Novel Sampling Clock Offset Estimation for DVB-T OFDM
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1 Novel Samplng Cloc Offset Estmaton for DVB-T OFD Hou-Shn Chen Yumn Lee Graduate Insttute of Communcaton Eng. and Department of Electrcal Eng. Natonal Tawan Unversty Tape 67 Tawan Abstract Samplng cloc offset estmaton and compensaton are mportant problems n an OFD system. Samplng cloc offset can cause a severe drft n symbol-tmng thus causng nter-carrer and nter-ofd-symbol nterference. In ths paper we propose a novel samplng cloc offset estmator for OFD systems that use scattered plots. The proposed algorthm maes use of the receved plot phases and the least-squares algorthms. Smulaton results show that when appled to the DFB-T standard the performance of the proposed estmator s very accurate and robust aganst multpath fadng and Doppler Spread. I. INTRODUCTION Terrestral Dgtal Vdeo Broadcastng (DVB-T) s a next-generaton standard for wreless broadcast of PEG- vdeo []. In order to provde the hgh data rate requred for vdeo transmsson concatenated-coded orthogonal frequency dvson multplexng (OFD) has been adopted nto DVB-T. In an OFD system synchronzaton ncludes symbol tmng estmaton carrer frequency offset estmaton and samplng cloc offset estmaton and compensaton. Symbol-tmng and frequency offset estmaton for OFD are wdely dscussed n the lterature. However relatvely few results are avalable for the estmaton of samplng cloc offset. Samplng cloc offset estmaton and compensaton are mportant n an OFD system because samplng cloc offset can cause a severe drft n symbol-tmng thus causng nter-carrer and nter-ofd-symbol nterference. The problem s especally severe when a large number of subcarrers s used. For example n DVB-T wth 48 sub-carrers (K mode) f the samplng cloc offset s parts per mllon () of the samplng tme duraton the resultng drft s about 77 samples per second. Therefore samplng cloc offset synchronzaton s an mportant ssue that needs to be solved for a practcal OFD system. In ths paper we propose an algorthm usng the DVB-T frequency-doman scattered plot pattern shown n Fg. [] for samplng cloc offset estmaton. Smulaton results show that the proposed algorthm can relably estmate the samplng cloc offset from to. The proposed algorthm can be used n AWGN or tme-varyng fadng frequency-selectve fadng channels. Furthermore channel estmaton or decson feedbac tracng loop [][3] are not requred therefore the proposed algorthm has farly low complexty. Smulaton results show that the estmator proposed n ths paper s very accurate and robust aganst multpath fadng and Doppler spread. II. SYSTE SPECIFICATIONS Although DVB-T allows flexble choce of many transmsson parameters n ths paper we assume that the DVB-T transmtter uses OFD wth 6-level quadrature ampltude modulated (6 QA) subcarrers. The number of subcarrers s N = 48 (K mode) and scattered plots are present n the OFD symbols as shown n Fg.. For K mode the useful part of an OFD has a duraton of T U = µs (values for 6Hz channels). The length of the cyclc prefx (CP) s assumed to be.5t U therefore the number of CP samples (chps) n an OFD symbol s = 56. The OFD sgnal s transmtted to the recever va the wreless channel whch s assumed to be a multpath Raylegh fadng channel corrupted by addtve whte Gaussan nose (AWGN). The multpath fadng channel s modeled usng the modfed Jaes fadng model [5] wth a carrer frequency of 5Hz. At the recever the receved sgnal s frst down-converted to the baseband fltered and sampled and the three ey steps of synchronzaton shown n Fg. are next performed. The sgnal s frst processed by the coarse symbol tmng and frequency offset estmators. The frequency offset s next compensated and the result s processed by the proposed samplng cloc offset estmator. III. CHANNEL DELAY ESTIATION FOR OFD Consder for the tme beng an OFD transmsson system wth N subcarrers operatng over an addtve whte Gaussan nose (AWGN) channel wth a constant delay of α samples where.5 α.5 n whch s the number of samples n the cyclc prefx (CP). Further assume that the two-sded power spectral densty of AWGN s N /. The receved frequency-doman subsymbol Y s related to the transmtted subsymbol X by [4] πα / N Y = X e + n () where and are the OFD symbol and subcarrer ndces respectvely and n s the addtve Gaussan nose. Assumng that n the -th OFD symbol plot subsymbols are avalable at subcarrers P where P s the number of plot subsymbols an estmate of α can be obtaned as a functon of Y [ Y LY P ] and X [ X L X P ]. The estmator s gven by K max=74 f K Kmn= Kmax=687 f 8K TPS plots and contnual plots between Kmn and Kmax are not ndcated boosted plot data Fg. The plot nserton pattern of DVB-T system. symbol 67 symbol symbol symbol symbol /3/$7. 3 IEEE. 7
2 Freq. RF RX ADC r[n] Coarse Tmng Frequency compensaton Samplng Cloc. P P P P α () P P N = ( ; ) = = Y X π P P P = = where P = p nπ (3) n whch Y [ ] Im X = [ ] p tan Y Re (4) X and n s an nteger that satsfes n.5) π < p p < ( n.5 π. (5) ( + ) Note that the quantty n () s the slope of the least-squares (LS) best-ft-lne of P aganst where P defned n (3) s an estmate of πα/n usng Y as observaton and X as reference. Assumng that there s no samplng cloc offset the receved plot subsymbol n () can be re-wrtten as θ πα / N Φ Y Xe = Ae + Be (6) where A = E X B s a Raylegh dstrbuted random varable wth mean-square N and Φ s random varable that s ndependent of B and unformly dstrbuted n [π]. Note that n (6) we have omtted tme ndces whenever approprate. From (6) we have sn( / ) sn Φ tan A πα N + B θ = ( ) Acos( πα + B cosφ sn(πα/ N + Φ) = tan tan( πα + ( A/ B)cos (πα + cos(πα cosφ (7) Usng a frst approxmaton (7) becomes θ = πα + + tan (πα B sn(πα / N + Φ) (8) Acos (πα / N ) + B cos(πα / N )cosφ Defnng the phase estmaton error caused by AWGN as e = + tan (πα B sn(πα / N + Φ) (9) Acos (πα / N ) + B cos(πα / N )cosφ Fg.. Bloc dagram of the synchronzaton. the mean and varance of the estmator n () can be computed. Example numercal values are shown n Table for α= and N = 48. It can be seen from Table that the estmator n () s approxmately unbased and has very small varance even at low sgnal-to-nose rato (SNR) when there s no samplng cloc offset. In the presence of samplng cloc offset the receved plot sub-symbol can be approxmated by [] Y Ts [π ( + α)] N T = e n) snc( X + n + n () where snc(x)=sn(πx)/πx n s the same addtve Gaussan nose as () s the samplng cloc offset normalzed by the samplng perod of the transmtter (to be formally defned n the next secton) and n s addtonal nose caused by samplng cloc offset caused wth varance [] gven by π Var[ n ] ( ). () 3 Note that << n most practcal cases thus snc() and n. In ths case the effect of samplng cloc offset can be approxmated smply as an addtonal phase rotaton. It can therefore be argued that n the AWGN channel the estmator n () s stll accurate even n the presence of samplng cloc offset. IV. PROPOSED SAPLING CLOCK OFFSET ESTIATOR We next consder the estmaton of samplng cloc offset n a multpath fadng envronment. Denotng the samplng nterval n the recever as T the normalzed samplng cloc offset s defned as T T = () T where T s the sample-perod of the transmtted OFD sgnal. The effect of samplng cloc offset can be roughly treated as an addtonal channel delay that vares wth the OFD symbol ndex. athematcally wth samplng cloc offset the -th OFD symbol roughly experences a delay (n samples) of α = α + (N + ) (3) Table ean and standard devaton of estmaton error of () A /N 5 db db 5 db db mean (samples) e Standard devaton (samples) /3/$7. 3 IEEE. 73
3 where α s the ntal delay experenced by the -th OFD symbol. Snce the estmator n () s relatvely unaffected by samplng cloc offset as prevously mentoned we can therefore buld upon the estmator n () and obtan a new estmaton algorthm for. The ey concept s to estmate α n several OFD symbols and compute the slope of the LS best-ft-lne of these tmng estmates aganst the OFD symbol ndex. In dong so specal measures are necessary to account for the random phase rotaton ntroduced by the multpath fadng channel so that the resultng estmate s robust aganst multpath fadng. The proposed algorthm s as follows: Step : Use () to compute α = α ( Y + 4 ; Y ) = F =. Step : Compute α α = = = = 4( N + ) = = (4) for = F. Step 3: Obtan a hstogram of L F. The samplng cloc offset estmate s the mode (value wth maxmum occurrng frequency) of the hstogram. Note that Step estmates the delay experenced by the (+4)-th OFD symbol usng Y +4 as observaton and Y as reference. In other words at each plot subcarrer the phase of Y +4 /Y s computed and substtuted nto (). Ths s because n DVB-T the plot patterns n the -th and (+4)-th OFD symbols are the same for all and. Usng Y nstead of X +4 as reference accounts for the random phase rotaton ntroduced by the multpath fadng channel and provdes a noncoherent estmate of the delay experenced by the (+4)-th OFD symbol. In step n (4) s the slope of the LS best-ft-lne of α aganst and s an estmate for based on the observatons Y +4 =. Note that the estmaton accuracy of mproves as ncreases. However when the channel Doppler-spread s large a small s desrable. Therefore the choce of provdes a trade-off between estmaton accuracy and robustness aganst Doppler-spread. Fnally Step 3 provdes the fnal estmate from the nosy estmates L F. The method descrbed n Step 3 s chosen emprcally based on some prelmnary smulatons. Other approaches e.g. tang the average of L F are also possble. However the method descrbed n Step 3 seems to yeld the best results. V. SIPLIFICATIONS FOR THE AWGN CHANNEL The proposed samplng cloc offset estmaton algorthm can be greatly smplfed when the OFD system s operatng n an AWGN channel. Frst n Step we can smply compute the phases of the receved scattered plots to obtan α wthout worryng about random phase rotatons ntroduced by the multpath fadng channel. Second n Step we can set F = thus elmnatng the need for Step 3. The resultng smplfed algorthm for the AWGN channel s as follows: Step : Use () to compute α = α( Y + 4 ; X ) = =. Step : Compute α α = = = = 4( N + ) = = for =. Accurate estmaton s achevable as long as s suffcently large. Due to dmnshng returns when s suffcently large only a margnal performance mprovement s achevable by further ncreasng. VI. SYBOL TIING AND FREQUENCY OFFSET ESTIATION Although the focus of ths paper s samplng cloc offset estmaton symbol-tmng and frequency-offset estmaton are also performed n the computer smulatons. The algorthms for symbol tmng and frequency offset estmaton are descrbed as follows :. Symbol Tmng Estmaton [6] Symbol tmng estmaton s accomplshed by explotng the cyclc nature of OFD symbols. We defne the autocorrelaton functon of the receved tme-doman OFD sgnal as = * [] n = r[ n ] r [ n N ] x (5) and compute an average autocorrelaton functon defned as L x [ n] x[ n l( N + ) ] (6) L l= where L s the number of OFD symbols observed for symbol-tmng estmaton. Assumng that the receved sgnal has been frame-synchronzed the optmal tmng (sample ndex of the begnnng of the frst OFD symbol) s gven by n arg max x[ n] δ (7) n< N where δ s an nteger margn ntroduced to to ensure that the constant delay α s wthn the range of.5 α.5.. Frequency Offset Estmaton and Compensaton After symbol-tmng s determned the frequency offset s next estmated and compensated for usng a three-step frequency synchronzaton algorthm. Assumng that the frequency offset between the transmtter and recever oscllators s gven by f = ( K + b) (8) T U where K s an nteger and.5 b <.5. It can be easly verfed that when there s no nose the phase dfference between a sample n the cyclc prefx of a receved OFD /3/$7. 3 IEEE. 74
4 symbol and the sample T U seconds later s roughly πb. Therefore an estmate for b s gven by b Arg( x[ n ]) (9) π where Arg(x) s the phase angle (modulo π) of x. On the other hand K can be estmated by mang use of the contnual plots defned n DVB-T. We defne the average correlaton coeffcent as * R( + p + ) R ( p + ) ρ ( ) () R( + + ) R( + ) p where <> denotes averagng over the contnual plot subcarrer ndex p. It can be easly argued that when there s no nose ρ( ) s maxmzed when = K. Therefore a reasonable estmate for K s gven by K max ρ () ( ) The estmated frequency offset s then gven by (K +b )/T U Hz. Prelmnary smulatons show that when b.5 separately usng (9) and () for frequency offset estmaton may result n poor performance n the presence of nose. For example f K + b =.45 and K = 3 then the error n K cannot be completely compensated because b.5. In order to solve ths problem n ths paper the recever frequency synchronzaton s done n three steps. In the frst step (9) s evaluated to obtan an estmate b. The receved sgnal s then frequency-compensated by b /T U Hz to mae the resdual frequency offset approxmately equal to a multple of the carrer spacng. In the second step () s evaluated to obtan an estmate K and the receved sgnal s frequency-compensated by K /T U Hz. Fnally (9) s evaluated agan to recover the remanng frequency offset. VII. SIULATION RESULTS The samplng cloc offset estmaton algorthm proposed n ths paper s evaluated usng computer smulatons. The transmtter s smulated accordng to the DVB-T standard. The wreless channel s modeled as Raylegh multpath fadng channel wth exponental power-delay profle wth RS delay spread of 5. µs and corrupted by AWGN. The carrer frequency offset s.5/t U. At the recever the receved sgnal s fltered and sampled at a rate of /T. Coarse symbol-tmng recover and frequency-offset compensaton s next performed. Samplng cloc offset estmaton s fnally performed usng the proposed method wth F=63 and = n the fadng channel and F= and =3 n AWGN channel. The root-mean-square (RS) resdual samplng cloc offset s shown n Fg. to Fg.3 for the AWGN quas-statc frequency-selectve and tme-varyng frequency-selectve fadng channels as functons of E s /N for dfferent values of where E s s the average symbol energy per subcarrer. In Fg. 3 the maxmum normalzed Doppler-spread of the channel s f m T U =.5 whch corresponds to a vehcle speed of m/h. It can be seen that for the frequency-selectve fadng channels at hgh SNR the RS resdual samplng cloc offset s less than even when s as hgh as. p The channel bt error rate (BER) s plotted as functons of E s /N n Fg. 4 for frequency-selectve fadng channels wth f m T U = (quas-statc) and f m T U =.5. The samplng cloc offset s = 5. In each case three recevers are smulated: ) a recever that estmates the samplng cloc offset usng the proposed approach and uses the snc nterpolaton for compensaton (labeled as PROPOSED ) ; ) a recever wth perfect samplng cloc offset compensaton (labeled as PERFECT ); and 3) a recever (labeled as NO SYNC ) wthout samplng cloc offset compensaton n each frame (68 OFD symbols). All recevers use the same symbol-tmng and frequency offset estmaton algorthms. It can be seen that f uncompensated a samplng cloc offset of 5 causes sgnfcant degradaton n BER. Furthermore the proposed algorthm s very effectve and acheves almost the same performance as the perfect case. Fnally the proposed algorthm s robust aganst Doppler-spread because t acheves roughly the same performance for both values of f m T U. Fg. 3 - RS Resdual Samplng Cloc Offset () Es/N RS resdual samplng cloc offset () n AWGN channel. RS Resdual Samplng Cloc Offset () Es/N Fg. RS resdual samplng cloc offset () n a frequency selectve fadng channel wthout Doppler effect. Ths s equal to the RS samplng cloc offset estmaton error /3/$7. 3 IEEE. 75
5 Fg. 3 RS Resdual Samplng Cloc Offset () Es/N (db) RS resdual samplng cloc offset () n a frequency selectve fadng channel wth maxmum Doppler-spread f mt U =.5. REFERENCES [] ETSI Dgtal Vdeo Broadcastng: Framng Structure Channel codng and odulaton for Dgtal Terrestral Televson European Telecommuncaton Standard EN3744 Aug [] Baoguo Yang Zhengxn a and Zhgang Cao L-Orented DA Samplng Cloc Synchronzaton for OFD Systems Internatonal Conference on Communcaton Technology Vol. pp [3] Baoguo Yang K. B. Letaef Roger S. Cheng and Zhgang Cao An Improved Combned Symbol and Samplng Cloc Synchronzaton ethod for OFD Systems IEEE Wreless Communcaton and Networng Conference WCNC 999 Vol. 3 pp [4] Yong-Jung Km Dong-Seog Han and K-Bum Km A New Fast Symbol Tmng Recovery Algorthm for OFD Systems IEEE Transactons on Consumer Electroncs Vol.44 No.3 pp.34-4 August 998. [5] P. Dent G.E. Bottomley and T. Croft Jaes fadng model revsted Electroncs Letters Vol.9 No.3 pp.6-63 June 993. [6] Rchard van Nee Ramee Prasad OFD for Wreless ultmeda Communcatons Artech house. BER - FADING NO SYNC f T =.5 m u FADIING NO SYNC f m = FADING PROPOSED f m =.5 FADING PROPOSED f T = m u FADING PERFECT f T =.5 m u FADING PERFECT f m = Es/N (db) Fg. 4 BER of perfect samplng cloc compensaton the proposed algorthm and wthout samplng cloc offset compensaton n frequency selectve fadng channels. VIII. CONCLUSION In ths paper we propose a samplng cloc offset estmaton algorthm usng the DVB-T frequency-doman scattered plot pattern. The algorthm bulds upon a least-squares estmator for channel delay and can be used n AWGN or tme-varyng fadng frequency-selectve fadng channels. Channel estmaton or decson feedbac tracng loop [][3] are not requred therefore the proposed algorthm has farly low complexty. Smulaton results show that the proposed algorthm the estmator proposed n ths paper s very accurate and robust aganst multpath fadng and Doppler spread and can relably estmate the samplng cloc offset from to /3/$7. 3 IEEE. 76
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