On Timing Offset and Frequency Offset Estimation in LTE Uplink *

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1 On mng Offset and Frequency Offset Estmaton n LE Uplnk * Juan Lu, Bn Wu, and Pngan L School of Informaton Engneerng, Wuhan Unversty of echnology, No.22 Luosh Road, Hongshan Dstrct,Wuhan, Hube, Chna, Lujuan000@26.com, wubn460@hotmal.com, pngan_lwhut@yahoo.com.cn Abstract. In ths paper, the tmng offset and frequency offset estmaton n LE uplnk s studed. he approaches proposed are based on the demodulaton reference sgnals (DMRS) n PUSCH for FDD mode. Wth the channel estmaton n the frequency doman at the recever by usng the two DMRS,.e., DMRS located n two OFDM symbols, wthn one sub-frame, tmng offset estmaton s conducted by explorng the phase shft between dfferent sub-carrers for each DMRS, whle the frequency shft estmaton s mplemented by studyng the phase rotaton between the two DMRS for each sub-carrer. Statstcal average s used to enhance the performance of estmaton. Smulaton results demonstrate that the proposed algorthms can offer satsfactory performance even at relatvely low sgnal to nose ratos n the addtve whten Gaussan nose envronments. Keywords: Channel estmaton, tmng offset, frequency offset, LE. Introducton By the end of 2004, the thrd Generaton Partnershp Project (3GPP) started the 3G long term evoluton (LE) project to ensure ts long-term comparatve advantage of wreless standards. In LE systems, the uplnk transmsson scheme s based on sngle-carrer frequency dvson multple access (SC-FDMA) transmsson wth cyclc prefx[,2].compared wth orthogonal frequency dvson multple access (OFDM) scheme, a promnent advantage of SC-FDMA over OFDM s that ts transmtted sgnal has a lower peak-to-average power rato (PAPR)[3]. Nomnally SC-FDMA leads to a sngle-carrer transmt sgnal, n fact, the sgnal s based on multple frequency bns for every symbol and s under the nfluence of frequency offset and tmng errors. hs s because that mperfect synchronzaton can generate nter-carrer nterference (ICI) and nter-symbol nterference (ISI), thus wll nduce both co-channel and nter-channel nterference[4]-[6]. Moreover, carrer frequency synchronzaton for the uplnk of SC-FDMA system s more dffcult, snce the frequency recovery for one user may result n the msalgnment of the other synchronzed users [7]-[9]. * hs work s supported by the Natonal Specal and Important Project under Grant: No. 2009ZX P. Sénac, M. Ott, and A. Senevratne (Eds.): ICWCA 20, LNICS 72, pp , 202. Insttute for Computer Scences, Socal Informatcs and elecommuncatons Engneerng 202

2 266 J. Lu, B. Wu, and P. L Untl now, several tmng and frequency synchronzaton technques for LE uplnk system have been studed [0]-[2]. [0] has proposed an accurate tmng and frequency offsets estmaton algorthm for SC-FDMA uplnk, however, the work only consders the tmng and frequency offsets of a new user enterng the system and assume all the other users have already been perfectly synchronzed. In our work, we should consder the tmng and frequency offsets of all actve users. In [], a maxmum-lkelhood (ML) based jont channel and frequency offset estmaton algorthm for SC-FDMA system s proposed usng one tranng block. he algorthm has good estmaton performance and fast convergence rate. However, the computatonal complexty s prohbtvely hgh due to too much matrx nverson calculaton, partcularly when the number of sub-carrer s large. he tmng synchronzaton method proposed n [2] s based on a raw channel estmaton usng the soundng reference sgnal (SRS) of the respectve channels for each antenna and tme slot n PUCCH, PUSCH. Frst the phase devaton between neghborng sub-carrers s calculated, then a weghted averagng n MAC layer s carred out to convert the phase nto a tme offset estmaton value. hs algorthm has good estmaton performance over a large number of samples. However, t just consders the phase devaton between adjacent sub-carrers, whle we wll explore n ths paper all the phase devatons between a sub-carrer couple wth m (m s an nteger larger or equal to ) sub-carrer nterspacng to acheve a more accurate tme offset value by averagng the estmates correspondng to dfferent and possble m values. he method to present n the followng sectons s based on channel estmaton by usng DMRS n PUSCH n LE uplnk. Wth effcency n computaton, the approach shows hgh accuracy n estmaton even at a relatvely low SNR. 2 System Model 2. DMRS Sequence n LE Uplnk he DMRS postons n a sub-frame of a LE system n the frequency dvson duplex (FDD) s gven n Fg.. In LE FDD, each rado frame of 0ms conssts of 20 slots of length 0.5ms, numbered from 0 to 9[3]-[4].A sub-frame s defned as two consecutve slots each consstng 2 or 4 OFDM symbols, dependng on whether normal or extended cyclc prefx s used. In PUSCH, the plot occupes the fourth SC-FDMA symbol n each slot of a sub-frame wth normal cyclc prefx. he two plot sequences n a sub-frame are the same. 6ORW PV 6ORW PV '056 6XEIUDPHPV '056 GDWD Fg.. DMRS n LE uplnk

3 On mng Offset and Frequency Offset Estmaton n LE Uplnk 267 he DMRS for PUSCH n the frequency doman wll be mapped to the same set of physcal resource blocks (PRB) used for the correspondng PUSCH transmsson wth the same length expressed by the number of sub-carrers. 2.2 Structure of Our Proposed Algorthm he smplfed block dagram of our proposed algorthm n LE SC-FDMA system s llustrated n Fg.2. At the transmtter n base-band, the bnary nformaton bts are frstly grouped and mapped to the 6QAM symbol before the SC-FDMA modulaton. o generate a SC-FDMA symbol, an M-pont DF s appled to a group of 6QAM symbols before mappng to consecutve M sub-carrers at the nput of an N-pont IFF operator. Furthermore, Cyclc Prefx (CP) wth a length larger than channel maxmum delay s added. At the recever, the CP s removed from receved symbol frst. After N-pont FF and sub-carrer de-mappng, channel estmaton s carred out to estmate tme offset and frequency offset. Fg. 2. System model of our proposed algorthm n base-band 3 mng Offset Estmaton From Fg., we can see that these are two DMRS symbols n each sub-frame. In the tme-doman, each DMRS can be denoted by a -dmensonal samplng vector N x( n) = [ x(),..., x( NRS)], =,2, where NRS s the length of the demodulaton reference sgnal. If there s a tmng offsetτ, then the correspondng reference sgnal n the frequency-doman at the recever can be wrtten as Y( k) = exp( j2 πτ k / N) H ( k) X ( k) + W( k), =, 2, k = 0,, M () where H ( k) s the channel frequency response of the th DMRS wthout tme offset, W( k) = FF( w ( n)), w( n ) denotes the addtve whten Gaussan nose (AWGN). In RS

4 268 J. Lu, B. Wu, and P. L (), τ s the normalzed tmng offset,.e., τ = τ / wth beng the samplng perod. From (), the least square channel estmaton based on DMRS can be mplemented by O Y ( k) H ( k) =, k = 0,..., M (2) X ( k) o present the proposed approach more explctly, let us consder the receved sgnal wthout AWGN. In ths case, the receved sgnal n the frequency-doman can be rewrtten as Y( k) = exp( j2 πτ k / N) H ( k) X ( k), =,2 (3) For the sgnal model (3), we have O H ( k) = exp( j2 πτ k / N) H ( k) = A exp( j2 πτ k / N) exp( jθ ), =, 2 (4) where A and θ denote the ampltude and phase of H (k). Wthout AWGN, the frequency response of channels wll be an accurate evaluaton by usng (4). Let us defne R ( k, k ) = ( H ( k )) ( H ( k ) O * O 2 2 = A exp( j2 πτ m/ N), =, 2 (5) And ϕ = 2 πτ m / N, =,2 (6) m, m= k k s the nterspacng between sub-carrer k and sub-carrer k 2. hen, where 2 we can get φ m, Im{ R ( k, k )} 2 = atan 2( ) = 2 πτ m/ N, =, 2 Re{ R ( k, k )} 2 (7)

5 On mng Offset and Frequency Offset Estmaton n LE Uplnk 269 where the functon atan2(*) s defned by y arctan( ) x > 0 x y π arctan( ) y 0, x < 0 x y π + arctan( ) y < 0. x < 0 atan 2( y, x) = x π y > 0, x = 0 2 π y < 0, x = 0 2 undefned y = 0, x = 0 he normalzed tme offset can be calculated as φ N τ 2π m he actual tme offset s gven by φm, N φm, τ = τ = = 2πm 2πmΔ (8) m, = (9) where Δ represents the nterspacng between each two neghborng SC-FDMA sub-carrers n the frequency doman. For a system wth 20MHZ bandwdth, Δ has a value of 5KHZ defned by 3GPP LE specfcatons []. he tmng offset calculated by usng (0) for model (3) s an accurate evaluaton value. In practce, however, AWGN should be consdered and (0) s an estmate for correspondng channel estmates by usng (2). In ths case, a second average can be further used over dfferent m to acqure a more precse tmng offset estmate. 4 Fractonal Frequency Offset Estmaton In ths secton, a channel estmaton based fractonal frequency offset estmaton approach n PUSCH s presented. It s well known that a frequency shft s equvalent to a phase rotaton n tme doman by assumng that the channel durng a sub-frame s fxed. hs assumpton s deal but s reasonable for the very short sub-frame duraton n LE. In deal AWGN envronments, the receved sgnals n tme-doman correspondng to the two DMRS n PUSCH, x ( n) and x ( ) 2 n, can be expressed by (0)

6 270 J. Lu, B. Wu, and P. L y ( n) = exp{ j2 πδ n/ N} x ( n) + v ( n) () y ( n) = exp{ j2 πδ ( n+ Q) / N} x ( n) + v ( n) (2) Where n = 0,, NRS, δ s a fractonal frequency offset normalzed by the sub-frame nterspacng Δ, v ( n) and v ( ) 2 n denote AWGN ntroduced n the receved sgnals. o present the proposed approach fractonal frequency offset estmaton, let us gnore the AWGN component for an deal wreless channel wth no any nose. In ths case, the receved sgnal correspondng to the two DMRS n a sub-frame can be expressed, respectvely, by (3) and (4). x ( n) = exp{ j2 πδ n/ N} x ( n) (3) x ( n) = exp{ j2 πδ ( n+ Q) / N} x ( n), n =, 2,..., N RS (4) 2 2 In (4), Q denotes the ntegral samplng pont devaton between the frst samplng ponts of the two reference sgnals. he value of Q s decded by the bandwdth of LE system. For bandwdths of 5MHz, 0MHz and 20MHz, Q are 3840, 7680 and 5360, respectvely. After N -pont FF operaton at the recever, the output of the reference sgnal n frequency-doman correspondng to (3) and (4) can be wrtten as And N = π + δ n= 0 X ( k) exp{ j2 ( k ) n/ N} x ( n) = X ( k + δ ) (5) X ( k) = exp{ j2 πδq/ N} X ( k + δ ) (6) 2 2 In practce, the receved sgnals wll suffer from the nfluence of the multpath propagaton. Hence the receved sgnal components n the frequency-doman correspondng to (5) and (6) after the FF converson can be further expressed as X ( k) = H ( k) X ( k + δ ) (7) X ( k) = exp{ j2 πδq/ N} H ( k) X ( k + δ ) (8) Snce the transmtted two DRMS are the same n one sub-frame, and we can also assume that the channel durng a sub-frame s fxed, the fractonal frequency offset value can be obtaned by calculatng

7 On mng Offset and Frequency Offset Estmaton n LE Uplnk 27 N N δ = atan 2([ [ H ( k)] H ( k)]) 2 N 2π Q k = 0 (9) Where N ΔN df = δδ = a tan 2([ [ H ( k)] H ( k)]) 2 2π Q N H k = 0 X ( k) =, =,2 X ( k + ) (20) δ (2) In practce, we do not know X ( k + δ ) for each DMRS. In addton we have to consder the effects of AWGN. herefore, we use the followng estmates n (20) to get the fractonal frequency offset estmates,.e. ˆ Y ( k) H =, =,2 X ( k) For a system wth a bandwdth of 20MHZ, Δ= 5KHz. he range of fractonal frequency offset estmaton algorthm can reach[, ] and the correspondng 5 5 range of the actual frequency offset s [ KHz, KHz]. (22) 5 Numercal Examples In ths secton, performance of the proposed tmng-offset and frequency offset estmaton algorthms for LE system s evaluated through smulatons. he deal AWGN channel s assumed. A 6QAM-SC-FDMA system wth a samplng frequency of 30.72MHZ s consdered pont FF/IFF wth sub-carrer nterspacng 5KHz s used. he lengths of CP are 60 samples n the frst SC-FDMA symbol and 40 samples n the rest sx symbols, respectvely. Durng the smulatons, 2 SC_FDMA symbols and 2 reference sgnals n each sub-frame are generated. 00 resource blocks (RB) are adopted for PUSCH data transmsson. hat means that durng the 2048 sub-carrers, 200 sub-carrers are used for plots and data transmsson. In Fg.3, a tmng offset of length 00 samplng perods are set, the root mean square error (RMSE) of the SC-FDMA symbol tmng offset estmaton measured n samples s plotted aganst the sgnal to nose rato (SNR). As for the low SNR case the estmaton s very accurate too, the estmaton error s as low as samplng perods n SNR of 0dB. hen n a hgh SNR of 30dB, the error s reduced to 0.00 samplng perods, almost to zero. hs means that proposed tmng offset estmaton algorthm can offer a very excellent performance n AWGN channel.

8 272 J. Lu, B. Wu, and P. L Fg. 3. mng offset n terms of the RMSE vs. the SNR, measured n numbers of samplng perods Fg. 4. Frequency offset n terms of the RMSE vs. the SNR, measured n numbers of sub-carrer spacng

9 On mng Offset and Frequency Offset Estmaton n LE Uplnk 273 In Fg.4, a frequency offset of 0.05 sub-carrer spacngs are set n ths smulaton example. he RMSE of the SC-FDMA symbol frequency offset estmaton measured n sub-carrer spacng s plotted aganst the SNR. It can be seen that the proposed fractonal frequency offset estmaton approach also demonstrates satsfed performance n AWGN even at relatvely low SNR values. 6 Concluson Remarks he paper deal wth the tmng and frequency offset estmaton n PUSCH of LE systems. A tmng offset algorthm and a frequency offset estmaton approach are presented. Both the approaches are based on the channel estmaton n the frequency-doman and exhbt low costs n computaton. he proposed algorthm show excellent performance n deal AWGN. In addton, the approaches can be also appled to the soundng channel and PUCCH channel for tmng error estmaton and frequency offset estmaton. References. 3GPP S 36.2 V8.8.0: Evolved Unversal errestral Rado ACCES (E-URA); Phyccal Channel and modulaton (September 2009) 2. R EURA SC-FDMA Uplnk Plot/Reference Sgnal Desgn. 3GPP RAN WG meetng 47, November 6-0 (2006) 3. Myung, H.G., Ln, J., Goodman, D.J.: Sngal Carrer FDMA for Uplnk Wreless ransmsson. IEEE Vehcular ech. Magazne (September 2008) 4. Wang, Y., Zheng, A., Zhang, J., Yang, D.: A Novel Channel Estmaton Algorthm for Soundng Reference Sgnal n LE uplnk ransmsson, December 7 (2009) 5. Khalwat, M., Reza Soleyman, M.: Enhanced Uplnk Frequency Synchronzaton Algorthm for OFDM Systems n a Mult-Path Fadng Envronment. In: IEEE Conference on Electrcal and Computer Engneerng, November 5, pp (2007) 6. sa, Y., Zhang, G.: me and Frequency Synchronzaton for 3GPP LE Long erm Evoluton Systems. In: IEEE Vehcular echnology Conference, 65th VC 2007-Sprng (Aprl 2007) 7. Lee, J.-H., Km, S.-C.: me and Frequency Synchronzaton for OFDM Uplnk System usng the SAG Algorthm. IEEE rans. Commun. 6(4) (Aprl 2007) 8. Sun, P., Zhang, L.: Low Complexty Plot Aded Frequency Synchronzaton for OFDMA Uplnk ransmsso. IEEE rans. Commun. 8(7) (July 2009) 9. Hoeher, P., Kaser, S., Robertson, P.: Plot symbol aded channel estmaton n tme and frequency. In: Proc. of Communcaton heory Mn-Conference wthn IEEE Global elecommuncatons Conference, pp (997) 0. Morell, M.: mng and frequency synchronzaton for the uplnk of an OFDMA system. IEEE rans. Commun. 52(2), (2004)

10 274 J. Lu, B. Wu, and P. L. Pun, M., Morell, M., Kuo, C.: Maxmum-lkelhood synchronzaton and channel estmaton for OFDMA uplnk transmssons. IEEE rans.commun. 54(4), (2006) 2. ack, J., Kratzert, A.: UL mng Algnment based on PUCCH, PUSCH and SRS, August 25 (2009) 3. Wang, Y., Zheng, A., Zhang, J., Yang, D.: A Novel Channel Estmaton Algorthm for Soundng Reference Sgnal n LE uplnk ransmsson. In: IEEE Conference on Communcatons echnology and Applcatons, December 7, pp (2009) 4. Hou, X., Zhang, Z., Kayama, H.: DMRS Desgn and Channel Estmaton for LE_Advanced MIMO uplnk, July 25 (200)