Robust frequency offset estimator for OFDM over fast varying. multipath channel

Transcription

1 Robust equency oset estmato o OFDM ove ast vayng multpath channel L We, Youyun Xu, Yuemng Ca and Xn Xu Ths pape pesents a obust cae equency oset(cfo) estmaton algothm sutable o ast vayng multpath channels. The poposed algothm estmates CFO both n tme-doman and equency-doman usng two caeully desgned sequences. Ths novel technque possesses hgh accuacy as well as lage estmaton ange and woks well n ast vayng channels. Intoducton: Fequency oset estmaton s one o the most mpotant task n OFDM eceve. Vaous equency estmatos have aleady been developed n the lteatue, ncludng blnd sem-blnd and data-aded algothms. Showng geat supeoty n estmaton accuacy speed and complexty, data-aded algothms attact much nteest n ecent yeas. The nomalzed equency oset s usually dvded nto ntegal equency oset(ifo) and actonal equency oset(ffo), whch may be estmated sepaately o jontly. Most data-aded algothms have a lmted estmaton ange and can only be used to ecove FFO. Moell poposed a tme-doman peamble based algothm, whch utlzed an OFDM symbol wth multple dentcal pats and can estmate the ntegal and actonal pats smultaneously []. Howeve, the algothm s estmaton ange s estcted when a satsactoy accuacy s equed. In []~[4], the deental nomaton between two consecutve OFDM symbols s used to estmate IFO by assumng that the channel s nvaable ove at least two OFDM symbols duaton. Ths condton s not met any moe ove ast vayng multpath channel. In ths Lette, two specal CAZAC sequences ae stly desgned o peamble pupose. The actonal pat o CFO s then estmated and compensated n tme-doman explotng auto-coelaton popety o eceved peamble. Coelatng two compensated peamble wth local eeental peamble n equency-doman and makng ull use o the nomaton o the locatons coespondng to two coelaton peaks, we may obtan the estmaton o IFO. Due to the ndependence n seachng o the peak locaton, the channel s pemtted to vay ndependently

2 om symbol to symbol. Ths tat makes the new method moe sutable o ast vayng channel compaed wth the method n []~[4]. Sgnal model: In ths lette, we adopt two CAZAC sequences as peamble o t s peect coelaton popety [5]. The st sequence s used o FFO estmaton. The st and the second sequence ae both utlzed o IFO estmaton ate compensaton. The CAZAC sequence n tme-doman s n the om: x( n) exp j n N n, N () These two CAZAC sequences have deent paamete and. Ate tmng ecovey and CP emoved, the eceved sgnal y( n ) may be epesented as: L j ( n/ N ) ( ) ( ) ( ) ( ) m y n h m x n m e w n () whee a Raylegh adng channel model wth exponental powe delay pole s used. E h( l) exp( l D) (3) L s the numbe o path; w( n) s whte Gaussan pocess wth zeo mean and vaance FFO estmaton: The FFO s estmated by use o the auto-coelaton o eceved sgnal (nose s not consdeed): N N / L R, t ( / ) ( ) ( ) / y n N y N N n h m e n m j ( / ) w. (4) Let denote the ntegal and actonal pat o,and / s the ntege pat o /, mod, /.Then we get the estmaton o FFO: ag Rt, ag Rt, ag Rt, / / / (5) We note that the esult s ambguous by multples o subcae spacng. Ths ambguty wll be elmnated by IFO estmato and has no nluence on the whole estmaton. IFO estmaton: It s known that the DFT o a CAZAC sequence s also a CAZAC sequence. The

3 IFO estmato s on the bass o ths act. Denng X(k) X () X( N -) FFT x(n) x(n)= x() x( N -), we have: j n N y( n) y( n) e n N (6) N n j k Z( k) y( n) e N (7) N n R,, X k Z ( k) N mod N N k L j m j N h m m e mod N m L j m j N h m m N e m ( ) ( ) When the paamete and o the CAZAC sequence satsy the elaton L N / L, all the local maxmal locatons o R,, and R,, (8) can be dstngushed om each othe(shown n Fg.). Ths s the man dea o IFO estmato. Consdeng all possble elatonshp between the locatons o two global maxmums, we may depct the algothm as ollows:. Fnd the peak locaton o the two coelatons espectvely. ag max,,, Lmax ag max R,, L R max. I L max N, go to step 3, else go to step Whle Lmax N L L ; Whle Lmax Lmax Lmax Lmax max max modn 4. Whle L max Lmax and L max Lmax Lmax 5. L max mod N. ; I N, N (assumng N / ). The estmaton ange o ths estmato eaches the whole sgnal bandwdth.. Go to step 5. Smulaton and dscusson: Smulatons have been un unde the ollowng condtons:, 8,, Raylegh adng channel wth 4 L and E h l ( ) exp( l ). Channel s assumed to be ndependent o deent OFDM symbol. Both N 64 and N 8 ae smulated. Fg. shows that the peaks o two coelatons can be dented by locaton, whch oms the oundaton o ou IFO estmato. In ode to llustate the peomance o IFO estmato, we smulate the alue pobablty o IFO estmato n the absence o FFO estmato and compae 3

4 t wth the alue pobablty usng SCA method n []. The alue pobablty P s dened as: P. We ee to the channel that vaes om OFDM symbol to symbol but emans unchanged dung one OFDM symbol as vayng channel. Fom Fg., t s obvous that the poposed method s supeo to SCA algothm n tems o alue pobablty o both vayng channel and statc channel..7.6 coelaton peak o the st peamble wth =[ 8 6 4].5 ABS(R).4.3 ovelap locaton coelaton peak o the second peamble wth =[ 4 4] ght sht ndex, Fg. Relaton between two coelatons R,, R,, n peak locaton wth N=8 SNR=dB and - - P SCA N=64 vayng channel SCA N=8 vayng channel SCA N=64 statc channel SCA N=8 statc channel Poposed N=64 vayng channel Poposed N=8 vayng channel SNR(dB) L We, Youyun Xu, Yuemng Ca and Xn Xu ( Depatment o moble communcaton, Insttute o Communcatons Engneeng, PLA Unvesty o Scence and Technology, Nanjng, Chna ) E-mal: wlnb@hotmal.com Fg. Falue pobablty compason between ou method and SCA algothm. Reeences. Moell, M., and Mengal, U.: An mpoved equency oset estmato o OFDM applcatons, IEEE Commun. Lett, 999, 3, pp Schmdl, T.M., and Cox, D.C.: Robust equency and tmng synchonzaton o OFDM, IEEE Tans. Commun., 997, 45,pp Moell, M., D Andea, A. N., and Mengal, U.: Fequency ambguty esoluton n OFDM systems, IEEE Commun. Lett.,,4, pp Chen, C., and L, J.: Maxmum lkelhood method o ntege equency oset estmaton o 4

5 OFDM systems, Electoncs Lettes, 4,4, (3), pp Bome, L., and Antwele, M.: Peect N-phase sequences and aays, IEEE J. Select. Aeas Commun., 99,, (4), pp