Symbol Synchronization at the BPSK-OFDM Receiver

Transcription

1 Symbol Synchronzaton at the BPSK-OFDM Recever Cheng-Yng Yang, Gwo-Ruey Lee, Wen-Hu Kuan and Jyh-Horng Wen, 3 cyang@nfu.edu.tw Department of Computer Scence and Informaton Engneerng, atonal Formosa Unversty o.64, Wen-Hwa Rd., Hu-We, Yun-Ln, Tawan, R.O.C. The Insttute of Electrcal Engneerng, atonal Chung Cheng Unversty o.68, Unversty Rd., Mn-Hsung, Cha-Y, Tawan, R.O.C. 3 The Insttute of Communcaton Engneerng, atonal Ch an Unversty o., Unversty Rd., Pu-l, an-tou, Tawan, R.O.C. Abstract OFDM has been proposed for IEEE 8.6, WMax system. At the recever, the knowledge of symbol tmng s requred for the sgnal demodulaton n the system. Wthout symbol synchronzaton, the effects of ISI wll degrade the system performance n the system. Ths paper proposes a non-data aded symbol synchronzaton algorthm employng the conjugate symmetry character n the BPSK-OFDM modulated sgnal. Under an AWG channel, based on the performance of synchronzaton error rate and the estmator mean square error, the proposed algorthm s wth a tremendous mprovement compared wth prevous proposed method. Besdes, under a multpath fadng channel, the performance on the estmator mean square error wth the proposed algorthm s smlar to that wth the prevous proposed one. However, the performance of synchronzaton error rate wth the proposed algorthm s better than that wth the prevous proposed method. Keywords: Symbol synchronzaton, Conjugate symmetry character, on-data-aded synchronzaton, OFDM systems I. Introducton WMax system wth nherent advantages n throughput, latency, spectral effcency and advanced antennae support has been proposed for the upcomng communcaton applcaton. Orthogonal frequency dvson multple (OFDM) technology s the major technology to provde provdes operators wth an. effcent means to overcome the challenges of non-lne-of-sght (LOS) propagaton n WMax. Obvously, t becomes sgnfcant n the future communcatons [-4]. Whle usng OFDM appled system, tmng estmaton s requred to demodulate the receved sgnal [-3, 5-9]. The recever requres the symbol boundares and the optmal tmng nstants to reduce the effects of ntersymbol nterference (ISI) [, 9]. Wthout correct tmng estmate, the system performance wll be degraded. Hence, symbol synchronzaton s a momentous ssue. Among the OFDM tmng estmate schemes, both data-aded and non-data-aded synchronzaton algorthms have been proposed [-7]. Based on a tranng symbol or plot, the robust and accurate symbol synchronzaton s guaranteed [-3, 5]. However, the throughput n those systems s decreased when the data-aded scheme s used. For the bandwdth effcency concerns, the non-data-aded schemes have been proposed [6-9, 7]. The OFDM symbols constructed wth cyclc prefx and data symbol could be used to fnd the peak correlaton and, then, the predcton to tmng and frequency offset can be made. Based on the second-order cyclostatonarty of the receved OFDM symbols, the estmator uses cyclc correlaton to explore the nformaton of symbol-tmng and frequency offset [7]. Besdes, the algorthm usng the rank behavor of certan autocorrelaton matrces constructed wth the receved sgnal s proposed to acheve the symbol synchronzaton [8]. The symbol tmng could be estmated when the autocorrelaton matrx wth a mnmum rank. Moreover, the estmator based on the maxmum correlaton of cyclc prefx and data symbol s used to make the estmaton [6]. Generally, the longer cyclc prefx performs better on the tmng and frequency offset estmaton n the OFDM system. Functonally, the cyclc prefx s descrbed to reduce the effects of ISI and ICI and ts length s suggested to be the quarter length of data symbol [-4]. Accordng to prevous works on OFDM synchronzaton, the ncreasng cyclc prefx length benefts the system performance. However, consderng wth the bandwdth effcency, the symbol synchronzaton could be fnshed wthout addng the extra length of cyclc prefx. In ths work, the conjugate characters of the bnary phase shft keyng (BPSK) modulated sgnal are employed to predct the tmng and frequency offset. As the prevous researches, the mnmum mean-squared error estmator s presented to fnd the symbol tmng offset n the synchronzaton [8]. In ths paper, the proposed algorthm uses the correlaton between the conjugated data wthn the slde wndows. When the maxmum correlaton happens, the tmng estmaton could be decded. Hence, n ths study, the conjugate symmetry character s derved for the OFDM symbol wth the BPSK mappng scheme. Also, the analyss on the synchronzaton error rate and estmator mean square error wth the proposed algorthm s presented based on the comparson wth Borjesson s algorthm [6]. The organzaton of ths paper s as follows. The system model and the conjugate symmetry character of BPSK-OFDM symbol are descrbed n Secton II. In Secton III, the proposed synchronzaton algorthm usng the conjugate symmetry character of BPSK-OFDM symbol s presented to determne the symbol tmng for the BPSK-OFDM system. The smulaton results are shown n Secton IV. Fnally, a concluson s gven n Secton V /7/$5. 7 IEEE.

2 II. The System Model and the Conjugate Symmetry Character of BPSK-OFDM Symbol OFDM system could be consdered as the one of frequency dvson multplex (FDM) technque that s acheved by subdvdng the avalable bandwdth nto multple channels [, 4]. The system s obtaned by usng parallel data transmsson. Then, each parallel data transmsson s modulated by dfferent carrer frequences usng phase shft keyng (PSK) or quadrature ampltude modulaton (QAM),.e., an OFDM sgnal contans a sum of subcarrers that are PSK or QAM modulaton. Also, OFDM can be treated as a modulaton technque wth the vew of the relaton between nput and output sgnals. To reduce the complexty of OFDM modem mplementaton, the fast Fourer transform (FFT) s employed to replace the banks of snusodal generator and the demodulaton sgnfcantly. In general, an OFDM system at least contans the functon of parallel transmsson, sgnal mappng and IFFT/FFT [-4]. Fg. llustrates the block dagram of the baseband, dscrete-tme FFT-based BPSK-OFDM systems model. Each parallel data s mapped wth BPSK scheme and, then, those data are modulated by an IFFT on -parallel subcarrers. The resultng OFDM symbol extended wth a cyclc prefx s serally transmtted over a dscrete-tme channel. The recever performs the nverse process of the transmtter, the data are retreved by a FFT and, then, demapped wth BPSK to obtan the estmated data. BPSK Mappng x IFFT s ( CP) s ( ) s ( ) P/S s ( k ) r( k) Channel S/P r ( CP) r ( ) r( ) FFT y BPSK De- Mappng Fg. The model of baseband, dscrete-tme BPSK-OFDM system Wthout tmng offset, the baseband dscrete-tme transmtted sgnal s (k) s as [5] π j nk s ( k) =,, x e k (), n n= where denotes the IFFT wndow sze, s (k) represents the kth sample of the th OFDM symbol, and x,n represents the nth subcarrer n the th symbol nterval. In ths equaton, x,n s a real value when BPSK mappng s used. The equatons of the IFFT output have the followng characters: π j nk π real s( k) = real x, ne = x, ncos( nk) n= n= π j nk π mag s( k) = mag x, ne = x, nsn( nk) n= n= π j n ( k ) π real s( k) = real x, ne = x, ncos( nk) n= n=, (-), (-), (-3) π j n ( k ) π mag s( k) = mag x, ne = x, nsn( nk) n= n=, (-4) where real(x) and mag(x) denote the real part and mage part of complex number x. In Eq., t s the character for the real and mage part of BPSK-OFDM symbol. Also, t can be expressed n Eq. (3). * s( k) = s ( k), k or, (3) where * ndcates the complex conjugate. It s clear n Eq. (3) that s (k) and s (-k) have the character of conjugate symmetry. Both s (k) and s (-k) are belonged to the th OFDM symbol. Hence, t s called as the conjugate symmetry character of BPSK-OFDM symbol. Wth ths character, the structure of BPSK-OFDM symbol wth cyclc prefx could be wrtten as that n Fg.. Cyclc Prefx OFDM symbol Data Symbol * * * * s( CP),, s() s(), s(),, s ( ), s( ), s( ),, s () Fg. The structure of BPSK-OFDM symbol wth the conjugate symmetry character Before demodulatng the receved OFDM sgnal, the recever has to make the symbol and frequency synchronzaton. Thus, the recever should remove the cyclc prefx. However, the synchronzaton should be done to remove the prefx. Once, tmng nformaton provded by the synchronzaton algorthm, one could exactly remove the prefx and use FFT to extract the transmtted data. Hence, synchronzaton s the most mportant work n the OFDM system. Actually, the carrer frequency synchronzaton algorthm n [9], for nstance, could be used to compensate the effect of frequency offset. In ths study, the carrer frequency synchronzaton s not consdered. In the next secton, the conjugate symmetry characters appled synchronzaton algorthm to obtan the symbol tmng of BPSK-OFDM symbol s proposed. III. The Proposed Synchronzaton Algorthm At the OFDM recever, the receved sgnal of the th OFDM symbol nvolves the symbol tmng offset can be wrtten as [6] ( τ ) r k = s k + w k, (4) where τ s the tmng shft and w(k) s Gaussan nose. Based on the conjugate symmetry character gven n Eq. (3), s (k) can be expressed as j, = s k A e θ, k k * j, θ, (5-) k s k = s k = A, ke, k or /, 3

3 s j, ( ) A e θ, (5-), (5-3) j,,, s A e θ (5-4) where A,k s the kth samplng ampltude for th symbol, and θ,k denotes the phase of s (k). The proposed algorthm uses the conjugate symmetry character gven n Eq. (5-) to determne the poston of the symbol tmng. In Eq. (4) and Eq. (5), when sample r (/+τ) s the central pont between the two opposte samples r (/+τ-m) and r (/+τ+m), t has the character gven n Eq (6). r + τ + m r + τ m = A, m, k. (6) Eq. (6) results just one avalable tmng r (/+τ). When the avalable tmng r (/+τ) s estmated, the correct symbol tmng τ could be obtaned. In order to obtan the poston of the symbol tmng r (/+τ), the proposed algorthm uses slde wndows wth length /- to fnd the poston of the symbol tmng. Frst, multply the correspondng symmetrc samples wthn the slde wndow to fnd the angle of the product and, then, store those data as Bk, = angle( r( k + ) r( k ) ), Bk, = angle( r( k + ) r( k ) ), (7) B = k, angle( r( k + ) r( k + ) ), where angle(x) denotes the angle of complex number x, B k ={ B k,, B k,,, B k,/- } s the set of these multplcatons. The mean of B k s E B angle r k m r k m L L L L { B k} = k, m = ( ( + ) ( )), (8) m= m= where L=/- s the length of slde wndows and the defned cost functon f{k} s defned as {} L f k = Bkm, E{ B k}. (9) L m = In the slde wndows, the central poston s located at the sample wth the ndex k. Wth the conjugate character, the mean of B k n the case k = /+τ can be derved as E B [ ] k k= /+ τ = E [ angle( r ( / + τ + m) r ( /+ τ m) )] = πε, () Also, the cost functon could be derved as f k ( k = / + τ ) ( ( / τ ) ( / τ )) { /+ } = E angle r m r m E B τ =. () Wth the conjugate symmetry relatonshp, when k=/+τ n the correspondng slde wndows, the cost functon f{/+τ} s zero and, then, the tmng offset could be found. Based on ths property, the proposed algorthm uses the slde wndows to obtan the mean of B k and the cost functon. In the observaton regon, the cost functon f {k} wth the mnmum value s chosen, and, then, the tmng offset τ could be obtaned wth the correspondng ndex k. Based on the proposed algorthm, smulatons are gven n the followng. IV. Smulaton Results Smulatons wth the proposed algorthm are performed over an AWG and the multpath fadng channel. The number of subcarrers and the length of the cyclc prefx were =64 and CP=6, respectvely. In each smulaton wth runnng tmes, t s assumed sgnal-to-nose power rato to be to 8 db, tmng delay to be 73 samples and then the actual symbol tmng s located n the 73-th sample. The multpath fadng channel s assumed three paths wth exponental power decayng. The performance s evaluated based on the synchronzaton error rate and the estmator mean square error and, then, the comparson s made wth the one based on Borjesson s estmaton [6]. The estmator mean square error s defned as MSE = t ( ˆ τ τ ), () t j= where τ s the actual symbol tmng, τˆ s the estmated symbol tmng and t s the number of smulaton tmes. Smulaton results under an AWG channel are shown n Fg. 3 and Fg. 4. Fg. 3 shows the hstograms of tmng estmaton wth Borjesson s algorthm (3-a) and that wth the proposed algorthm (3-b). Borjesson s algorthm uses the cyclc prefx and the tal of OFDM symbol to estmate the symbol tmng. When the movng wndow has a lttle devaton away from the correct poston, the correlaton s stll large wth comparng to the maxmum correlaton, t leads a wrong decson. In the other words, when the slde wndow shfts to the correct poston, the value of the correlaton vares slowly, t s not clear to determne the symbol tmng. When the nose s consdered, t easly makes erroneous judgments that the sample located around the correct poston s chosen as the symbol tmng. Therefore, the probablty of the synchronzaton error rate on Borjesson s estmaton s qute large. The proposed algorthm uses the conjugate symmetry character of the BPSK-OFDM symbol to estmate the symbol tmng. Thus, when the central pont of the slde wndows shfts to the correct poston, the value of the correlaton wll serously decay. Therefore, the correct poston can be obtaned easly. In the proposed algorthm, the conjugate symmetry character of a BPSK-OFDM symbol s located n r (/+τ) and r (τ) as the central pont of the two opposte samples. When r (/+τ) s the central pont of the two opposte samples, t has /- pars of self-symmetrcal ponts. Also, t could get a large correlaton n sample r (τ) and make erroneous judgments. The estmated symbol tmng wth the proposed algorthm s almost located at the actual symbol 4

4 tmng. The others are located n the 5-th, 4-th, -th, -th and 4-th sample ndvdually. The estmated symbol tmng s located n the 4-th sample when the central pont for two opposte samples s the sample r (τ). The estmated symbol tmng s located n the -th sample when the central pont for two opposton samples s the sample r + (τ). Moreover, the other samples are estmaton errors because of the nose. The number of detected symbol tmng wth the proposed algorthm s larger than that wth Borjesson s estmaton algorthm under an AWG channel. As shown n Fg. 4, the synchronzaton error rate and estmator mean square error wth the proposed algorthm s smaller than that wth Borjesson s estmaton algorthm under an AWG channel. The reason s that the number of used samples wth the proposed algorthm s larger than that wth Borjesson s method. Smulaton results under the multpath channel are shown n Fg. 5. These results show the conjugate symmetry character s sutable to acheve the symbol synchronzaton. Synchronzaton Error Rate AWG Channel - - Proposed algorthm Borjesson's algorthm SR(dB) 3 AWG Channel Proposed algorthm Borjesson's algorthm 8 x 4 Borjesson's Algorthm Mean Squared Error Counts SR(dB) Sample Index, n Fg. 4 Synchronzaton error rate and Estmator mean square error of Borjesson s estmaton and the proposed algorthm under an AWG channel x 4 9 Proposed Algorthm Mult-path channel (3 paths) 8 Counts Synchronzaton Error Rate - Proposed algorthm Borjesson's algorthm Sample Index, n SR(dB) Fg. 3 The hstograms for Borjesson s estmaton algorthm, the proposed algorthm at SR=8 5

5 Mean Squared Error 3 Mult-path channel (3 paths) SR(dB) Proposed algorthm Borjesson's algorthm Fg. 5 Synchronzaton error rate and Estmator mean square error of Borjesson s estmaton and the proposed algorthm under the multpath fadng channel V. Concluson In ths paper, the proposed synchronzaton algorthm employng the conjugate symmetry character of the BPSK-OFDM symbol to acheve the symbol synchronzaton. In the BPSK-OFDM symbol, the number of used samples wth the proposed algorthm s 6 and the used samples wth Borjesson s estmaton algorthm s 6. The number of used samples wth the proposed algorthm s larger than that wth Borjesson s estmaton algorthm. From the smulaton results, the estmated symbol tmng wth the proposed algorthm s almost located at the actual symbol tmng. The proposed algorthm provdes a better performance than that wth Borjesson s estmaton algorthm. In the future works, the frequency synchronzaton algorthm applyng the conjugate symmetry character wll be nvestgated to estmate the frequency offset caused by the Doppler shft and the msmatch between transmtter and recever oscllators. VI. References [] Rchard van ee, Ramjee Prasad, OFDM wreless multmeda communcaton, Artech House Boston London,. [] Mark Engels, Wreless OFDM Systems: How to Make Them Work? Kluwer Academc Publshers, st edton,. [3] Ramjee Prasad, OFDM for Wreless Communcatons Systems, Artech House, Aug. 4. [4] Zou W.Y. and Yyan Wu, COFDM: An overvew, IEEE Transactons on Broadcastng, vol. 4,no., pp. 8, Mar [5] Guanglang Ren, Yln Chang, Hu Zhang and Hunng Zhang, Synchronzaton method based on a new constant envelop preamble for OFDM systems, IEEE Transactons on Broadcastng, vol. 5, no., pp , Mar. 5. [6] Jan-Jaap van de Beek,. Magnus Sandell, and Per Ola Borjesson, ML estmaton of tme and frequency offset n OFDM systems, IEEE Transactons on Sgnal Processng, vol. 45, no. 7, pp. 8 85, July 997. [7] Byungjoon Park, Hyunsoo Cheon, Eunseok Ko, Changeon Kang and Daesk Hong, A blnd OFDM synchronzaton algorthm based on cyclc correlaton, IEEE Sgnal Processng Letters, vol., no., pp , Feb. 4. [8] Roht eg and John M. Coff, Blnd OFDM symbol synchronzaton n ISI channels, IEEE Transactons on Communcatons, vol. 5, no. 9, pp , Sep.. [9] B. Yang, K. B. Letaef, R. S. Cheng and Z. Cao, Tmng recovery for OFDM transmsson, IEEE Journal on Selected Areas n Communcatons, vol. 8, no., pp. 78 9, ov.. [] Magnus Sandell, Jan-Jaap van de Beek and Per Ola Borjesson Tmng and frequency synchronzaton n OFDM systems usng the cyclc prefx, Proceedngs of Internatonal Symmposum on Synchronzaton, pp. 6 9, Dec [] A.J. Coulson, Maxmum lkelhood synchronzaton for OFDM usng a plot symbol: algorthms, IEEE Journal on Selected Areas n Communcatons, vol. 9, no., pp , Dec.. [] J.H. Manton, Optmal tranng sequences and plot tones for OFDM systems, IEEE Communcatons Letters, vol. 5, no. 4, pp. 5 53, Apr.. [3] A.J. Coulson, Bt error rate performance of BPSK modulated OFDM synchronzed usng a plot symbol, Proceedngs of IEEE Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons, vol., pp. F-86 F-89, Sept. Oct.. [4] Fredrk Tufvesson, Ove Edfors and Mke Faulkner, Tme and frequency synchronzaton for OFDM usng P-sequence preambles, Proceedngs of IEEE Vehcular Technology Conference, vol. 4, pp. 3 7, Sep [5] Zhang Z., Long K., Zhao M. and Lu Y., Jont frame synchronzaton and frequency offset estmaton n OFDM systems, IEEE Transactons on Broadcastng, vol. 5, no. 3, pp , Sept. 5. [6] Wen Le, Janhua Lu and Jun Gu, A new plot asssted frequency synchronzaton for wreless OFDM systems, Proceedngs of IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol. 4, pp. IV 7-3, Apr. 3. [7] B. Chen and H. Wang, Blnd OFDM carrer frequency offset estmaton va oversamplng, Proceedngs of Sgnals, Systems and Computers, Conference, vol., pp , ov.. [8] Maro Tanda, Blnd symbol-tmng and frequency-offset estmaton n OFDM systems wth real data symbols, IEEE Transactons on Communcatons, vol. 5, no., pp. 69-6, Oct. 4. [9] C.R.. Athaudage and V. Krshnamurthy, A low complexty tmng and frequency synchronzaton algorthm for OFDM systems, Proceedngs of IEEE Global Telecommuncatons Conference, vol., pp.44 48, ov.. 6