Residual Frequency Offset Correction for Coherently Modulated OFDM Systems in Wireless Communication

Transcription

1 Reidual Fequency Offet Coection fo Coheently Modulated OFDM ytem in Wiele Communication V.. Abhayawadhana, I.J. Waell aboatoy fo Communication Engineeing, Depatment of Engineeing, Unieity of Cambidge, UK Abtact Othogonal Fequency Diiion Multiplex (OFDM) ytem ae ey enitie to fequency offet caued by tuning ocillato intabilitie and Dopple hift induced by the channel. The chmidl and Cox Algoithm (CA) i quite obut in etimating the fequency offet fo ytem with lage OFDM ymbol length. It ue two OFDM ymbol fo taining with the fit one haing two identical hale. The fequency offet i etimated by coelating a eceied equence of ample equal to half the OFDM ymbol length with the following eceied ample. The effect of Additie White Gauian Noie (AWGN) in the etimation poce i mitigated only if the numbe of ample ued in the coelation, and hence the OFDM ymbol ize i lage. Howee to be uccefully applied to Boadband Fixed Wiele Acce (BFWA) ytem, OFDM hould pefom well een with malle ymbol length. In thi pape we peent the Reidual Fequency Offet Coection Algoithm (RFOCA), which ue the CA fo initial fequency offet acquiition and follow it with a tage which educe the initial eidual fequency offet by tacking the phae of the decoded data. We how though imulation that the RFOCA achiee an eo aiance that i many ode of magnitude lowe than at the end of the acquiition tage uing the CA alone. I. INTRODUCTION Vaiou olution hae been uggeted a contende to oecome the challenge of tanmitting data to the ubcibe at high data ate demanded by futue boadband application, fo example Boadband Fixed Wiele Acce (BFWA), Digital ubcibe ine (D), Cable Modem and atellite Communication. Thi pape will adde BFWA, owing to it adantage of eae of deployment and cot. Othogonal Fequency Diiion Multiplex (OFDM) ha been the mot popula phyical laye tandad fo BFWA ytem due to it obutne and efficiency mainly becaue it ue a imple Fat Fouie Tanfom (FFT) of finite length fo modulation and demodulation. Among the tandad that hae placed thei confidence in OFDM ae HIPERAN-2 [1] and IEEE a [2]. The othogonality of the conecutie OFDM ymbol i maintained by appending a length cyclic pefix (CP) at the tat of each ymbol []. The CP i obtained by taking the lat ample of each ymbol and conequently the total length of the tanmitted OFDM ymbol i ample. Fo each OFDM ymbol to be independent and to aoid any Inte ymbol Intefeence (II) o Inte Caie Intefeence (ICI), the length of the Channel Impule epone (CIR) hould be le than ample. Hence the ditotion caued by the CIR only affect the ample within the CP. The eceie dicad the CP and take only the lat ample of each OFDM ymbol fo demodulation by the eceie FFT. In uch a cae, the linea conolution of the tanmitted ignal with the CIR i coneted into a cicula one. Conequently, fo coheently modulated OFDM ytem the effect of the CIR can then be equalized by an aay of one-tap Fequency Domain Equalize (FEQ) following the FFT. Thi i becaue the fequency electie fading channel can be appoximated by a um of flat fading channel, poided the numbe of ubchannel i lage enough. ome- Out In Demap. Mappe FEQ N-point IFFT N-point FFT Add P/ Channel CP tip CP /P Fig. 1. Block Diagam of the OFDM ytem AWGN TEQ time a Time Domain Equalize (TEQ) may be ued to hoten the effect of the CIR [4]. Figue 1 how the block diagam of the ytem, whee P/ and /P epeent the Paallel to eial and eial to Paallel function epectiely. Unfotunately, OFDM ha been poen to be ey enitie to fequency offet and phae noie caued by tuning ocillato inaccuacie o Dopple hift induced by the channel. The uual deployment cenaio fo a BFWA ytem employ a point to multipoint configuation. Hee, a ingle bae tation (B) tanmit data in hot but to many ubcibe unit (U) placed at the ue location. The economic feaibility of a BFWA deployment depend heaily on the cot of the U. The ue of low cot component, paticulaly the ocillato, i a majo iue ince thei accuacy and tability ae diectly elated to cot. Hence it i impeatie that if OFDM i to be ued fo BFWA tanmiion, it hould be able to opeate effectiely uing ocillato with only modeate pefomance and cot. An OFDM ytem effectiely conit of inuoidal ubca- i the actie ym- ie with fequency pacing, whee bol peiod of each ubcaie. The th ubcaie will thu be at!, whee i a efeence #" fequency. Without lo of geneality, we can aume. The modulated ubcaie oelap pectally, but ince they ae othogonal oe a ymbol duation, they can be eaily ecoeed a long a the channel doe not detoy the othogonality. An unwindowed OFDM ytem ha ectangula ymbol hape. Hence, in the fequency domain the indiidual ubchannel will hae the fom of inc function whee the fit idelobe i only ome 1 db below the main lobe of the ubcaie. In the eent of a fequency offet between the tanmitte and the eceie the ubchannel will not align. The effect of fequency offet i two fold, it will educe the ignal powe of the deied ubchannel output and alo intoduce ICI futhe inceaing the intefeence leel. The ICI powe can be ignificant een fo mall fequency offet in OFDM due to the high idelobe powe of the ubchannel. Thu the eduction of fequency offet i citical in OFDM ytem. Thi pape i oganied a follow, +

2 F Y / ) $ F < / < ection II analye the effect of fequency offet in OFDM analytically. ection III biefly intoduce the chmidl and Cox Algoithm (CA) [5] and ection IV intoduce the noel Reidual Fequency Offet Coection Algoithm (RFOCA) that compliment the CA and impoe the pefomance. ection V how eult obtained by compute imulation and ection VI conclude and popoe futue wok. II. EFFECT OF FREQUENCY OFFET IN OFDM All analyi and imulation in thi pape ae pefomed in the digital complex baeband domain. The $ th ample of the % th OFDM ymbol geneated by the Inee FFT (IFFT) at the tanmitte i &('*) + -, #.0/ ;:=<=>@?BA CED "F HGI (1) i the data ymbol modulated on to the th ubcaie of the % th OFDM ymbol. The data i coneted into a eial equence, then the CP of length i added. Thu the % th tanmitted OFDM ymbol i & J%K & DPOQORD & D & D;OROQD & '*). The eceie dicad the ample of the CP and ue the ample of the actie OFDM ymbol.*/nm fo decoding..0/21 We aume.0/61tvu a finite length CIR with XW ample, Y DPOQORD Y, whee ]\^XWG_. We aume that i lage enough uch that the fequency electie channel i diided into contiguou.[z/61 flat VU fading ubchannel. If we aume that coect fame and timing ynchoniation i achieed, then the eceied equence afte tipping the CP can be expeed a, `P +, ba@.0/21 542c de9 :=<=> A(fg?ihkjVl C m on + (2) "]F fo $ pg_ d. Hee i the tanfe function of the channel at the ubchannel index, n + i the Additie White Gauian Noie (AWGN) tem and q i the fequency offet elatie to the intecaie pacing. The ymbol afte FFT demodulation i, ` + 9.0/ :=<T>t A C D "ufw[f xgw () ubtituting (2) into () allow the output of the th ubchannel to be expeed a the um of thee component. '*) d 6q5 9;:=>~ C k C 6q5} ƒ I (4) The fit tem on h of equation 4, denoted heeafte, how that the deied tem d expeience amplitude eduction and phae ditotion. A ˆ 6q, 6q5} can be appoximated by 6q. Hence the degadation of the equied tem anihe when the eceied data doe not expeience any fequency d offet. In pactice, the effect of the channel tanfe function i emoed by the FEQ following the FFT. Note that the FEQ i tained by tanmitting a known taining ymbol occupying the OFDM ym- ) DPOQORD bol numbe Š, Œ. Uually the taining ymbol i placed at the beginning of the fame. The atio of the...0/21tvu CTIR (db) Theoetical imulated (N=256) imulated (N=64) Ž Relatie Fequency Offet (ε) Fig. 2. Analyi of CTIR Relatie Fequency Offet, decoded ample of the taining ymbol ), to the locally geneated copy of ) "F_F, whee ˆG, i ued to calculate the coefficient fo the FEQ...@ The econd tem in equation (4) i the ICI and the thid tem i due to the AWGN. The ICI tem i gien a, ƒ.*/61?i?p t d y=zr{ q G q G =} 9 :=>š 5 ~ gœ C k C (5) If we aume that the tanmitted data i zeo mean and uncoelated (i.e. and Ÿž " ), then. Hence the ICI powe i, ƒ ƒ < < #" 6q.0/21?=?; kt d < oq G =5 <; J) < (6) To appeciate the eeity of fequency offet on the Caie to Intefeence Ratio (CTIR) in an OFDM ytem, we define CTIR d < ƒ <. Auming the channel tanfe function, i unity and with zeo AWGN, (i.e. " ), then?i?p t CTIR.*/61 oq G 6q5} =} < () A imila analyi on the effect of fequency offet on OFDM can be found in [6] and []. Figue 2 how CTIR in decibel a a function of q. imulated alue fo «and uing QPK data mapping ae alo hown. It how that the CTIR dop ignificantly when elatie fequency offet, q inceae beyond 0.1. An impotant obeation i that the CTIR i independent of. III. CHMID AND COX AGORITHM (CA) One of the moe obut cheme to etimate both fame ynchoniation and fequency offet i the CA. It ue two taining ymbol with the fit one haing a epetition within half a ymbol peiod. Fame ynchoniation i achieed by eaching fo a taining ymbol with two identical hale. If, the um

3 ¼ ± ³ Ô q of conecutie coelation between pai of ample paced apat i found a, ± ²š ³ + 42 /61 ` ž + ` + (8) Receied Æ X FFT Demod ǾÈkÉÊ FEQ To QPK lice ÇTÈšÉÊ elect Channel ǾÈkÉ Ì Ç¾ÈkÉ Í Ì The output of the coelato, a gien by (8) will each a peak at the end of the CP of the fit taining ymbol. If µ W G and KG WĢ (, the peak i actually maintained fo ample jut befoe the end of the CP of the fit taining ymbol. Thu the coelato output will take the fom of a plateau. Thi i becaue the lat few ample of the CP, equal to the length of, ae not coupted by the CIR. Timing ynchoniation i achieed by locating the end of thi plateau, denoted by ²k¹»º}Š. ince the CP enue that thee i no Inte Block Intefeence (IBI) between OFDM ymbol, the effect of the CIR in the fit taining ymbol i cancelled if the conjugate of a ample fom the fit half i multiplied by the coeponding ample fom the econd half. Hence the phae diffeence between the two hale of the fit taining ymbol i caued by the fequency offet, ¼ 6q. It can be etimated a ½ ¾ º+ 42 ² ¹Àº}Š GÁ$. If q8â_ thee i no phae ambiguity in ¼ ½ and the fequency offet can be etimated a q5ãkäå ½ ¼2 ½ (9) In ode to eole potential ambiguity ue can be made of the econd taining ymbol, a detailed in [5]. The effect of AWGN on the patial etimation gien by equation (9) i inignificant only if, and hence the numbe of FFT point, i lage. The CA pefom well fo OFDM ytem with in exce of 1000 [5]. Fo BFWA ytem, data i tanmitted in hot but, paticulaly in the uplink. In thi ituation, it would be wateful to ue an OFDM ytem with lage. Beide lage alue of will gie ie to the additional poblem of high peak-to-aeage powe atio and will alo intoduce latency which educe potocol efficiency. Typically BFWA ytem utilie lowe alue of uch a 64 to 256 a peented in [1] and [2]. When the CA i ued fo ytem with lowe alue of, the etimateq½ i not ufficiently accuate. Thi eo eult in a eidual fequency offet that otate the eceied contellation at a educed ate, but one that i till ignificant enough to caue bit eo in coheently demodulated OFDM ytem. In thi pape we peent the Reidual Fequency Offet Coection Algoithm (RFOCA) that compliment the CA by following it with a tacking function that continuouly compenate fo the eidual fequency offet eo. Othe appoache that ae ued fo fequency offet coection include fo example the ue of null ymbol [8]. The ue of a null ymbol i not pactical in a but mode ytem a the tanmiion will alway be a null while no data i tanmitted. Othe uggetion utilie the coelation between the cyclic pefix and the lat few ample of the OFDM ymbol [9] and the elf-cancellation cheme peented in [10] and [], whee the ame data i ent in moe than one ubchannel. Both cheme ae not ey pactical when i a low alue with the latte two appoache haing the additional poblem of educing the numbe of ueful ubchannel by at leat half. Note that the RFOCA doe not utilie any pilot no null ymbol yet will be hown to effectiely eliminate the eidual offet. The popoal in [11] alo attempt to tack the Ñ(ÒgÓ [.] Ð È Ð È Update ÐÍ È Find Gadient ÕTÖ Block Count Î Ï Unwap Phae Î Ï Buffe foõ¾ö Block ag[.] - Î ÈšÉÌ ag[.] Fig.. Reidual Fequency Offet Coection Algoithm (RFOCA) eidual fequency offet. Hee, the eidual offet coection facto i updated at the end of each OFDM ymbol. Howee ou tet indicate that the etimate i not ey accuate when only one ymbol i ued, hence we update the eidual offet coection facto only afte analying a block of X, (X ]µ_ ) OFDM ymbol. IV. REIDUA FREQUENCY OFFET CORRECTION AGORITHM (RFOCA) In the popoed appoach, an initial fequency offet acquiition i made uing the CA. We popoe to etimate the eidual fequency offet, qœ by tacking the ate of phae change at the FEQ output, ½ a hown in Figue. Howee, the etimate of Œ could be eiouly affected by ubchannel with a low NR eulting d d fom pectal null in the channel epone. An etimate of i made by taking the atio of the tanmitted and decoded output of the econd taining ymbol d of the CA. Hence we only elect thoe ubchannel with aboe a cetain thehold. We call thi ubet of ubchannel ² Ø " d D;ORO ˆG. The citeia applied i to elect ubchannel with in exce of a tandad deiation aboe the mean. Fo ymbol %, the output of thee ubchannel ½ ae ent though a lice to obtain Œ, whee ²eÙK². Fo ymbol % ae found a, the phae eo between ½ '*) and Œ, namely ½ G Œ (10) The phae eo ae toed in a buffe, Û fo a block of OFDM ymbol. Note that only the elected ubchannel will be toed. Hence if the numbe of ubchannel elected in ² i then the length equied fo the buffe i only. The Maximum ikelihood (M) etimate of the eidual fequency offet qœ i calculated a the gadient of the alue toed in the buffe. Note, in thi pape we hae aumed QPK data mapping though the technique could be extended to othe contellation. Initially, qœ can be quite high and if the alue of the phae eo, µw, then it eult in decoding eo being poduced by the lice which. Hence ubequently eult in phae wapping of at Ü0 it i impeatie that we fit unwap '*) befoe the calculation of

4 ½ ½ ½ à œ. â Î Ï Ý AW(. ) Î Ï Þ5ß Fig.4. Phae Unwapping Algoithm q Œ. Although accuate phae unwapping algoithm ae aailable, they ae ey complex. ince we ae only inteeted in the phae gadient and not the exact phae alue, a imple cheme wa elected fo the unwapping of the phae [12]. Fo pupoe of claity, we denote the â á th ample â of the wapped phae and the unwapped phae a and ½, epectiely. The phae unwapping algoithm can be expeed a â â oã AW â G½ â Z -1 Î Ï (11) whee AW O i a awtooth /21 function that/21 limit the output to Ü0 and ã i a paamete that contol the aiance of the unwapped phae. The algoithm i illutated in Figue 4. The eo due to fequency offet i compenated by multiplying the pe-fft eceied ymbol, `P + 9 : +åä ~ æ ç with, whee in geneal q ' ½ i the fequency offet coection facto fo ymbol %, which i initialied to q5ãkäå ½ at the acquiition tage. At ymbol numbe è, q5é ½ i updated accoding to q5é ½ q é qœ é, whee è i an poitie intege. Fo OFDM ymbol èeg- B D è wg-.@ê, q.ê. ê /61. ê ½ é i ued a the fequency offet coection facto. In othe wod q ' /21.@ê ½ i updated once eey X OFDM ymbol block. The choice of i citical a a lage alue will caue the up- q ' with too high a latency. Howee afte a few update dating of ½ the alue of qœ ae quite mall, hence to get a bette etimate in the peence of AWGN a lage alue of will educe the aiance. The RFOCA can be ummaied a follow. 1. Do an initial fequency offet acquiition q½ ÃkÄÅ uing the CA. 2. elect the ubet of ubchannel with magnitude exceeding the defined thehold in the channel tanfe function, ², at the tat of the but.. Obtain ½ fom the FEQ output and then Œ by ue of a lice fo each ymbol %, whee ²ÙE². Calculate and toe fo a block of X OFDM ymbol. 4. Find the unwapped phae ½ fom the wapped phae. Find the gadient of ½, namely q Œ. Thi poce i done once eey ymbol. 5. Once eey X OFDM ymbol block, calculate the new fequency offet coection facto q½ é.. ê _ D ( ë D V. IMUATION PARAMETER AND REUT OFDM ytem with hae been imulated at a ampling ate of 20 MHz with a guad inteal equal to 20 ample, thu the ubcaie pacing ae appoximately 12 khz, 156 khz and 8 khz epectiely. QPK mapping fo all ubchannel ha been employed and all the ubchannel ae ued. A but of data bit i aumed to be tanmitted. Each data point in the imulation eult i obtained by aeaging oe 500 uch but. In ode to tet the pefomance of the RFOCA with fequency offet alone, we hae aumed pefect ymbol and fame Eo Vaiance CA N64 CA N128 CA N256 RFOCA N64 RFOCA N128 RFOCA N NR (db) Fig. î¾ïðiñiò5ó(ð ò5ô5î 5. Compaion of Eo Vaiance of CA and RFOCA in AWGN fo ì í and ŽNíõ(ö ô ynchoniation fo the imulated coheent OFDM ytem. A moe obut ymbol ynchoniation algoithm that itually guaantee pefect fame ynchoniation will be the ubject of a futue publication. Afte much teting, the alue elected fo wee " D " D ( fo b D ( ë D q '. Figue 6 how the pefomance, epectiely. Figue 5 how the compaion of eo aiance at the end of the acquiition tage uing the CA and the tacking tage uing the RFOCA fo D ( ë D a a function of the ignal to Noie Ratio (NR), with q p" O. It how that the RFOCA eo aiance i many ode of magnitude lowe than at the end of the acquiition tage. Thee appea to be a thehold effect in RFOCA at aound an NR of 16 db, below which the eo aiance inceae apidly. It i mainly due to the eo peent in the elected ubchannel of ², which ubequently ceate etimation eo in the eidual offet, Œ of the RFOCA in tem of Bit Eo Rate (BER) NR again in AWGN. The BER i itually zeo at alue of NR aboe 16 db but uddenly inceae below 16 db. Thi eult i a diect conequence of the thehold effect obeed with the peiou eo aiance eult. It i obeed that at an NR of 16 db only a few out of the total of 500 eceied but gie ie to eo. Howee, thee eo ae ignificant giing ie to a high oeall BER. uch occuance became moe common when the NR i educed below 15 db, thu inceaing the BER ey apidly. Appopiate model fo BFWA channel ae in the poce of being defined. The tanfod Unieity Inteim (UI) channel compie 6 model fo diffeent teain condition [1]. All of them ae imulated uing tap, each haing eithe Rayleigh o Ricean amplitude ditibution. The channel i aumed to be wide-ene tationay uncoelated catteing (WU) and each tap of the CIR i modeled a Y â ø!â 9 :Tùú øûâ, whee the amplitude and the phae ¼ ae elected independently [14]. The but take le than 10 m to tanmit at the elected ampling fequency, conequently the channel i aumed contant fo the duation of each but. We hae elected the UI-2 channel model, petaining to teain with low tee denitie and with antenna haing a diectiity of 0 degee at the U and 120 degee at the B. The channel i chaacteied by a RM delay pead of 0.2 ü. Figue allow a compaion of the eo aiance of the CA

5 N64 N128 N N64 N128 N BER BER NR (db) Fig. 6. Pefomance of RFOCA in AWGN fo ìií î¾ïðiñiò5ó(ð»ò5ô5î and ŽNíýõ(ö ô NR (db) Fig. 8. Pefomance of RFOCA with AWGN and UI-2 CIR fo ìþí î¾ïðiñiò5ó(ð ò5ô5î and ŽNíõ(ö ô Eo Vaiance CA N64 CA N128 CA N256 RFOCA N64 RFOCA N128 RFOCA N NR (db) Fig.. UI-2 CIR fo ìwí î¾ïðiñiò5ó(ðàò5ô5î and Žûíõ(ö ô Compaion of Eo Vaiance of CA and RFOCA with AWGN and «" O in the UI- and the RFOCA fo an OFDM ytem with q 2 channel. A new channel in accodance with the UI-2 pofile i andomly geneated fo the tanmiion of each but. The RFOCA eo aiance i een to be many ode of magnitude lowe than at the end of the acquiition tage depite the peence of the UI-2 channel. Figue 8 how the pefomance of the RFOCA in tem of BER NR fo the UI-2 channel and q " O. The thehold effect now occu at an NR in the egion of 20 db owing to the effect of the UI-2 channel. VI. CONCUION We hae peented a Reidual fequency Offet Coection Algoithm (RFOCA), that compliment the fequency acquiition poce pefomed by the chmidl and Cox Algoithm (CA). The RFOCA continuouly tack and compenate fo the eidual fequency offet that i peent afte the acquiition tage. We hae applied the RFOCA fo AWGN and BFWA channel, namely the UI-2 channel pofile, and hae hown a ignificant eduction in the eo aiance bought about by the ue of the RFOCA following the initial acquiition tage. Although the algoithm may appea to uffe fom a thehold effect it till gie a ignificant pefomance adantage at ealitic ignal to noie atio. In the futue we hope to adde the thehold effect by impoing the phae unwapping and inetigating othe citeia fo the election of the ubchannel. We alo hope to impoe the pefomance of the CA in a fame ynchoniation ole. REFERENCE [1] ETI, Boadband Radio Acce Netwok (BRAN); HIPERAN-2; Phyical aye, Apil [2] R. an Nee, G. Awate, M. M. H. Takanahi, M. Wete, and K. Halfod, New high-ate wiele AN tandad, IEEE Communication Magazine, ol., pp , Decembe [] A. Peled and A. Ruiz, Fequency domain data tanmiion uing educed computationally complexity algoithm, in Poceeding of IEEE Intenational Confeence of Acoutic, peech and ignal Poceing, (Dene), pp , Apil [4] V.. Abhayawadhana and I. J. Waell, Fequency caled time domain equalization fo OFDM in boadband fixed wiele acce channel, in Poceeding of the IEEE Wiele Communication and Netwoking Confence, to be peented. [5] T. M. chmidl and D. Cox, Robut fequency and timing ynchoniation fo OFDM, IEEE Tanaction on Communication, ol. 45, pp , Decembe 199. [6] P. H. Mooe, A technique fo othogonal fequency diiion multiplexing fequency offet coection, IEEE Tanaction in Communication, ol. 42, pp , Octobe [] Y. Zhao and.-g. Haggman, Intecaie intefence elf-cancellation cheme fo OFDM mobile communication ytem, IEEE Tanaction on Communication, ol. 49, pp , July [8] H. Nogami and T. Nagahima, A fequency and timing peiod acquiition technique fo OFDM ytem, in Poceeding of Peonal, Indoo and Mobile adio Communication (PIMRC), pp , petembe [9] J.-J. an de Beek and M. andell, M etimation of time and fequency offet in OFDM ytem, IEEE Tanaction on ignal Poceing, ol. 45, pp , July 199. [10] J. Amtong, Analyi of new and exiting method of educing intecaie intefeence due to caie fequency offet in OFDM, IEEE Tanaction on Communication, ol. 4, pp , Mach [11] H. Kobayahi, A noel coheent demodulation fo M-QAM OFDM ignal opeating in the but mode, in Poceeding of the IEEE Vehicula Technology Confeence (Fall), ol., pp , eptembe [12] H. Mey, M. Moeneclaey, and. Fechtel, Digital Communication Receie; ynchonization Channel Etimation and ignal Poceing. John Wiley & on Inc., [1] V. Eceg, K. Hai, et al., Channel model fo fixed wiele application, tech. ep., IEEE Boadband Wiele Acce Woking Goup, Januay [14] K. Pahlaan and A. eeque, Wiele Infomation Netwok. New Yok: J. Wiley & on, 1995.