ICI Mitigation with CFO Compensation for OFDM in Mobile-to-Mobile Channel

Transcription

1 ICI Mtgton wth CFO Comenston or OFDM n Moble-to-Moble Chnnel ) Ttek Suryn, n ) Gmntyo Henrntoro Electrcl Engneerng Dertment Insttut Teknolog Seuluh Noember Surby, Inones ) ttks@ee.ts.c., ) gmntyo@ee.ts.c. Abstrct In moble-to-moble chnnels, the Doler sht s ecte by moble termnl veloctes o the trnsmtter n the recever en. Hence, the Doler requency becomes very hgh both termnls move very st. In ths conton, the chnnel wll chnge rly n cuse lrge nter-crrer-ntererence (ICI) n OFDM system. A chnnel estmton technque usng ece-wse lner roxmton hs revously been eveloe or ICI mtgton technque emloyng requency-omn-equlzer (FEQ). Unortuntely, ths chnnel estmton technque s lmte by normlze mxmum Doler sht o., below whch neglgble error results. In ths er, the crrerrequency oset (CFO) comenston technque s roose to mrove ths ICI mtgton technque, so tht lner chnnel estmton stll works well lthough normlze mxmum Doler sht s lrger thn.. The CFO comenston requency o tht shoul be e eens on trnsmtter Doler sht n hs n otml vlue,.e. o. 55 or moble-to-xe chnnels n o.6 or moble-to-moble chnnels. The chnnel estmton usng lner roxmton technque cn be le wth neglgble error u to normlze Doler sre. 4 ( % hgher thn systems wthout CFO comenston) n the sum T hgher thn.4 or moble-to-moble chnnels tht s nversely roortonl to the rto /. Furthermore, ssumng or moble-to-moble chnnel, the BER erormnce ncreses sgncntly CFO comenston s le. Keywors- OFDM; Doler; ICI; CFO comenston; chnnel estmton; lner ece-wse; hgh-see. I. INTRODUCTION Multlexng technques usng severl numbers o orthogonl crrers,.e. OFDM (Orthogonl-Frequency Dvson Multlexng), s one o the trnsmsson technques tht s wely use or hgh see t trnsmsson. OFDM technque hs mny vntges, one o whch s ecent bnwth requrement. Ths s ossble becuse the subcrrers re orthogonl, llowng the subcrrer sectr to overl ech other. The orthogonlty llows sgnl sectrum to be serte wthout ny ntererence or ower loss ue to lekge to other subcrrers. Unortuntely, tme vryng chnnel wth hgh Doler sht coul estroy the orthogonlty, resultng n severe ICI n egrng the systems BER erormnce more serously. The Doler sht wll ncrese the termnl moves ster or mult-ho moble chnnel conton exsts. Hgher Doler sht wll esclte crrer requency oset n sectrum serson resultng n lrger ICI. A lot o eorts re me to overcome the ICI. Generlly, the mtgton technques re ve by two tyes. One ttemts to mnmze the ICI reventvely beore t occurre n the other ttemts to remove t. Usully, the ormer technque consumes more bnwth n uses cong to mnmze the ICI by controllng the sub-crrer sectrum, whle the secon requres more comlex sgnl rocessng to remove ICI. One o the ICI mtgton technques o the secon tye tht h been stue s usng FEQ (Frequency-Domn Equlzer) []-[4]. FEQ s esgne bse on chnnel estmton results. Hence ts erormnce eens on estmton error. In tme vryng chnnel, the chnnel estmton n the FEQ esgn rmeter must be ute urng ech OFDM symbol ntervl. Hence, smle n low comlexty chnnel estmton technque s neee. A smle chnnel estmton technque usng ece-wse lner roxmton ws roose by [5]. Unortuntely, ths technque s only lcble normlze Doler sht (to the sub-crrer scng, ) s less thn.. Normlze Doler shts more thn. wll be more lkely to occur n moble-to-moble stuton, becuse both moble termnls nvolve n communcton wll contrbute to the Doler sht. Moreover, how lrge ther contrbutons re eenng on both moble veloctes. In ths er, we roose CFO comenston technque to be e to the exstng ICI mtgton s exlne bove, so tht the chnnel estmton wth ece-wse lner roxmton cn stll be use or ICI mtgton n hgh normlze mxmum Doler sht contons (lrger thn.). The urose o CFO comenston s to reuce the chnnel vrton rte, so tht t requres mxmum Doler sht estmton. We ssume tht the mxmum Doler sht chnges reltvely slowly comre to the symbol rte, hence t s ssume to be erectly estmte. Moreover, the Doler sectrum o the moble-to-xe chnnel s erent rom tht o the moble-to-moble chnnel, n so s ther mct on ICI. Hence, the erormnces o ICI mtgton technque wth CFO //$6. IEEE 43 ICTC

2 comenston nee to be nvestgte n comre or both tyes o chnnels. The er s orgnze s ollows. Secton II roves chnnel n system escrton. In secton III we ocus on our roose technque,.e. CFO comenston. Secton IV escrbes the nlyss o ICI mtgton wth CFO comenston. Fnlly, conclusons re gven n secton V. II. CHANNEL AND SYSTEM DESCRITION The tme-vryng chnnel wth Doler cn tke the orm o moble-to-xe (MF) or moble-to-moble chnnel (MM). In ths er, we ot moble-to-moble chnnel moel wth ouble-rng sctterers hvng the comlex enveloe ene s [6], [7]: h t t cos t Q j D cos D q q e, Q q () ; 4 (q q ) q 4Q where D v D / D,, s the mxmum Doler sht ue to trnsmtter ( = ) n recever ( = ) n moton wth velocty vd n crrer wvelength D. Inex reers to the -th rogton th rom the trnsmtter to the th o the sctterers locte on the rng surrounng the trnsmtter, whle nex q reers to the q -th rogton th rom the q -th o the scttereres locte on the rng surrounng the recever to the recever. n Q re the numbers o sctterers locte on the trnsmtter n recever rngs, resectvely. ~ U, s the rnom ngle o erture (AOD) n q ~ U, s the rnom ngle o rrvl (AOA) o the or q -th th mesure wth resect to the Tx or Rx velocty vectors, resectvely., q s the hse sht ue to relecton coecent o sctterers. All ngles re neenent rom ech other or ll n q. The ynmc behvor o the chnnels cn be exresse by the tme uto-correlton uncton, s Rk z Jo DzT J o DzT whch hs unt ower, where T s symbol ero n J o the zeroth-orer Bessel uncton. In ton, the Doler sectrum s gven s [6]: S D K D () (3) (4) Doler Sectrum where D / D, n K. s the comlete elltc ntegrl o the rst kn. A lot o Doler sectr or,.5, s gven n Fg.. For moble-to-xe chnnel moels, we use sngle-rng sctterrers moel t the trnsmtter en n obtn rom () [7], [8]: h = CFO Com. t, t j D cos e The moble-to-xe chnnel hs tme uto-correlton unctons gven s Rk z J o D zt, n hs unt ower. The Doler sectrum s the well-known U-she Jkes moel [9]. The receve sgnl, whch s rogte through the multth-ng chnnel wth tve whte Gussn Nose (AWGN), cn be wrtten s: r Chnnel Estm. S/ L l l N-ont FFT Equlzer Coe. Estm. t h t xt wt where l h l t s the chnnel s comlex enveloe or l -th th s moele s () or w t s the AWGN, n s the ely o l -th rogton th, (5), L s the number o ely ths, xt s the trnsmtte OFDM sgnl. C =.5 = ICI Mtgton (FDE-ZF) For generlzton, the mxmum Doler sht requency wll be normlze by requency scng o two jcent subcrrers ( / T ), where T s OFDM symbol ero. Furthermore, the multth chnnel rouces nter-symbol ntererence (ISI) storton, whch cn be elmnte by ng sucent cyclc rex n OFDM sgnl. For smlcty, becuse we ocus on ICI, ISI s ssume to be elmnte comletely by usng ths cyclc rex. Hence the chnnel moel s smle nto sngle th o unt energy. OFDM systems re nlyze bse on Fg. n [5], n outut Fst Fourer trnsorm (FFT) s exresse s ollows: l /S Estmton 3 Demng Fg.. - CFO -.8 Comenston n ICI Mtgton..4n OFDM.6.8 Recever /(D+D) Fg.. Doler sectr o moble-to-moble chnnels (5) (6) 43

3 N Y H X, H, X W N, ICI N where W s the FFT o AWGN, w, n the secon rt o the rght hn se s ICI. ICI cn be reuce usng requency omn equlzer esgne n ccornce wth the chnnel estmton results. The roose CFO comenston technque or mrovng ICI mtgton or system workng n hgh Doler requency envronment s escrbe n the ollowng secton. III. CFO COMENSATION IN MOBILE-TO-FIXED CHANNEL For reucng chnnel tme vrton rte we roose CFO comenston technque. The mount o CFO comenston requency tht must be e eens on the mxmum Doler sht. Thereore, the mxmum Doler sht estmte s requre. For ths estmton, the Doler sre estmton lgorthm n [] cn be use, but here we ssume tht the estmton s erect. The grm block o ICI mtgton technque wth CFO comenston n OFDM system s shown n Fg.. Alterntvely, or moble trnsmtter, the relzton o CFO comenston cn be emloye t trnsmtter, whch s resonble snce the Doler sht eens only on the vehcle velocty n the crrer requency (wvelength). The grm block o the system s gven n Fg. 8 n Aenx. Wth the velocty estmton, the Doler sht cn be clculte n the CFO requency, o, cn be etermne. Ater ng CFO comenston wth requency, o, the chnnel mulse resonse cn be wrtten s: h' h' t t CFO Com. Chnnel Estm. C S/ t N-ont FFT Equlzer Coe. Estm. ICI Mtgton (FDE-ZF) t (7) h' e o h (8) j e o j cos t e (8) j o / cos t cos e (8b) /S Estmton Demng Fg.. CFO Comenston n ICI Mtgton n OFDM Recever In (8), DT s the normlze mxmum Doler sht. The utocorrelton uncton o the rel rt o the new chnnel mulse resonse cn be erve s: R ' ' hchc R ' ' hchc R ' ' h c h c ' ' E h t h t c [( o E cos( ( ) t cos )) cos cos( ( o )( t )cos )] cos o E[ cos( ( ) cos )] c cos Anlogous to [6], equton (9) cn be exresse s: R ' ' hchc / cos( ( o ) cos ) cos (9) (9) (9b) () To see the mct o the CFO comenston we nlyze the verge resul SIR (Sgnl-to-Intererence Rto) ter ICI mtgton s le on the system, wth n wthout CFO comenston. Wthout nose, the receve sgnl cn be wrtten s [5]: Usng chnnel estmton results, x ( xˆ ) s obtne s : y h ( ) x () ĥ, the estmtes o y e x ˆ x x ) ( ) hˆ( hˆ () ( ) ( ) where ˆ e h h. The FFT outut o the bove estmton s: X ˆ X A (3) where A, ssume s ntererence, s the FFT o e x. The verge resul SIR cn be ene s: ) hˆ( X ve (4) A 43

4 ve s relte to resul ICI s the consequence o usng lner roxmton or chnnel estmton. The exresson o ve s uncton o hs been erve n eq. (36) n [5]. In Fg. 3 we exmne tht ve ncreses sgncntly CFO comenston s le. In ths gure, the grh rom smulton s lso comre to the nlytcl result whch s tken rom the grh n Fg. 4 o [5]. I we choose o /, t cn be seen tht usng CFO comenston, the ve vlue ncreses sgncntly,.e. bout ve o system wthout CFO comenston. It s lso event tht CFO comenston cn reuce the chnnel tme vrton rte ue to hgh Doler, so tht the ece-wse lner roxmton cn stll be use or chnnel estmton technque lthough.. Furthermore, wth the CFO comenston, o /, rom Fg. 3. It cn be exmne tht ve o system wthout CFO comenston wth normlze mxmum Doler sht (or nstnce,. 6 ) s equl to the system wth CFO comenston wth twce (or nstnce,. ), hence usng CFO comenston, the chnnel estmton wth lner roxmton cn stll be le or normlze mxmum Doler sre u to.4 (twce mxmum o system wthout CFO comenston). It s lso necessry to n the otml vlue o o. By usng the uto-correlton uncton o moble-to-xe chnnel, we ene the equton to n otml vlue o o, s : ve Fg. 3. z =. =.3 =.4 ICI mtgton w/ CFO com. (sm.) ICI mt. w/o CFO com. (sm.) ICI mt. w/o CFO com. (nl.) norm ves uncton o or system wth ICI mtgton technque o, otml rg mx o, o Z wth Z o, or moble-to-xe chnnel s gven s : (5) o/ Fg. 4. z s uncton o o / or moble-to-moble chnnel Z / o o cos (6), cos / cos Usng (5) n (6), we ene z Z o,, we cn use the grh o z s uncton o o / s resente n Fg. 4 to obtn the otmum vlue o o,.e. o, otml. 55. IV. CFO COMENSATION IN MOBILE-TO-MOBILE CHANNEL In the cse o moble-to-moble chnnels, the mxmum Doler sht mght ossbly be twce hgher thn tht n moble-to-xe chnnels, becuse there re two mxmum Doler shts,.e. n, whch mght hve equl contrbuton on the totl mxmum Doler sht, T, where rom [6]: Nevertheless, Doler sectrum. T n (7) hve erent eects on the contrbutes more to the sectrum sht. From mkes the Doler sre more thn to the sre, wheres t s the contrry or Fg., t s event tht concentrte t center. To exmne whether SIR vlue ncreses or not CFO comenston s le, here we ene o s o o o, where o o, /, o comenstes or, whle o comenstes or. Anlogous to (6) or the moble-to-xe cse, usng () n eq. (43) n [6] we ene Z o, t or moble-to-moble to obtn the otml vlue o o n the ollowng equton. 433

5 z =. =.3 =.4 =. =.3 =.4 o= o= ve =. =.3 =.5 =.7 =.6.4. Fg o/ z s uncton o o / or moble-to-moble chnnel wth. 5 Fg o/ ve s uncton o o / or moble-to-moble chnnel /, t cos / cos Z o o cos o / cos cos cos (8) - MM Ch.,=.3, =., w/o CFO com. MM Ch.,=.3, =., w/ CFO com. MF Ch.,=.3, w/o CFO com. MF Ch.,=.3, w/ CFO com. Rylegh Ch.,no ICI Now, usng (5) n (8), n Fg. 5 we lot z s uncton o / o. From gure 5, we exmne tht or. 5 the otmum vlue o o s or o, n.6 or o. To n the otmum vlue o o or vrous vlues o, we exmne ve s uncton o / o or vrous n Fg. 6, wth =.. Ths evluton s me by wy o smulton, whch s tken becuse the ercentge o o or o to o n (8) s unknown. From Fg. 6, the otmum CFO comenston or moble-to-moble chnnel s oun to be.6. The uer-boun o ntegrton n secon term n (8) revents the reucton o by CFO comenston, but ects the otmum CFO comenston vlue. Furthermore, we exmne the moble-to-moble Doler sectrum n Fg., t s event tht ects the Doler sre more omnnt thn the Doler sht, n contrst to. Hence t s resonble tht cnnot be reuce by CFO comenston. To nvestgte the mct o ICI mtgton wth CFO comenston technque n reucng the eects o ICI, the BER erormnce o OFDM system wth QSK moulton s nlyze. Here we ssume erect m-ont chnnel estmton tht s neee or lner chnnel estmton. The smulton result s gven n Fg. 7. From ths gure, t s event tht wth CFO comenston the BER erormnce mroves sgncntly rochng the Rylegh chnnel wthout ICI conton, eseclly or the moble-to-xe BER Eb/No (B) Fg. 7. BER erormnce o OFDM system wth ICI mtgton n CFO comenston n MM Chnnel chnnel. Furthermore, ICI cuse by Doler cnnot be suresse merely wth CFO comenston, becuse the Doler oes not only mke the sgnl suer rom requency shts but lso sectrl sres, thereore the ICI mtgton nee requency-omn-equlzer (FEQ). In ths er, or smlcty we use FEQ-ZF (Zero Forcng). However, FEQ-ZF lso hs wekness,.e., nblty to elmnte the ICI the chnnel comlex envelo s close to zero. In ths cse, block error occurs n remns n the error loor. The BER erormnce s not exctly equl to tht n Rylegh chnnel wthout ICI becuse the error n chnnel estmton roxmton remns n resul ICI. V. CONCLUSIONS It hs been shown tht CFO comenston technques cn be use or reucng chnnel tme-vrton rte n mrovng mtgton technque usng lner roxmton or chnnel estmton. The CFO otmum vlue tht shoul be 434

6 e eens on Doler requency cuse by the trnsmtter s moton,.e. o. 55 or moble-to-xe chnnel, n o.6 or moble-to-moble chnnel. Wth CFO comenston, the chnnel estmton usng lner roxmtons technques cn be le wth neglgble error u to normlze Doler sre. 4 ( % hgher thn system wthout CFO comenston) n n rnge.4 T.6 or the moble-to-moble chnnel tht s nversely roortonl to the rto o the mxmum Doler shts. AENDIX Block grm o the system wth CFO comenston lcton t trnsmtter se s shown n Fg. 8. bt N-ont IFFT Mng to Constellton S/ D/A /S Vehcle velocty sensor Mxmum Doler sht clculton C e o j o to chnnel Fg. 8. Doler estmton n CFO comenston t trnsmtter ACKNOWLEDGMENT The reorte work s rt o reserch rogrm une by Grute Reserch Grnt No. 639/IT.6/KU/ rom the Inonesn Mnstry o Ntonl Eucton. REFERENCES [] A. Stmouls, S. N. Dggv, n N. Al-Dhhr, Intercrrer ntererence n MIMO OFDM, IEEE Trns. Sgnl rocessng, vol. 5, , Oct.. [] I. Brhum, G. Leus, n M. Moonen, Tme-omn n requency omn er-tone equlzton or OFDM n oubly-selectve chnnels, Sgnl rocessng, vol. 84, , Nov. 4. [3] L. Rugn,.Bnell n G. Leus, Smle Equlzton o Tmevryng Chnnels or OFDM, IEEE Communctons Letters, Vol. 9, No. 7, July 5. [4] Lu, S., n Al-Dhhr, N., Coherrent n erentl ICI cncellton or moble OFDM wth lcton to DVB-H, IEEE Trns. On Wreless Communctons, vol. 7, no.,. 4-46, Nov. 8, [5] Y. Mosto, n D.C. Cox, ICI Mtgton or lot-ae OFDM Moble Systems, IEEE Trnsctons on Wreless Communctons, Vol. 4, No., Mrch 5. [6] C.S. tel, G.L. Stüber, n T.G. rtt, Smulton o Rylegh-Fe Moble-to-Moble Communcton Chnnels IEEE Trnsctons on Communctons, Vol. 53, No., , Nov. 5 [7] LC Wng, WC Lu, n YH Cheng, Sttstcl Anlyss o Mobleto-Moble Rcn Fng Chnnel Moel, IEEE Trns. on Vehculr Technology, Vol. 58, No.,. 3-38, Jn. 9. [8] G. L. Stuber, rncles o Moble Communcton, n e. New York: Kluwer Acemc,. [9] W.C. Jkes, Mcrowve Moble Communctons, sctwy, NJ: IEEE ress, 994. [] X. Zho, T. eng, M. Yng, n W. Wng, Doler Sre Estmton by Trckng the Dely-Subsce or OFDM Systems n Doubly Selectve Fng Chnnels, IEEE Sgnl rocessng Letters, VOL. 6, NO. 3, Mrch