Michael Bank, Y. Barish, S. Tapuchi, Miriam Bank, B. Hill, M. Haridim

Transcription

1 Phas Divrsity Mthod in Mobil Counication Systs Michal Ban Y. Barish S. Tapuchi Miria Ban B. Hill M. Haridi T Abstract Phas divrsity tchniqus ar usd in any counication systs including PAL TV syst FBS thod and th Alaouty algorith for MIMO. Phas divrsity algoriths hav provd ffctiv in itigating phas distortion in wirlss channls. In this articl w prsnt a nw thod of phas divrsity procssing that is basd on phas arithtical suing. Kywords FBS MIMO Dopplr OFDMA. PALTV Phas suing I. ITRODUCTIO HE Divrsity is a wll-nown tchniqu for iproving th prforanc and rliability of wirlss counications ovr fading channls. In this approach signals ar transittd through ultipl channls ach having an indpndnt fading and cohrntly cobin th at th rcivr. Diffrnt typs of divrsity (frquncy ti spac phas) ar widly usd today in odrn counication systs. Gnrally it is nown that rpating th inforation bits is an ffctiv ans for rducing th rror rat. But divrsity is not a sipl rpating of th signal. In this cas signals ar transittd with diffrnt paratrs and/or diffrnt conditions. For xapl in cas of frquncy divrsity th signal is transittd twic or or but in diffrnt frquncy bands. Th dsird signals ar sud using an arithtical thod whras nois coponnts ar sud using an RMS thod. As a rsult th signal to nois ratio is iprovd (siilar to sprad spctru systs). In th sa annr in spac divrsity inforation signals ar sud using an arithtical thod. Howvr indpndnt fading is only partially copnsatd. Signal to nois ratio ay b iprovd by ans of patch divrsity and Ra rcivr whr th lattr is synchronizd with ach patch sparatly. In this thod as in abov ntiond thods th rcivr pics up so idntical signals with diffrnt nois lvls.\ Manuscript rcivd Octobr 8 20: Rvisd vrsion rcivd March Authors ar Michal Ban with th Jrusal Collg of Tchnology JCT Isral (ail: banichal@gail.co) Yonatan Barish with Holon Institut of Tchnology (HIT) Isral (-ail: yonatan.barish@gail.co) Saad Tapuchi with SCE - Sai Shaoon Collg of Enginring Br Shva (-ail: tapuchi@sc.ac.il) Miria Ban with th Jrusal Collg of Enginring and Institut of Mathatics Hbrw Univrsity of Jrusal (-ail: iriab@ath.hui.ac.il) Boris Hill with ss TSG (Tchnologis and Systs Group) (ail:boris.hill@gail.co)\\ Motti Haridi with Holon Institut of Tchnology (HIT) Isral (-ail: haridi@hit.ac.il) This papr is ddicatd to phas divrsity thods for xapl in PAL TV OFDMA and MIMO systs [ - 7]. II. PHASE DIVERSITY I PAL TV SYSTEM Th influnc of th channl ipairnts including Dopplr Effcts [3 5] can b significantly rducd by transitting ach sybol twic; first th original sybol and thn its phas-conugat sybol. In th rcivr th phasconugat sybol is first rturnd to its original phas and thn addd to th original signal. In this annr any phas distortion introducd by th channl in canclld out. This phas divrsity thod was first proposd by Waltr Bruch for PAL TV systs [6]. Fig. shows th phas shift cancllation in PAL TV. Lt s assu that th transittd signal has a phas and th channl shifts th signal phas by an unnown aount of Δ such that th rcivd signal's phas is + Δ. If as ntiond abov w transit th signal twic first with and thn with th rcivd phass will b + Δ and + Δ rspctivly. Th rcivr rvrss th phas of th scond signal such that upon adding th phass of th two signals th phas shift Δ cancls out. Fig.- Phas shift copnsation in PAL TV syst In Mthod significantly iprovd th quality of TV signals rcption. This phas divrsity thod has bn applid and in othr systs too although not always hav a rfrnc to th PAL TV. This is phas divrsity thod. Th phas is transitting two tis with opposit valu (+ and -). This allows iproving rciving quality. 64

2 III. THE EFFECT OF DOPPLER SHIFT O THE OFDMA SIGALS In a ulti-path channl th duration of a rcivd sybol is frquncy changs by th sa factor d th nubr of carrir cycls in ach sybol dos not chang rgardlss of how fast th Transittrs (Tx) or Rcivrs ( Rx) ov. So in cas of Dopplr Shift th frquncy f and sybol ti T ar varid by a factor of d givn by [3] V d cos () c whr V is th oving obct vlocity c is th light vlocity and φ is th angl btwn th dirctions of signal propagation and th oving obcts.ot that undr ths circustancs th orthogonal condition prvails: [( f f ) ] [ T / ] i i d In ral situations howvr th orthogonal proprty of th subcarrirs will b violatd to so xtnt. Sinc th rcivr s synchronization syst cannot ract instantly to changs in th sybol priod or in th FFT paratrs w ay assu that th Rx sybol ti st by th sybol synchronization syst rains at a fixd valu. A Dopplr shift of Δ introducd an a phas shift of Δt in th rcivd signal and an additional phas shift du to incopatibility btwn carrir frquncis and th spctral coponnts aftr FFT Furthr influncs includ ICI (Intr-carrir intrfrncs) du to partial loss of th orthogonality changs of th pilot signals paratrs and a ti dlay (or forstalling) d subct to changs du to th variations in th lngth of th signal propagation path. Th chang of th signal duration will b dnotd hraftr by factor d. Howvr sinc th btwn adacnt sybols du to incopatibility btwn of th rcivd sybol duration and Rx cloc synchronization syst [3]. Fig. 2 dpicts an xapl of a typical HAP syst using th OFDMA tchnology syst [9] with sybol duration 0.s frquncy diffrnc btwn carrirs (F) 0Hz cntral frquncy in th 2GHz L band rang and fro 5.85 to GHz allocatd by th ITU for th futur HAPS. Ths highr frquncy bands ar rquird spcially for broadband obil radio vhicls at spd of up to 300 /h and vn or for aircrafts. Th angl shift chang as function of th distanc btwn th HAP and th vhicl.? Using quation () th Dopplr shift is stiatd as 2.8 Hz or 30% of F. It should b notd that also th rflctd signals undrgo a Dopplr shift. To itigat th ICE ffcts of a randoly changing Dopplr frquncy shift OFDMA uss pilot signals which lads to a significant incras in powr and syst rdundancy [89]. Th HAP systs on th othr hand ar charactrizd by th favorabl Rician distribution as th highr altitud and th rsulting transission angls produc a lin of sight. This lads to a lowr lvl of fading and Dopplr ffcts. In addition th highr opration rangs of a fw hundrd rsults in a significant rduction of hand ovr stps. For siilar scnarios HAPS will b or advantagous than Satllits du to thir significantly lss disprsion losss and lowr cost. Fig. 2- Scnario of th radio counication lin btwn HAP and a obil high spd train 65

3 W now procd with th athatical dscription of th OFDMA signal variations du to Dopplr shift. Th discrt x is givn by Fourir transfor (DFT) of 0 0 x 2 i 0... (2) and th invrs discrt Fourir transfor is givn by 2 i 0... (3). 0 x Hr x 0... ar sapls in ti doain and 0... ar spctral T 2 coponnts. Dfining: t Eq.s (2) T and (3) can b rwrittn as it ( ) xt it x x( t ) In gnral (4). (5) is a coplx nubr whos absolut valu and angl ar th aplitud and phas of th th frquncy coponnt. Sinc 0 DFT is sytric i.. th coplx conugat of x is a ral signal its * (whr ). * dnots As statd abov th Dopplr shift lads to spctru variations [8 0]. Du to th Dopplr frquncy shifts th frquncy of ach ~ coponnt is shiftd to 2 T whr and dnots th rlativ shift of th th coponnt. In th ti doain th nw signal is x x( t ) 0 0 i 2 i 0 2 i 0 ot that sinc 0 t i t (6) ~ x is a ral signal i... Th spctru of th nw signal is 0 x 2i 2 2i i i i n i 0 0 Thrfor ~ a( ) (7) 0 whr a 2 i ( ) (8) 0 In othr words w can obtain th nw spctru vctor ~ of lngth by ultiplying th atrix a by th original spctru vctor of lngth. Matrix lnt a ( ) shows how th original th spctral coponnt affcts th nw th spctral coponnt. Th atrix lnts can b coputd using Eq. (8). If 0 thn 66

4 a 0) 0 ( (9.). For sall 0 0 for a q q ( 0 q q ( ) 2 i ( ) a q ) using w obtain 2 i 0 i2 2 i i2 2 i i2 2 i i2 2 i 0 (9.2) is a x atrix whos ntris ar coplx nubrs dpnding on 0. If 0 for all 0... thn (9.) iplis that ( ) a 0 ~ is th idntity x atrix and in this cas for all In othr words if thr ar no frquncy shifts thn th spctru is not changd as xpctd [8]. Th rlation a iplis a * ( ) ( ). ot that th spctral coponnts affctd by th Dopplr ffct can b coputd by Eq.s (7) (8). Rarably ths nurical siulation and calculations do not rquir FFT siz incrasing. W bliv that this can b a significant contribution to siulation dsign. IV. FBS METHOD Th FBS thod is basd on a cobination of th PAL phas copnsation thod with th Walsh functions [3]. Walsh functions ar orthogonal squncs. As an xapl Tabl shows th fourth ordr Walsh function (Walsh Hadaard Matrix - WHM). Tabl - Fourth ordr WHM WHM is usd in CDMA systs for transitting diffrnt signals ovr th sa frquncy band. W'll illustrat th opration of th FBS thod using a sipl xapl of an OFDMA signal with MPSK odulation. W ta four subcarrirs with phass (s Fig. 3) Fig. 3 Th spctru of OFDMA with four carrirs According to th FBS thod ach signal.g. th signal with phas is transittd four tis on all four subcarrirs whr th phass of th signals ar odifid according to th WHM of Tabl. Fig. 4 shows th phass of th transittd signal. Fig. 4- FBS with four carrir spctru 67

5 For transitting signals on carrirs th FBS signals ar: s ( ) l FBS El 0 [2f t( ) Wl (0) ( )] whr E l - coponnt agnitud l = 0 - or Walsh- Hadaard atrix lins θ l - initial phas chosn for a crtain signal. For xapl it is ithr 45 0 or othr β l - inforation sybol of th l th FBS signal (BPSK or QPSK rprsntation) f = f 0 +f - FBS carrir frquncis = 0 - or Walsh-Hadaard atrix coluns W l - squnc of phass of th l th FBS carrir pattrn. To rciv on of ths signals for xapl signal nubr 2 th following algorith ust b iplntd: th S 2 rcivr rcivs all signals togthr as FFT obtains four spctral coponnts (aplituds and phass) changs th phas signs of coponnts 3 and 4 (corrsponding to th third signal. Th ain advantag of th FBS is its ability to copnsat fast phas changs in fading channls and Dopplr shift influnc without using any pilot signals [3 4]. V. ALAMOUTI MIMO ALGORITHM MIMO systs usually rfr to a patch divrsity syst. It ths systs th signals on both th transitting and th rciving antnnas ar cobind in such a way that th probability of dp fading bcos sallr but not zro. In th cas of a 22 MIMO syst for xapl such situation xists if th two transittd signals hav th sa aplituds and opposit phass. l l scond row of th Walsh-Hadaard atrix in Tabl.). Th rsult will b qual to th phas su dividd by four. Th phas su of th othr 3 signals should b qual to zro W calculat arithtical (not vctor) su of all signals on ach carrir and us aplitud corrsponding to: Fig. 6 illustrats th ain advantag of using th FBS- thod. Fig. 5- FBS signal aftr phas changing for rciving th Th wll-nown Alaouti algorith allows liinating ths cass by transitting ach sybol twic naly th original signal and its phas conugat [7]. Actually this algorith is a ind of phas divrsity sch. In Alaouti algorith th sybol and its phas conugat ar transittd. For xapl signals S0 and S ar transittd on two diffrnt antnnas A0 and A during two tact s. A0 transits S0 and A transits S during first th tact ( s Fig. 6). During th scond tact A0 transits S* and A transits S0*. Thn A0 transits S3 and A transits S4 during th 3rd tact. During th 4th tact A0 transits S3* and A transits S4* (s Fig. 7) 68

6 Fig. 6. th Alaouti algorith VI. ARITHMETICAL PHASE PROCESSIG I PHASE DIVERSITY SYSTEM In this sction w'll show th arithtical phas procssing by its iplntation in th cas of th FBS syst. As shown in Fig. 3 ach data phas is transittd on svral carrirs as drivd fro th Walsh atrix dinsion. Th FBS thod is basd on arithtical su of th data phass ultiplxd by Walsh cod bfor OFDM odulation. Th ain challng during th rsarch was to find a solution for a phas that xcds rang. Th first solution that was tstd usd aplitud changing in ordr to "ar" th liits of th phas for xapl: Fig. 7- Signals S aftr changing polarity and phas () In th Alaouti sch th rcivr rcivs th su of two signals propagating in diffrnt paths. It is possibl to show that vn in cas that th rcivd signals hav opposit phass; th dcodr can xtract th corrct signal. That is w can assu that th Alaouti algorith is anothr xapl of th us of phas divrsity. - is th ral transittd aplitud -is an indx non by th rcivr for any spcific phas cycl. - th corrspondd phas valu insid th rang of 69

7 BER BER BER 0 0 OFDM&FBS without Dopplr OFDM-QPSK FBS-QPSK-idal FBS-QPSK OFDM&FBS without Dopplr OFDM FBS Eb/o tru (db) Fig. 8- QPSK in OFDM & FBS Fig. 8 shows th FBS and OFDM prforanc in an AWG channl without Dopplr ffcts. Th blac lin rfrs to FBS with no probl of phas xcding; this can b achivd only in siulation that controls th transittd data. Th grn lin is FBS prforanc with aplitud changing. Th FBS-Idal prforanc givs good potntial for th nw thod but it is wll shown that th us of aplitud changing is not rlvant in tr of E B / 0. This thod is problatic bcaus aplitud idntification is snsitiv to nois and it crats nw probls of frquncy disordrs. In ordr not to xcd th phas rang of during th arithtical procdur w shall us highr ordrs of MPSK odulation and iplnt only part of th phass for data coding. Using this high ordr odulation prvnts phas ovrflow. Obviously th disadvantag of this thod is lowr fficincy in trs of BER vs. E b / 0 prforanc. Th xapl copars th OFDM standard thod using Pilot Signals and FBS thod without Pilot signals. Th Matlab siulation includs AWG channl and Dopplr Effcts. Th siulation iplnts 4 OFDM carrirs. Th OFDM is basd on QPSK odulation whras th FBS syst uss 6PSK odulation. For iplnting 4 carrirs in FBS only 4 phass ar usd during odulation: Eb/o (db) Fig. 9- FBS prforanc copard to OFDM Fig.0 shows th FBS and OFDM prforanc in an AWG channl including Dopplr ffcts. Th Dopplr-% paratr rfrs to frquncy chang that is proportional to th frquncy gap btwn two OFDM subcarrirs. It can b sn that th prforanc of th FBS thod is alost indpndnt on th Dopplr intrfrnc whil th OFDM prforanc is significantly dgradd OFDM&FBSI with Dopplr OFDM-dop=% OFDM-dop=3% OFDM-dop=5.5% FBS-dop=% FBS-dop=3% FBS-dop=5.5% Fig.0 shows th FBS prforanc copard to OFDM in th absnc of Dopplr ffcts. Th FBS syst in this cas nds 5-6dB or powr in ordr to aintain th OFDM prforanc. This FBS disadvantag is xpctd sinc 6PSK nds or powr in ordr to obtain th QPSK prforanc Eb/o (db) Fig. 0- FBS prforanc copard to OFDM in a Dopplr channl Th FBS signal without Pilot signal has a bnfit in pa to avrag ratio. OFDM 2. EBS_QPSK 2.4 FBS_6PSK ~.5 70

8 Fig. 0 and pa to avrag ratio shows th coparison btwn FBS and OFDM. It is wll shown that FBS prforanc is vry good in that cas. Th signal without Pilot Signal utilizs both th bandwidth ant powr or fficintly. VII. COCLUSIO Th currnt cllular syst ust oprat in a channl with vry difficult options. This is du to high frquncis a larg nubr of rflctd signals and traffic at high spd. Th solution of ths probls can hlp phas divrsity thod including th FBS syst and Alaouti algorith. In ths cass it ay b applid th phas arithtic suation thod proposd hr. An iportant consqunc of this thod is th possibility of unwantd phas shift copnsation in OFDM channl without using Pilot Signals. Dopplr Effct influnc is violating ortogonality condition. In this cas pilot signals ar a aor caus of incrasing th nubr of rrors (BER). Rfrnc. OFDM for Wirlss Counication Systs by R Prasad British Library Cataloguing in Publication Data Th principls of OFDM RF signal procssing by Louis Liwin and Michal Pugl RF signal procssing January Dopplr Effct liiting valus in OFDM cllular syst by Miria Ban Michal Ban and Boris Hill Th IUP Journal of Tlcounication (IJTC005) May 200 (7 3) 4. Miria Ban Michal Ban Boris Hill Uri Mahlab: "OFDMA Cllular Systs Pilot Signals and Dopplr Effct" IEEE Counications Lttrs Tiun Wang Proais J.G. Masry E. Zidlr Jas R.: "Prforanc dgradation of OFDM systs du to Dopplr sprading" IEEE TRASACTIOS O WIRELESS COMMUICATIOS VOL. 5 O. 6 JUE Townsnd B. PAL Color Tlvision Cabridg Univrsity Prss Alaouti S. M. A sipl transit divrsity tchniqu for wirlss counications Slctd Aras in Counications IEEE Journal6(8): D. Grac C. Spillard T. C. Tozr High Altitud Platfor Rsourc Managnt Stratgis with Iprovd Connction Adission Control IEEE Wirlss Prsonal Mobil Confrnc Octobr pp. 9. T.C. Tozr D.Grac High altitud platfors for wirlss counication Elctronics & counication nginring ournal. Jun200 pp (27-37). 7