Robust quncy ost stmato o OFDM ov ast vayng multpath channl L W, Youyun Xu, Yumng Ca and Xn Xu Ths pap psnts a obust ca quncy ost(cfo stmaton algothm sutabl o ast vayng multpath channls. Th poposd algothm stmats CFO both n tm-doman and quncy-doman usng two caully dsgnd squncs. Ths novl tchnqu posssss hgh accuacy as wll as lag stmaton ang and woks wll n ast vayng channls. Intoducton: Fquncy ost stmaton s on o th most mpotant task n OFDM cv. Vaous quncy stmatos hav alady bn dvlopd n th ltatu, ncludng blnd sm-blnd and data-add algothms. Showng gat supoty n stmaton accuacy spd and complxty, data-add algothms attact much ntst n cnt yas. Th nomalzd quncy ost s usually dvdd nto ntgal quncy ost(ifo and actonal quncy ost(ffo, whch may b stmatd spaatly o jontly. Most data-add algothms hav a lmtd stmaton ang and can only b usd to cov FFO. Moll poposd a tm-doman pambl basd algothm, whch utlzd an OFDM symbol wth multpl dntcal pats and can stmat th ntgal and actonal pats smultanously []. Howv, th algothm s stmaton ang s stctd whn a satsactoy accuacy s qud. In []~[4], th dntal nomaton btwn two conscutv OFDM symbols s usd to stmat IFO by assumng that th channl s nvaabl ov at last two OFDM symbols duaton. Ths condton s not mt any mo ov ast vayng multpath channl. In ths Ltt, two spcal CAZAC squncs a stly dsgnd o pambl pupos. Th actonal pat o CFO s thn stmatd and compnsatd n tm-doman xplotng auto-colaton popty o cvd pambl. Colatng two compnsatd pambl wth local ntal pambl n quncy-doman and makng ull us o th nomaton o th locatons cospondng to two colaton paks, w may obtan th stmaton o IFO. Du to th ndpndnc n sachng o th pak locaton, th channl s pmttd to vay ndpndntly
om symbol to symbol. Ths tat maks th nw mthod mo sutabl o ast vayng channl compad wth th mthod n []~[4]. Sgnal modl: In ths ltt, w adopt two CAZAC squncs as pambl o t s pct colaton popty [5]. Th st squnc s usd o FFO stmaton. Th st and th scond squnc a both utlzd o IFO stmaton at compnsaton. Th CAZAC squnc n tm-doman s n th om: xn ( xp j π n = n =,L ( Ths two CAZAC squncs hav dnt paamt and. At tmng covy and CP movd, th cvd sgnal yn ( may b psntd as: L j( πε n/ + φ ( = ( ( + ( yn hmxn m wn ( wh a Raylgh adng channl modl wth xponntal pow dlay pol s usd. { } E h( l = xp( l D (3 L s th numb o path; wn ( s wht Gaussan pocss wth zo man and vaanc σ w. FFO stmaton: Th FFO s stmatd by us o th auto-colaton o cvd sgnal (nos s not consdd: / L Rt ( ε, = y( n+ / y ( n = h( m / j( πε / (4 Lt ε ε dnot th ntgal and actonal pat o ε,and ε / s th ntg pat o ( mod ε /, ε = ε, ε = ε / + ε + ε.thn w gt th stmaton o FFO: { } ( ε ˆ ε = ag { Rt ( ε, } = ag Rt ( ε, + ag Rt, π π { } ε + ε ε < / = ε + ε / ε < ε + ε + < ε / (5 W not that th sult s ambguous by multpls o subca spacng. Ths ambguty wll b lmnatd by IFO stmato and has no nlunc on th whol stmaton. IFO stmaton: It s known that th DFT o a CAZAC squnc s also a CAZAC squnc. Th
IFO stmato s on th bass o ths act. Dnng X(k = { X ( X ( - } = FFT ( x(n L x(n= { x( Lx( -}, w hav: jπεˆ n y ( n = y( n n (6 n j π k Zk ( = y ( n (7 R ˆ,, X k Z ( k ( τ = ( τ mod k = ( (( ˆ L π j m jφ h mδτ ε ε m ε ˆ ε > mod = L π j m jφ ( ( ˆ h mδ τ ε ε ˆ + m ε ε < ( ( Whn th paamt and o th CAZAC squnc satsy th laton L < / L, all (8 th local maxmal locatons o R ( ε ˆ ε,, τ and R ( ˆ ε ε,, τ can b dstngushd om ach oth(shown n Fg.. Ths s th man da o IFO stmato. Consdng all possbl latonshp btwn th locatons o two global maxmums, w may dpct th algothm as ollows:. Fnd th pak locaton o th two colatons spctvly. = ag max { ( ˆ,, τ }, Lmax = ag max R ( ˆ,, τ L R max τ. I L max <, go to stp 3, ls go to stp 4. { } τ { } 3. Whl ( Lmax L = ( L + ; Whl ( Lmax < Lmax { Lmax ( Lmax } 4. Whl L L and max max mod ( max < max ( Lmax > { Lmax ( Lmax } ( = +. 5. % ε = L ; I % ε >, % ε = % ε (assumng ε < /. max mod Th stmaton ang o ths stmato achs th whol sgnal bandwdth. = +. Go to stp 5. Smulaton and dscusson: Smulatons hav bn un und th ollowng condtons: =, = 8, ε =, Raylgh adng channl wth 4 L = and { } E h( l = xp( l. Channl s assumd to b ndpndnt o dnt OFDM symbol. Both = 64 and = 8 a smulatd. Fg. shows that th paks o two colatons can b dntd by locaton, whch oms th oundaton o ou IFO stmato. In od to llustat th pomanc o IFO stmato, w smulat th alu pobablty o IFO stmato n th absnc o FFO stmato and compa 3
t wth th alu pobablty usng SCA mthod n []. Th alu pobablty { ε } P s dnd as: P % ε. W to th channl that vas om OFDM symbol to symbol but mans unchangd dung on OFDM symbol as vayng channl. Fom Fg., t s obvous that th poposd mthod s supo to SCA algothm n tms o alu pobablty o both vayng channl and statc channl..7.6 colaton pak o th st pambl wth τ=[ 8 6 4].5 ABS(R.4.3 ovlap locaton colaton pak o th scond pambl wth τ=[ 4 4].. 4 6 8 4 ght sht ndx,τ R ˆ ε ε,, τ R ( Fg. Rlaton btwn two colatons ( ε ˆ ε,, τ n pak locaton wth =8 SR=dB and ε ˆ ε = - - P -3 SCA =64 vayng channl SCA =8 vayng channl -4 SCA =64 statc channl SCA =8 statc channl Poposd =64 vayng channl Poposd =8 vayng channl -5-5 -4-3 - - 3 4 5 SR(dB Fg. Falu pobablty compason btwn ou mthod and SCA algothm. L W, Youyun Xu, Yumng Ca and Xn Xu ( Dpatmnt o mobl communcaton, Insttut o Communcatons Engnng, PLA Unvsty o Scnc and Tchnology, anjng, Chna E-mal: wlnb@hotmal.com Rncs. Moll, M., and Mngal, U.: An mpovd quncy ost stmato o OFDM applcatons, IEEE Commun. Ltt, 999, 3, pp.75 77. Schmdl, T.M., and Cox, D.C.: Robust quncy and tmng synchonzaton o OFDM, IEEE Tans. Commun., 997, 45,pp. 63 6 3. Moll, M., D Anda, A.., and Mngal, U.: Fquncy ambguty soluton n OFDM systms, IEEE Commun. Ltt.,,4, pp. 34 36 4. Chn, C., and L, J.: Maxmum lklhood mthod o ntg quncy ost stmaton o 4
OFDM systms, Elctoncs Ltts, 4,4, (3, pp. 83-84 5. Bom, L., and Antwl, M.: Pct -phas squncs and aays, IEEE J. Slct. Aas Commun., 99,, (4, pp.78-789 APPEDIX Makng us o th unqu popty o CAZAC squnc, w can obtan th autocolaton uncton o yn ( as (poo o (4: / Rt ( ε, = y( n+ / y ( n / / L L = hmxn ( ( + / m h( m x( n m / m = j( πε / = + + + / L L j( πε / hmh ( ( m xn ( / mx ( n m hm ( xn ( / mx ( n m / mm, = ( m m = + + + L / / L j( πε / hmhm ( ( xn ( / mxn ( m hm ( xn ( / mxn ( m / mm, = ( m m Wh = + / L L j( πε / hmh ( ( mw ( mm, hm ( W( mm, (9 mm, = ( m m / W( m, m = x( n+ / m x ( n m / π j ( / + m m( n+ / m m = / π j n( / + m m + ( / m / + m m = / jπ ( m m j nm ( m = π ( / m = m m ( W thn av at ou nal sult: ( ε L j( πε / R, = h( m ( t Th poo o (8 s also shown : R ˆ,, X k Z ( k ( τ = ( τ mod k = ( k τ q j π p jπk x( p y ( q k= p= q= = L ( k τ q jπ p jπk jφ j ( ˆ / π ε ε q h ( m x( p x ( q m k= p= q= = ( Dnotng ( τ k= p= q= ( k τ q jπ p jπk j ( ˆ π ε ε q/ W m, = x( p x ( q m 5
( ˆ ( ( ˆ π pτ+ ( ε ε q π kq p πp τ+ ε ε j j j = xpx ( ( q m + xpx ( ( p m k= p, q= ( p q k= p= W nally obtan: R ( ε ˆ ε,, τ π pm ( + τ ( ε ˆ ε π j j m = k= p= ( (( π j m δ τ ε ε m > mod = π j m δ τ + m < ˆ ˆ ( ( ˆ ˆ ( (( ˆ L π j m jφ h ( m δ τ ε ε m ε ˆ ε > = h ( m δ ( τ ( ε ˆ ε ˆ + m < mod L π j m jφ (3 (4 6