Receiver Architectures for FMT Broadband Wireless Systems

Transcription

1 Rcivr Architcturs for FMT Broadband Wirlss Systms Nvio Bnvnuto, Stfano Tomasin and Luciano Tomba Dipartimnto di Elttronica Informatica, Univrsity of Padova, via Gradnigo 6/A, I-3131 Padova, Italy Abstract Orthogonal Fruncy Division Multipling (OFDM) and in particular Discrt Multiton (DMT) modulation has bn proposd for th physical layr of widband wirlss local ara ntworks As an altrnativ, Filtrd Multiton (FMT) modulation can b also considrd, sinc it hibits significantly lowr spctral ovrlapping btwn adacnt subchannls, so providing highr transmission fficincy than DMT In this contribution, w invstigat th possibl advantags of FMT ovr DMT modulation for broadband wirlss applications in vry disprsiv channls and, in particular, w prsnt som simpl and ffctiv ualization algorithms 1 Introduction In this papr w considr multicarrir (MC) systms whr th intrpolating filtrs ar fruncy shifts of a givn prototyp filtr and th spacing btwn adacnt subcarrirs is th sam for all subcarrirs In fact, only in this cas th systm may b fficintly implmntd by mans of a (invrs) fast Fourir transform ((I)FFT) and a ntwork of polyphas filtrs [1, ] Morovr, w rstrict our analysis to two cass: i) DMT, whr th prototyp filtr has an idal rctangular tim-domain amplitud charactristic, and ii) FMT, whr th prototyp filtr has a narly rctangular fruncy domain amplitud charactristic Th scond choic implis invitabl intrsymbol intrfrnc (ISI) at th rcivr, whil intrcarrir intrfrnc (ICI) btwn subchannls is almost ngligibl whn an appropriat dsign of th prototyp filtr is carrid out Anothr possibl choic of th prototyp filtr is th suar-root Nyuist shap [3] In this cas, ICI is liminatd by incrasing th spacing btwn adacnt subcarrirs, at th pns of a lowr bandwidth fficincy Th pculiarity of DMT systms is that ualization of disprsiv channls is prformd simply by multiplying th signal at th output of ach subchannl by a cofficint that is rlatd to th channl fruncy rspons Howvr, this simpl schm works only if rdundancy, in trms of a prfi 1 of suitabl lngth [4], is insrtd in th transmittd signal, which, on th othr hand, lowrs th systm s spctral fficincy For this rason FMT has bn considrd and som simpl ualization schms for wirlss applications ar invstigatd This papr is organizd as follows In Sction w brifly outlin th systm modl In Sction 3 w invstigat som possibl ualization mthods for FMT systms and lastly in Sction 4 som prformanc comparisons ar prsntd Systm Modl W considr a multicarrir schm whr data signals,,,, with symbol rat! #", ar multipld in fruncy by using a bank of bandpass $!%'& finit impuls rspons (FIR) intrpolating filtrs )( +*,-, *, to produc th transmittd signal / +1, 134, at tim 1"768917: ; In particular th critically sampld filtr bank modulation [1, ] is dscribd; hnc th subcarrir spacing is ual $=& to! #" At th rcivr, a bank of FIR dcimation filtrs, >(?*,-, slcts $!%'& th information )( $@& for ach subchannl W assum that +*,- and )( +*,- ar non-zro only for *ACBED3F 3 Hr th transmit and rciv filtrs ar, rspctivly, th fruncy shift of two prototyp filtrs $#%?*,- and $?*,-, namly % & )(?*,GIHJLKCMON PEQ % +*,7 & >(?*,RSHJLKCMON PEQ?*,T (1) 1 Traditionally in wirlss applications, DMT with a cyclic prfi, is dnotd as orthogonal fruncy division multipling (OFDM) Notation: signals ar indicatd with lowrcas lttrs, whil thir Fourir transforms ar indicatd with th corrsponding upprcas lttrs UWV X Y, Z and [ dnot pctation, compl conugat and transposition, rspctivly; \ is th st of intgr numbrs and ]R^A_ Òa 3 Without loss of gnrality, w assum that bgc is an intgr multipl of d

2 f r ~ } ¼ k rk k fk n o p gh i u l l m v w gh i n o p t gh i s gh i t gh i s gh i { z y t g i t g i s g i y z { } } } ƒ t v w gh i s v w gh i n o p v w gh i l l m n o p gh i Figur 1 Efficint implmntation by IFFT and FFT of a MC systm basd on a uniform filtr bank Morovr, th prototyp rciv filtr is matchd to th transmit on, i +*,G %@ˆ?B D OŠ*, Fig 1 shows th fficint implmntation by IFFT and FFT of a MC systm $ $#%Œ basd on a uniform filtr bank, whr +A- and? -, 1)Ž, Ž CB S, ar th polyphas componnts $#% $#% of?*,- $ and?*,-, rspctivly Th choic of?*,- dtrmins th particular typ of multicarrir systm; in particular, whn it is an idal rctangular $#% puls th systm is calld DMT [4] Instad, whn?*,- is dsignd to minimiz th ovrlap btwn th fruncy rsponss of two adacnt subchannls, th corrsponding systm is calld FMT [1] In this systm ngligibl ICI is prsnt at th rcivr, whatvr th transmission channl is; howvr, ISI is always prsnt and an ualizr is ndd at th rcivr W dnot by $ +1- th uivalnt discrt-tim channl impuls rspons which is th sampld vrsion of th composd channl givn by th cascad of thr filtrs: th digital-to-analog (D/A) convrtr, th analog basband uivalnt radio channl and th analog-to-digital (A/D) convrtr Th D/A and A/D convrtrs ar dsignd to approimat an idal suar-root raisd cosin shap with Nyuist fruncy # #"'6 Th channl modl w hav usd for simulation is basd on th masurmnts mad for th widband local ara systm dnotd Wind-Fl [] Ths masurmnts provid a charactrization of th indoor radio channl at 17 GHz Two scnario ar considrd: a no lin of sight scnario, with a man š!a/ dlay sprad œ ž ns and a lin of sight scnario, with Ÿ ns Fading statistics ar Rayligh in both cass In particular, w assum that +18 at most for 1GŒ LB R Additiv compl-valud zro-man whit Gaussian nois (AWGN), +1, with varianc K is assumd to b suprimposd to th rcivd signal 3 Eualization Schms In th FMT systm almost no ICI ariss whatvr th transmission channl is, whil ISI is always prsnt in ach subchannl, vn if th transmission channl is idal ± ²³ ²³ ± ²³ µ ª «µ µ ± ²³ µ ª «Figur DFME ualizr for th FMT systm Hnc, it is mandatory to fac two problms: ualization of th transmit filtrs and ualization of th transmission channl In this sction, som simplifid ualizrs ar prsntd and compard with othr known ualization procdurs Lt s introduc th -point FFT of th channl impuls rspons, i ¹»ºL¼7½ À 7Á H JLKLMON P?1TO C ÃG () Dcision fdback multichannl ualizr (DFME) Assuming no ICI, th fdforward filtrs work on a subchannl bas A gnral solution, with an fficint rcivr implmntation [1, ], is rportd in Fig, whr a DFE is insrtd at th output of ach subchannl Although this schm may not b convnint for high rat applications bcaus of its computational complity and th fact that th filtr cofficints must b updatd at last at rgular tim intrvals to cop with th tim varying natur of th channl, w now driv its uations for an uppr bound on th systm prformanc Onc dfind th ovrall impuls rspons of th -th subchannl as ¹»Å¼7½ ¹ º ¼'½ &?*,G )( 7Á?*, Ç * ½ % & )( 'Á +* ½ * Q È K +* K T $ É ÊÊ ÊÊ (3) lt s indicat with +*,-, *ÌÍ CB Î, th $ É ÊÏT fdforward filtr of th Ê Ï -th subchannl and with?*,-, *ÐÑ C LB th corrsponding fdback filtr Thn w dfin th vctor containing th fd-

3 ó Ý Û B ý ö ö Q % ô " forward filtr cofficints as Ò ÊÊŒ ÔÓ É ÊÊ Õ? É ÊÊ Õ! É Ê ÊŒ ÖB Th autocorrlation matri of?*, has ntris ¹àß ß Ý Ó ÚÜÛ W ÞK 7Á?* ½ ˆ?* ½?1,âáÖL ¹ ßã ÞK Q È ½ +* K äáœåfæ ÊÊ ˆ +* K ä1tåfæ,å èç Ý K Þ is th powr of ach zro-man indpndnt and is a suitabl d- with î, th fdforward and fdback filtr can b dsignd as whr K $ idntically distributd signal Ö Œ-, æ lay From ÚÜÛ and th cross corrlation vctor éëê ntris Ó é)û ë Þ ˆ ÊÊ K æìíáö, á7lb F! ÙØ (4) É ÊÏ7?*,Rï whr *ì LB Ò Ê ÊŒ Ú ¹ ê ßß ¼'½ Ý 7Á ÊÏ ¼'½ é Û () (6) É ÊÊ?áÖ?1TåFæŽâáÖ7 (7) W point out that this schm has an high computational complity bcausêê ñ at ach ÊÊ channl stimat it ruirs th invrsion of ðb matrics Post-FFT simplifid DFME (postdfme) Lt us assum that ovr ach subchannl th fruncy rspons of th transmission channl is flat, i it has both a constant amplitud and a constant phas This condition is rlatd to th numbr of subchannls of th multicarrir systm and to th ratio btwn th š!a/ dlay sprad and " 6 Undr this assumption, from (1) and () th convolution btwn th -th transmit filtr and th transmission channl yilds 7Á +*Šä* ½ % & )(?* ½ Gò % & )( +*, HJLKLMON P Q % +*,) whr *íslbed>ä Hnc, th transmission channl can b adaptivly ualizd by a on tap pr subchannl ualizr, (8) OÂSŒ C à (9) as for DMT systms with cyclic prfi, whil th transmit filtrs can b ualizd by a static DFE Morovr, for th -th subchannl th cascad of transmit and rciv filtrs turns out to b indpndnt of th subchannl ind In fact øù û ö øù ú û þ þ þ ÿ ü ö øù û ö øù ú û Figur 3 postdfme ualizr for th FMT systm from (1) w gt %Œ +*,G % & )( 7Á +* ½ & )(?*, * ½ 7Á +* ½ +*, à * ½ T (1) $ Hnc, th fdforward and fdback filtrs ( ß ß $ +*,- and ß ã +*,- ) ar th sam for all subchannls and thy can b dsignd by using th standard DFE tchniu outlind in () (7) whr % is rplacd by Th rsulting ualization schm is rprsntd in Fig 3 for th -th subchannl W can pct to obtain som prformanc improvmnt by assuming a transmission channl with a linar phas within ach subchannl This linar trm corrsponds to th dlay of th -th subchannl $ and can b stimatd asily from th cofficints 8- As a first-ordr approimation of th dlay on th -th subchannl, w assum ½ "ìoâsœ C ÃG (11) whr dnots th angl of a compl numbr in th rang Ó O, To simplify intrpolation at th output of th FFT, ach signal is drivd at th ovrsampld rat "ë Thn it is dlayd of th uantity by a variabl phas intrpolator to yild Õ Ö " å ½ ¼ *Üå "! Ö ä*, (1) In our simulations th numbr of cofficints of th intrpolator filtr is "Õž In ordr to obtain th ovrsampld signal $# * :, th rcivr has two paralll structurs composd of a srial K&% to paralll convrtr, a filtr bank and a FFT Th input to th first structur is signal š?1 and th output yilds th vn sampls Õ Ö "ë Th input to th scond structur is a dlayd vrsion of th rcivd signal, š?1@åâ I, and th

4 C I ½ > = > * +, - / ' ( ) * * ξ 6 ; ξ = ; 79 Figur 4 prdfme ualizr for th FMT systm L Ö åï! " A rlativ output ar th odd sampls, rcivr with th addd fatur of tim intrpolator will b namd fractionally spacd (FS) ualizr Pr-FFT simplifid DFME (prdfme) In th prdfme th DFME is instad dirctly applid to th rcivd signal In this cas rciv filtrs ualiz th transmit filtrs whil th channl is ualizd by th on-tap pr subchannl structur In particular, th fdforward and fdback subchannl $BAŒÊÏT $BAŒÊÊ ÊÊ filtrs, +*,-, *ÂÑ CB ÊÏ 9, and?*,-, *AŽ CB, ar computd as DFE of th corrsponding $#% polyphas componnts of th transmit prototyp filtr, +*,- ; hnc thy ar diffrnt for ach branch of th rcivr filtr bank Th rsulting ualization $DC schm is rprsntd in Fig 4 If w dnot by Ö - $ E, 9 S, th input of th FFT, and by Õ Ö -, Î I, th FFT of th transmit data, this structur minimizs th man suar rror FHGI E è $BA ÊÊŒ L Ö KKJ, ïœ C S Th dsign of filtrs +*,- $BA ÊÏ7 L and?*,- can b ralizd using () (7) with th substitution of % with As it will b sn, for th sam filtr lngth, th prdfme is mor fficint than th postdfme, bcaus it nds to ualiz only th transmit filtrs Also for th prdfme, a FS approach can b usd 4 Prformanc Rsults Th prformanc of th various modulation and ualization tchnius hav bn tstd for th Wind-Fl scnario [] and assuming 9 ÑM and!!"'6) ž MHz Th channl impuls rspons is assumd known at th rcivr (i prfct channl stimation) and static, at last for th duration of on symbol Th avrag signal-to-nois ratio (SNR), namly th ratio btwn th powr of th signal /! +1 and th powr of th nois +1, is assumd db Th lngth of th prototyp transmit filtr is B D ODP Th prformanc is valuatd in trms of achivabl bitrat QSRUTW indicats th signal-to-disturbanc ratio at th dcision dvic for th -th subchannl Following th considrations mad in [1], th modifid SDR of th -th subchannl, QSRUTW, is givn in db by QSRT VÏ $QSRUT VÏ HW (13) whr WâXP db Th achivabl bit rat pr subchannl is givn by Y= :[Z\N] K QSRT å, ÂI, ãs ½ Á whr QSRT ïô ^K_a` Ncb d Th achivabl bit-rat for transmission is thrfor obtaind by summing up th Y= valus ovr th activ ; ¼7½ subchannls allocatd for transmission, i Y4Xf 7Á Y@ Th complmntary cumulativ distribution function (cdf) of Y is usd to compar th prformanc of diffrnt ó systms For DMT w hav usd a cyclic prfi [4] hg?œ!"'6i)åfž, to includ th A/D and D/A intrpolation filtrs lngth, and th rsulting systm is indicatd with DMT-CP For FMT th numbr Ê Ê of cofficintsêïof th fdforward and fdback filtr is B ÔD and B ïd, rspctivly In ordr to obtain a fair comparison with th simplifid FSprDFME and FSpostDFME, th FSDFME is also considrd Bfor rporting thir prformanc, w rcall th maor faturs of th various schms Firstly, FMT has a bttr bandwidth fficincy than DMT-CP, bcaus it dos not us any cyclic prfi Morovr, th FMT nds fwr virtual carrirs than DMT, sinc in this cas th spctrum of th transmittd signal is lss distortd by th filtr includd in th D/A convrtr, as obsrvd in [7] On th othr hand, FMT ualization, both with prdfme and postdfme, is basd on th assumption of subchannl flatnss Hnc ths schms show a prformanc dgradation for highr valus of th ratio!" 6 Fig and 6 rport th prformanc rsults of both DMT and FMT with diffrnt ualizr structurs in th two Wind-Fl scnarios Th bst prformanc is obviously achivd whn a DFME is implmntd Howvr, this rsult is usful only as a bnchmark sinc a similar

5 ualizr is impractical for radio applications Roughly th sam prformanc of DFME is achivd by mor practical ualizrs lik FSprDFME and prdfme Prformanc dgrads whn th FSpostDFME and th postdfme ar usd Indd th introduction of th subchannl dlay rcovry, both in FSprDFME and in FSpostDFME, allows for a slight prformanc improvmnt with rspct to th simplr prdfme and postdfme schms In any cas th prformanc is bttr than th DMT-CP schm Conclusions complmntary cdf FMT: FSpostDFME FMT: FSprDFME FMT: postdfme FMT: prdfme FMT: DFME DMT CP In this papr w hav prsntd ualization tchnius for wirlss FMT systms From th numrical rsults w may conclud that FMT-FSprDFME yilds bttr prformanc (in trms of achivabl bit rat) than DMT-CP and also than FMT-FSpostDFME Hnc, although FMT ruirs a modratly highr computational complity than DMT, it may b considrd as a possibl candidat for high spd transmission in disprsiv indoor/outdoor wirlss channls Howvr, whn th numbr of subcarrirs is vry high (g 6 or mor), th rcivr must b vry simpl (g for consumr lctronics), and th whol systm is synchronous, thn DMT with cyclic prfi may still rprsnt th most convnint solution complmntary cdf FMT: FSpostDFME FMT: FSprDFME FMT: postdfme FMT: prdfme FMT: DFME DMT CP ABR [Mbit/s] Figur Prformanc of DMT and FMT for diffrnt ualizr structurs: 9 ÑM, kgbmlï db, no lin of sight channl ABR [Mbit/s] Figur 6 Prformanc of DMT and FMT for diffrnt ualizr structurs: 9! M, kobml db, lin of sight channl digital subscribr lin IEEE Commun Mag, 38(): 98 14, May [] P P Vaidyanathan, Multirat systms and filtr banks, Englwood Cliffs, Prntic Hall, 1993 [3] S Kondo and L B Milstin Prformanc of multicarrir DS CDMA systms IEEE Trans on Commun, 44(): 38 46, Fbruary 1996 [4] JAC Bingham Multicarrir modulation for data transmission: an ida whos tim has com IEEE Commun Mag, 8(): 14, May 199 [] J L Garcia, M Lobria Channl charactrization and modl Wind-Fl Rport IST , procts/windfldlivrablshtm, DIII1, Dcmbr [6] PJW Mlsa, RC Younc and CE Rohrs Impuls rspons shortning for discrt multiton transcivrs IEEE Trans on Commun, 44(1): , Dcmbr 1996 [7] M Faulknr and S HTh ffct of filtring on th prformanc of OFDM systms In Proc ACTS 98 Summit, Rhods (Grc): 817 8, Jun 1998 Rfrncs [1] G Chrubini, E Elfthriou, S Ölçr and JM Cioffi Filtr bank modulation tchnius for vry high spd