKING Th HIPERLAN/2 and IEEE80211a standards provid 2 training symbols in front of ach data burst and 4 pilot carrirs insid ach data symbol In cas of tim variant channl cofficints, th initial channl stimation suffics only for OFDM symbols nar th bginning of th burst Thrfor only 4 pilot carrirs ar not sufficint to supply channl tracking for a complt subcarrir cofficint st [7] In ordr to crat additional training symbols, rcivd and dcidd data can b r-modulatd to r-stimat th channl cofficints during data dmodulation, as it can b sn in figur 6 Th bst choic would b dcidd data fdback from th Vitrbi dcodr output, bcaus th bit rror rat () is much bttr than at th dcodr input Howvr cod trmination is only providd at th nd of ach
ù ÿ f Ô { ì # & = & c d Fš œžiÿk * d * ŽŽ ÑÓÒ ÁH Ã+Ä,Å õ öcø Õ?ÖW ~Ø Ù~Ú íêî íï íàñ3ò,ô Ð ÆÈÇÊÉGËÍÌÏÎ ä*å æêçêè#ëê ì úû þ ü;ûý ~ªE«* 2 ²±F³ ² 2µ ~}E^ ~ &ƒ> Û?ÜÞÝ ßàÛ2á â3ã Š*Œd 3 * dˆ E ¹*º2» ¼²½F¾ ²¹2À Fig 6 Block diagram of dcision dirctd channl tracking data burst Bfor cod trmination has bn rachd, a sufficintly saf data dcision will b at th xpns of som Vitrbi dcision dlay Figur 7 shows th simulatd bit rror rats subjctd to th dcoding dlay with diffrnt coding rats Th rsults of figur 7 ar summarizd in tabl I for all HIPERLAN/2 { mods In a worst cas scnario with, th Vitrbi dcodr nds a dlay of 100 dcodd bits With 1 OFDM symbol containing 36 data ë bits (9 Mbit/s mod), a maximum dcoding dlay of { complt OFDM symbols is rquird In ordr to obtain comparabl rsults, this dlay has bn usd for all mods Th othr fdback possibility is to us th non dcodd symbols î at th symbol dcodr output for r-modulation ) Figur 6 dmonstrats both options ( ë { " /*9 " / 287 " / 26 " / 25 " / 24!#"%$'&!)(*$"%+!),*$- " / & / - / + / " / /23 01/ /*/ "%& :';=<?> Fig 7 simulatd bit rror rats () of 27 Mbit/s mod vrsus dcoding dlay *ACBED (only AWGN) FG% HJILKiêë Mod z +z NMPO ig 6 1/2 24 Q 60 3 12 s 9 3/4 36 Q 110 3 12 s 12 1/2 48 Q 60 2 8 s 18 3/4 72 Q 110 2 8 s 27 9/16 108 Q 70 2 8 s 36 3/4 144 Q 110 1 4 s 54 3/4 216 Q 120 1 4 s Th first ë { TABLE I Estimatd dcoding dlay OFDM symbols ar dmodulatd by using th initial channl stimation Th dcidd data (bfor or aftr dcoding) must b r-modulatd Th dcision dlay is NCSLT J UWVX ç êëïì CZP[êXëUì modulatd by R Dividing by and applying th nois rduction algorithm will produc a nw channl stimation for th õxö OFDM symbol In ordr to ê\ ì ë rduc nois influnc, a first ordr loop filtr with paramtr ]2{ has bn introducd, as shown in figur 6 Finding an optimal loop paramtr ] { is a compromis btwn nois snsitivnss and tracking powr In ordr to simulat th nois influnc, a tim-invariant ò Raylighfading indoor channl modl (6f ns) has bn usd Figur 8 shows th simulatd vrsus ] { for both cass: dcidd data fdback bfor (uncodd) and aftr Vitrbi dcoding (codd) Th avragd nois powr is y ^ z { db In cas of ]2{, no tracking will b don and th must b idntical to that in figur 5 with NRA Of cours, with an incrasd ] {, th nois influnc on tracking basd on non-dcodd rfrnc symbols riss mor than for dcodd symbols With ]2{ (uncodd) and ]2{ (codd) a ngligibl loss can b obtaind For tracking powr simulations, a tim variant channl modl has bn usd, considring Jaks-distributd Dopplr-
} V } f_glk f_ gfj uncod fdback cod fdback %Š ˆ Š l no tracking ˆ =01, uncod ˆ =03, uncod ˆ =03, cod ˆ =05, cod PER f_gfi ŠFŒ f_gh a` b _a` c _a` d _a` f mn ŠFŽ Š ˆ Ša Š*Œ '? in m/s Fig 8 Simulatd bit s rror t%upv rats () of 27 Mbit/s mod vrsus loop paramtr oqp with r pxwzy{ db sprading drivd from mobil spd } ~ with wav lngth # g V (hr " ƒfƒ ò N m) (23) In figur 9 th simulatd packt rror rats (PER) of a HIPERLAN/2 systm (27 Mbit/s) in cas of high mobility is dpictd Th simulatd PH burst lngth is about 800 Without tracking, th PER bcoms vry high for mor than 3 m/s Applying channl tracking aftr xploiting Vitrbi dcoding, th systm functionality can b guarantd up to G% ú m/s V CONCLUSIONS In sction II, th PH layr of modrn wirlss LAN standards in 5 GHz band has bn prsntd Hr w focusd on OFDM fundamntals and th PH burst structur Th training symbol constllations of HIPERLAN/2 and IEEE80211a ar qual Sction III shows a frquncy domain basd channl stimation Th influnc of nois can b rducd by applying th nois rduction algorithm (NRA) It is basd on a tim limitd channl impuls rspons By prmutating th IDFT matrix, th run-tim costs of th NRA can b rducd to on matrix multiplication Th gain of about 13 db has bn vrifid by simulation rsults In cas of tim variant channl cofficints, channl tracking is ncssary Thus, a channl tracking schm, applicabl to HIPERLAN/2 and IEEE80211a, has bn prsntd in sction IV With Vitrbi dcoding placd insid th fdback loop, th channl stimation basd on r-codd and r-modulatd symbols yilds bttr rsults Although th Vitrbi dcodr nds a dcoding dlay, channl tracking with xploitation of channl dcoding prmits highr Dopplr frquncis and thus highr mobil spds This papr has shown an fficint mthod to stimat th subcarrir cofficints Furthrmor, th ncssity of channl tracking has bn dmonstratd and a practical solution has bn prsntd Fig 9 Simulatd packt s t%u v rror rats (PER) of 27 Mbit/s mod vrsus objct spd 1ACBED with r p wzy{ REFERENCES [1] ETSI HIPERLAN Typ 2 Functional Spcification Part 1 Physical PH Layr Tchnical Rport DTS/BRAN030003-1, ETSI EP BRAN, April, 2000 [2] IEEE Draft Supplmnt to STANDARD for Information Tchnology- Tlcommunications and information xchang btwn systms Local and mtropolitan ara ntworks Spcific Rquirmnts Part 11: Wirlss LAN Mdium Accss Control MAC and Physical Layr PH spcifications: High Spd Physical Layr in 5 GHz Band Tchnical Rport IEEE P80211a/D70, IEEE, 1999 [3] M Johnsson HiprLAN/2 - Th Broadband Radio Transmission Tchnology Oprating in th 5 GHz Band HiprLAN/2 Global Forum (wwwhiprlan2com), 1999 Vrsion 10 [4] J G Proakis Digital Communications McGraw-Hill, 3 dition, 1995 [5] K D Kammyr Nachrichtnübrtragung BGTubnr, Stuttgart, 2 dition, 1996 [6] H Myr, M Monclay, and S A Fchtl Digital Ccommunication Rcivrs John Wily, 1 dition, 1998 [7] M Fursängr, H Schmidt, and KD Kammyr An Itrativ Channl Estimation for a Hiprlan/2 OFDM Systm In Proc of 5 intrnational OFDM Workshop, Hamburg-Harburg, Grmany, Sptmbr 2000 [8] H Schmidt OFDM für di drahtlos Datnübrtragung innrhalb von Gbäudn PhD thsis, Univrsity of Brmn, Grmany, Arbitsbrich Nachrichtntchnik, Shakr Vrlag, April 2001 [9] R van N und R Prasad OFDM for Wirlss Multimdia Communications Artch Hous Publishrs, Boston, London, 2000