A Novel Timing Estimation Method For Ofdm Systems

A Novel Timing Estimation Method for OFDM Systems Byun 'oon Park, Hyunsoo Cheon, Changwn Kang, and Daesik Hon Information and%leco"unication Lab., Dept. of Electrical and Electronic Eng., $onsei Univ. 134 ShinchondongSeodaemungu, Seoul, Korea, 120-749

Abstmct-In this paper, we present a novel timing offset estimation method for orthogonal frequency division multiplexing(0FDM) systems. T h e proposed estimator is designed t o avoid the ambignity in timing offset estimation. The performance of proposed scheme is presented in t e r m of mean and mean-square error(MSE) sense. T h e simulation results show that the proposed estimator is unbiased and has significantly smaller MSE. I. INTRODUCTION Synchronization has been a major research topic in OFDM system due t o sensitivity to symbol timing and carrier frequency offset ill. Several approaches have been proposed to estimate time and frequency offset either jointly or individually [2],[3]. Various existing synchronization algorithms can be classified into blind and pilot-aided methods. If a preamble is used to estimate symbol and frequency offset, the corresponding synchronization schemes are considered to be pilot-aided [4]. On the other hands, if a preamble is not used, the corresponding estimation algorithms are classified as blind [ 5 ] , [ 6 ] .Blind methods are severely affected by channel condition, and have large complexity. For these reasons, pilot-aided synchronization methods are commonly used in OFDM applications. Among pilot-aided algorithms, the method proposed by Schmidl is most popular [7]. In 171, a preamble containing the two same halves is used to estimate the symbol timing and frequency offset. The Schmidl's estimator gives simple and robust estimates for symbol timing and carrier frequency offset. This method also provides a very wide acquisition range for the carrier frequency offset. However, the timing metric of Schmidl's method have plateau, which causes large variance of the timing estimate. To reduce the uncertainty due to the timing metric, Minn proposed a method as modification to Schmidl's [E]. The feature of Minn's preamble gives more sharp timing metric and smaller variance than Schmidl's. While Minn's estimator provides accurate estimation, the variance of estimator is quite large in IS1 channel. In this paper, we present a preamble and timing synchronization method for OFDM timing estimation as This work has been financiallysupported from the LG Electronic Cooperation.

0-7803-7632-3/02/$l7.00 02002 IEEE

269

modification t,o Schmidl's to avoid the timing metric plateau. Since the basic structure of proposed estimator is same to Schmidl's, it maintains the advantages of Schmidl's estimator. Moreover, the proposed method can make more sharp timing metric than Schmidl's and Minn's. The performance of the proposed estimator is shown in rayleigh fading environments by computer simulations. This paper is organized as follows. In the next section, OFDM signal model and timing estimation methods are introduced. Section 111 presents the proposed preamble and timing offset estimation method. In Section W , the performances of the proposed estimator and other estimators are compared in terms of mean-square error using computer simulation results. Finally conclusion is drawn in Section V. 11. SYSTEMDESCRIPTION

A . OFDM Signal Descllption Consider the general case of a linear, dispersive and noisy OFDM system. We use the standard complexvalued baseband equivalent signal model. The n-th received sample has the standard form

where h[n]is the channel impulse response, whose memory is denoted by L,and w[n]is the white gaussian noise. 4 1 1 1 is the time-domain OFDM sigual expressed by U-,

where N is the numberof suh-carriers and c,'s are the complex information symbols. At the receiver, timing offset is modeled as a delay in the received signal and frequency offset is modeled as a phase distortion of the received data in the time domain. These two uncertainties and the AWGN w[n] yield the received signal

where n, is the integer-valued unknown arrival time of a symbol, 9, is the frequency offset and 4 is the initial phase.

B. Schmidl's Method The form of preamble proposed by Schmidl is as follows.

Psch = [Asrh Asch], where Asc,, represents samples of length N / 2 and is usually PN sequence. The Schmidl's timing estimator finds the start of the symbol a t the maximum point of the timing metric given by (4)

Fig. 1. Comparison of timing metric

where NIP-1

Pi(d)=

r*(d+k).r(d+k+N/Z),

(5)

and

k=0

and

NIP--1

lr(d

Rl(d)=

+ k + N/2)I2.

(6)

k=O

The timing metric has a plateau which leads to some uncertainty as t o the start of OFDM symbol. To reduce this effect, a method to find the 90% of the maximum points t o the left and right in the time domain, and average these two 90% times is also proposed in [7]. Nevertheless, the mean-square error of the Schmidl's estimator is quite large.

6. Minn's Method To reduce the uncertainty due to the timing metric plateau and improve the timing offset estimation, Minn proposed a modified preamble and timing estimator. The preamble has the following form.

PM.M = [ A M w ~AM,"^

- A,wann

AM,"^],

where AM,,, represents PN sequence of length N/4 Then the timing metric is given hy

where

270

For training symbol of Schmidl's, the timing metric has its peak for the whole interval of cyclic prefix. The Minn's method has its peak a t the correct starting point of OFDM symbol since off that point, correlation of some samples results in negative values. For this reason, Minn's method eliminates the timing metric peak plateau, hence has smaller MSE. 111. PROPOSED SYMBOL TIMING METHOD

In this section, we present a n OFDM timing estimiltion method to reduce the uncertainty due t o the plateau of timing metric in Schmidl and Cox method. By the reduction of uncertainty, the performance of the proposed estimator is improved. In Minn's method, negative-valued samples are used at second-half training symbol to reduce the timing metric plateau. Correlation of these negative samples results in decrease of timing metric at incorrect FFT starting point. However, with reduction of timing metric plateau, the MSE of estimator is quite large in IS1 channel. It is because timing metric value at only one sample off from the correct starting point is almost same to peak timing metric value. Therefore, to enlarge the difference hetween peak value of timing metric and others is needed to improve the accuracy of estimator. From the observation of the two adjacent value of timing metric, it is clear that they have the same sum of the pairs of product, except only two pairs of product. For

this reason the difference hetween the value of timing metric and the next value is slight. Therefore, t o enlarge the difference between the two adjacent values of timing metric, it is needed t o maximize different pairs of product between them. This is dependent on the structure of training symbol and the definition of timing metric. For this reason, we propose a preamble and correlation method to get impulse-shaped timing metric, and make more accurate timing estimation possible. The symbol timing recovery relies on searching for a training symbol. The samples of the proposed preamble are designed to he of the form

4

-6

where Ap,, represents samples of length N J 4 generated by IFFT of P N sequence, and A;re means conjugate of Ap,,. Bp,, is designed to be symmetric with ApTo. This pattern of symbol can he easily obtained by using the properties of FFT. The training symbol is made by transmitting a real-valued P N sequence on the even frequencies, while zeros are used on the odd frequencies This means that at each even frequency one of the points of a BPSK constellation is transmitted. Then result of IFFT will produce the time-domain sequence as shown in Eq. (10). To estimate frequency offset using the same preamble, the basic form of proposed preamble is same to the Schmidl's preamble. Therefore, Schmidl's frequency offset estimation algorithm can he also applied t o the proposed preamble. The difference is that Bp,, is symmetric with Apr.. in the first-half. By using this symmetry, impulse-shaped timing metric is obtained. To use the property that Bp,, is symmetric with Ap,,, let define a new timing metric as follows.

0

SNI

w,

I*

Fig 2 Mean of estimators in HIPEFUANI2 indoor channel A

t ?1-.1

12

t6

I

m

9hw id81

Fig. 3. MSE of estimators in HIPERLANIZ indoor channel A where NI2

+

(12)

IHd + k)/*

(13)

r(d - k) . ~ ( d k)

~ 3 ( d= )

k=O

and N/2

R3(4 = k=O

The P3 is designed to have N / 2 different pairs of product between two adjacent values. I t is maximum different pairs of product. Therefore, the proposed timing metric has peak value at correct symbol timing, while have almost zero value at other position. Figure 1 shows the example of timing metric under no noise and distortion with 1024 sub-carriers and 128

271

cyclic prefix. The correct timing point is indexed 0 in the figure. The proposed timing metric is compared to that of Schmidl's and Minn's. As seen in the Fig. 1, the timing metric proposed in 171 makes plateau for the whole interval of cyclic prefix. The timing metric of Minn's method reduces plateau, and makes sharp timing metric. As mentioned above, the proposed method has impulse-like timing metric, thus it can achieve more accurate timing offset estimation.

IV. SIMULATION RESULTS The performance of the proposed estimator is evaluated by computer simulations. OFDM system with

64 subcarriers and 16 cyclic prefix is considered and HIpERLAN/2 indoor channel mode] [$ is used for sim. uhtions. The performance of the proposed estimator is evaluated by mean and mean-square error(MSE), and compared with that of Schmidl's and Minn's method. Figure 2 and 3 show the means and variances timing offset estimators in HIPEWAN/? indoor channel A . As seen in Fig. 2, mean of Schmidl's method is shifted to middle of the cyclic prefix, but on the other hand, mean of proposed estimator and Minn's is about correct timing point. This shows that reduction of timing metric plateau makes more accurate estimation. From MSE curve in Fig. 3, we can observe that the proposed timing offset estimator have much smaller MSE than other estimators. This improvement can be inferred from the impulse-like shape of the timing metric of proposed estimator. From the results of simulations, it is obvious that the performance of the proposed estimator is better than other estimators. Therefore, the proposed estimator is more favorable for the initial synchronisation of OFDM systems.

V. CONCLUSIONS

A efficient preamble and timing offset estimator is p r e sented in this paper. The proposed timing offset estimator reduces the plateau which makes the uncertainty of estimation in Schmidl's timing offset estimation method, and makes it possible to estimate symbol timing offset with much small MSE. Therefore, the proposed estimator is suitable for the initial synchronization of OFDM systems.

REFERENCES [I] T.Poilot, M. Van Bladel, and M. Moencclaoy, "Ber s e m i t i r ity of ofdm s y s t e m to carrier frequency offset and wiener phase noise," IEEE %m. Comm.. vol. 43, pp. 191-193, Fcb./Mar./Apr 1995. 12) +I H. Moose, "A Techniquc far Orthogonal Frequency Diviston Multiplexing Requency 0 6 e t Correction," IEEE 'Pam. Comm., vol. 42, pp. 2908-2914, October 1994. 131 7 . J . van de Beek, M. Sundell, and P.O. Borjesson, "ML estimation of Time and Requency Offset in OFDM Systems," IEEE 7bm. Signal Pmcessing, vol. 43, pp. 761-766, August 1997. [4] Taekwan Kim, Namshin Cho, .laehee Cho, Koukjoon Bang, Kwangchul Kim, Hyunchoil Park, and Daesik Hong, " A Fast Burst Synchronization for OFDM Based Wireless Asynchronous 'pransfer Mode Systems," Globecom'gg, pp. 543-547, 1W O

[SI Helmut Bolcskei, "Blind Estimation of Symbol Timing and Carrier Frequency Offset in Wireless OFDM Systems," IEEE 7bm. Comm.. vol. 49.. .. DP. 988-999. June 2W1. 161 Byungjoon Park, Eunscok KO, H&mo Cheon, Changmn Kang, and Daesik Hong , "A blind OFDM synchronization algorithm bared on cyclic correlation," Cfobecom'Of, pp. 3 1 1 6 3119, 2001.

212

[7] T.M. Schmidl and D.C. Cox, "Robust Frequency and Timing Synchronization for OFDhf." IEEE %De. CO"., vol. 45, pp. 161t1621 December 1997. 181 H.M~"", M.z&,~, and v.ti.BhargaM, timing offset =timation for ofdm systems," IEEE Communication letters, vol. 4, pp. 242-244, July 2000. 191 Jonas Modbo and Peter Schramm, "Channel Modols for HIPEHLANIZ in Different Indoor Scenarim," ETSI BRAN 3ER1085B' March 1gg8.

*on