A Novel Joint Synchronization Algorithm for OFDM Systems Based on Single Training Symbol

Transcription

1 A Novel Joint Synchronization Alorithm for OFDM Systems Based on Sinle Trainin Symbol 1 Hailon Zhao, Youjian Liu, 3 Jian Zhan, 4 Jie Zhou *1, Correspondin Author,3,4 Institute of Electronic Enineerin, China Academy of Enineerin Physics, Mianyan, China, zhaohailon_09@16.com Department of Enineerin Physics, Tsinhua University, Beijin, China doi : /jdcta.vol5.issue5.4 Abstract The Park s method suffers from symbol timin ambiuity and small acquisition rane for carrier frequency offset, and cannot estimate samplin frequency offset. To solve these problems, a new trainin symbol includin virtual carriers is desined, and the correspondin joint synchronization alorithm for orthoonal frequency division multiplexin (OFDM) systems is proposed. In the proposed method, symbol synchronization and fractional frequency offset estimation are accomplished by utilizin the ood correlation properties of the trainin symbol, and then interal frequency offset estimation is obtained by the position offset of virtual carriers. Based on symbol synchronization, samplin clock synchronization is accomplished by comparin the number of samples accounted from the receiver and that of the transmitter in L frames. The simulation results show that the proposed alorithm ives a more accurate estimation of symbol timin and samplin frequency offset and provides a wider acquisition rane for carrier frequency offset, compared with Park s alorithm. Keywords: OFDM, Joint Synchronization, Symbol Timin Synchronization, Carrier Frequency Offset Estimation, Samplin Frequency Offset Estimation, Virtual Carrier 1. Introduction Orthoonal frequency division multiplexin (OFDM) is well known as an efficient technique to mitiate the frequency-selective behavior of wideband communications channels. It has become an increasinly popular scheme in modern diital communications and is already bein applied in DAB, DVB-T/H, WiFi, WiMAX and so on. Several research topics about OFDM have been presented [1]-[3], where, synchronization is a major research topic because of increased sensitivity to synchronization mismatch problems [1]. Some synchronization alorithms for OFDM systems are reported either jointly or individually in the literature [4]-[11]. The most popular of the pilot-aided alorithm is the method proposed by Schmidl [4]. However, the timin metric of this method has a plateau, which causes a lare variance in the symbol timin estimation. To reduce the uncertainly arisin from the timin metric, Minn proposed a method as a modification to Schmidl s approach [5]. Minn s preamble yields a sharper timin metric than Schmidl s, but its estimation variance is quite lare in ISI channels. Park desined a repeated symmetric preamble in [6]. It produces an even sharper timin metric than Minn s. However, when the cyclic prefix (CP) lenth is a quarter of OFDM symbol lenth, its timin metric enerates two peaks which affect the timin performance. Moreover, the carrier frequency offset estimation ranes of Park method is narrow. Other synchronization techniques are proposed for OFDM systems in [7]-[11]. Unfortunately, these alorithms all inore the samplin clock synchronization. In continual OFDM systems, samplin clock frequency mismatch may result in sinal-to-noise ratio (SNR) loss [1]. In this paper, we desin a new trainin symbol includin virtual subcarriers, and propose a joint synchronization alorithm for samplin frequency, symbol timin and carrier frequency synchronization in OFDM systems. The proposed alorithm eliminates timin ambiuity, solves the problem of samplin frequency offset estimation, and provides a wide acquisition rane for carrier frequency offset

2 Thus this paper is oranized as follows. Section II introduces the OFDM sinal model and Park s method. Section III presents the proposed preamble and joint synchronization alorithm. In Section IV, the performance of the proposed estimator and the Park s estimator are compared in term of mean-square error usin computer simulation. Finally conclusion is drawn in Section V.. OFDM system description.1. OFDM sinal model Consider a eneral case of an OFDM system, usin the standard complex-valued baseband equivalent sinal model. The time-domain OFDM sinal is expressed by N 1 nk, k (1) n k 0 x() t d ( t nt) j fkt where, k e, t [0, T), d nk, is the complex data modulatin the k-th active subcarrier, T N T s is symbol spacin, T s is samplin period and N is the number of subcarriers in an OFDM symbol. An OFDM sinal transmitted throuh a frequency-selective fadin channel can be expressed as j t/ T rt () yt ( de ) () t () where, yt () ht () xt ()( ht () is the channel impulse response ), d is the inteer-valued unknown arrival time of a symbol, F I is the normalized frequency offset ( F is the fractional frequency offset, I is the interal frequency offset), () t represents the zero-mean complex additive white Gaussian noise (AWGN). The received sinal throuh local analo-to-diital converter (ADC) is rn ( ) rt ( ) t ˆ nts R 1 exp j ntˆ NT h( r) x( n d r) ( n) s s r 0 (3) where, T ˆs is local ADC samplin period, and R is the channel order. From (3), we can see that the synchronization oal is to estimate symbol timin offset (STO) d, carrier frequency offset (CFO) and samplin frequency offset (SFO) f 1/ T 1/( Tˆ T ). s s s s.. Park s method description Park desined a symmetric trainin symbol in [6]. It is produced by transmittin a real-valued PN sequence on the even frequencies, while zeros are used on the odd frequencies. The time-domain samples have the followin form P [ C D C D ] (4) park N/4 N/4 N/4 N/4 where, C N /4 represents samples of lenth N/4 enerated by IFFT of a PN sequence, D N /4 is desined to be symmetric with C N /4. Park defines a timin metric as follows:

3 Where M Park Pd ( ) ( d) (5) R( d ) N / Pd ( ) rd ( krd ) ( k) (6) N / (7) R( d) r( d k) The STO estimation is dˆ ar max( M ( d)) (8) d The CFO estimation is the same as that of Schmidl, and it can be represented by ˆ anle( Q( dˆ ))/ (9) Where park N / ˆ ˆ * ˆ Qd ( ) rd ( kr ) ( d k N/) (10) The timin metric of Park s method has its peak value at correct symbol timin, while the values are almost zero at all other positions. However, it is observed that the timin metric has lare side lobe at the positions with N ( N is CP lenth) samples spaced from the correct startin point of OFDM symbols, which will affect the accurateness of timin offset estimation. When N N / 4, the timedomain samples of trainin symbol includin CP are P [ D C D C D ] (11) P arkcyc N /4 N /4 N /4 N /4 N /4 Fi.1 shows an example of the timin metric under no noise and no channel distortion case with 56 subcarriers and 64 cyclic prefix. It can be observed that the timin metric of Park s method enerates two peaks in every OFDM symbol, thus timin synchronization cannot be accomplished. Minn s method [5] also has this drawback

4 1 0.8 Timin Metric Samples Fiure 1. The timin metric of Park s method 3. Proposed joint synchronization alorithm 3.1. New trainin symbol The CFO estimation rane of Park s method is only ±1 the subcarrier spacin. To enlare the acquisition rane, we desin a new trainin symbol includin virtual subcarriers. The new trainin symbol can be produced by transmittin a real-valued PN sequence on the even frequencies, while zeros are used on the odd frequencies, and the virtual subcarriers are located both at left and riht hands of c N/ with lenth of N v. Its frequency-domain samples have the followin form Cpro [ c0,0,, c i,0,,0, N / c,0,,0,,0] Nv Nv (1) where, c i is a real-valued PN sequence on the even frequencies, and N v is the number of virtual subcarriers. The time-domain samples of new trainin symbol have the same property as (4). 3.. Symbol timin synchronization To eliminate timin ambiuity of Park s method, we present two improved symbol timin synchronization alorithms. 1) The timin ambiuity can be eliminated by utilizin the correlation properties of the CP, a new timin metric is as follows N M pro1( d) MPark ( d) PCyc( d N ) (13) The STO estimation is d ˆ ar max( M ( d )) (14) pro1 pro1 d where d L 1 * Cyc( ) ( ) ( ) k d P d r k r k N (15) - 0 -

5 ) The timin ambiuity also can be eliminated with the property of two identical halves in the time domain of the trainin symbol in (1), a new timin metric is as follows: The STO estimation is N M pro( d) MPark ( d) Mc( d ) (16) d ˆ ar max( M ( d )) (17) pro pro d Where N 1 M c( d) PSch( d k) (18) N 1 N / 1 * Sch ( ) ( ) ( /) P d r d k r d k N (19) 3.3. Carrier frequency synchronization The CFO estimation is achieved in two separate steps throuh the use of trainin symbol. First, the fractional frequency offset is accomplished by usin eq. (9). Then, the fractional carrier frequency offset is corrected, and interal frequency offset estimation is obtained by the position offset of virtual carriers. Because the power of virtual subcarriers is less than that of data subcarriers, and interal frequency offset causes cyclic shift of subcarriers, we define a new interal frequency offset estimation formula The interal frequency offset estimation is where R( I ) N v I I I I m 1 Z( ) R( ) R( m) R( m) (0) ˆ ar max( Z( )) (1) I I is received trainin symbol in the frequency domain after takin the FFT Samplin frequency synchronization If there is samplin clock frequency mismatch, small samplin frequency offset ( f 1/ 1/( ˆ s Ts Ts Ts) ) happens between transmitter and receiver, which exhibits as a cumulative error for samplin of receiver. This cumulative error results in more or less samples of receiver than those of transmitter. As shown in Fi.1 and Fi., assumin that samplin spacin is T s in the receiver, the number of samples between two peaks is ( N N ) M, where M is the number of OFDM symbols in every frame. If T s 0, the number of samples between two peaks will be more than ( N N ) M, else less than ( N N ) M. I - 1 -

6 Accordin to the above characteristics, samplin clock synchronization can be accomplished by comparin the number of samples accounted from the receiver and that of the transmitter in L OFDM frames. Its estimation formula is T N N T r t s s () Nt where, N r is the number of samples at the receiver in L OFDM frames, and Nt ( N N) M L is the number of samples at the transmitter in L OFDM frames. T s 4. Simulation results T s T s 0 0 Tˆs Tˆs Fiure. The samplin frequency offset The performance of the proposed estimator is evaluated in the AWGN and TU-6 channel [1] by computer simulations. Six paths are chosen with path delays of 0,, 5, 16, 3 and 50 samples, and the amplitude of each path are -3dB, 0dB, -5dB, -6dB, -8dB and -10dB respectively. OFDM system with 56 subcarriers and 64 cyclic prefix is considered, and N v is 64. MSE of STO estimation Park's method Improved1 method Improved method MSE of STO estimation Park's method Improved1 method Improved method (a) AWGN channel Fiure 3. The MSE of STO estimation (b) TU-6 channel - -

7 MSE of CFO estimation Park's Method Proposed Method MSE of CFO estimation Park's Method Proposed Method (a) AWGN channel (b) TU-6 channel Fiure 4. The MSE of CFO estimation Fi.3 shows the MSE for the STO estimators in AWGN and TU-6 channel, and we can see that two improved timin methods all eliminate timin ambiuity, and the STO estimator has a much smaller MSE than Park s method. Fi.4 presents the MSE curve of the CFO estimation in AWGN and TU-6 channel ( =3.5). It can be seen that the proposed method has ood performance, while the performance of Park s method deteriorates because its CFO estimation rane is small. The mean of the CFO estimation for the TU-6 channel with SNR of 10 db is presented in Fi.5. It shows that the CFO estimation rane of the proposed method is much wider than Park s method, up to half the OFDM bandwidth theoretically. In Fi.6, it shows that the proposed method can estimate SFO accurately. Moreover the performance of estimator is related to L. The larer L is, the more accurate the estimator will be. Mean of CFO estimation Park's Method Proposed Method Frequency Offset Fiure 5. The mean of CFO estimation - 3 -

8 MSE of SFO estimation L=0 L=30 L=50 MSE of SFO estimation L=0 L=30 L=50 5. Conclusion (a) AWGN channel (b) TU-6 channel Fiure 6. The MSE of SFO estimation In this paper, we desin a new trainin symbol includin virtual carriers, and propose the correspondin joint synchronization alorithm for samplin frequency, symbol timin and carrier frequency synchronization in OFDM systems. The simulation results show that the proposed alorithm ives an accurate estimation of symbol timin and samplin frequency offset and provides a wide acquisition rane for carrier frequency offset. The proposed alorithm has low complexity, so it is suitable for enineerin applications in OFDM systems. 6. References [1] T. Pollet, M. Van Bladel, M. Moeneclaey, BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise, IEEE Transactions on Communications, vol. 43, no., pp , [] SHEN Weijie, SUN Haixin, CHENG En, ZHANG Yonhuai, SNR estimation alorithm based on pilot symbols for DFT-Spread OFDM systems over underwater acoustic channels, JCIT, AICIT, vol. 6, no., pp , 011. [3] S. M. Riazul Islam, Kyun Sup Kwak, On channel estimation in MB-OFDM UWB systems with time varyin dispersive fadin channel, JDCTA, AICIT, vol. 4, no., pp. 18-4, 010. [4] T. M. Schmidl, D. C. Cox, Robust frequency and timin synchronization for OFDM, IEEE Transactions on Communications, vol. 45, no. 1, pp , [5] H. Minn, M. Zen, V. K. Bharav, On timin offset estimation for OFDM systems, IEEE Communications Letters, vol. 4, no. 7, pp. 4-44, 000. [6] B. Park, H. Cheon, C. Kan, D. Hon, A novel timin estimation method for OFDM systems, IEEE Communications Letters, vol. 7, no. 5, pp , 003. [7] Guanlian Ren, Yilin Chan, Hui Zhan, Huinin Zhan, Synchronization method based on a new constant envelop preamble for OFDM systems, IEEE Transactions on Broadcastin, vol. 54, no. 1, pp , 005. [8] A. B. Awoseyila, C. Kasparis, B. G. Evans, Robust time-domain timin and frequency synchronization for OFDM systems, IEEE Transactions on Consumer Electronics, vol. 55, no., pp , 009. [9] J. W. Choi, J. W. Lee, Q. Zhao, H. L. Lou, Joint ML estimation of frame timin and carrier frequency offset for OFDM systems employin time-domain repeated preamble, IEEE Transactions on Wireless Communications, vol. 9, no. 1, pp , 010. [10] F. Alessio, S. Semih, OFDM symbol synchronization usin frequency domain pilots in time domain, IEEE Transactions on Wireless Communications, vol. 8, no. 6, pp ,

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