IEEE SIGNAL PROCESSING LETTERS, VOL. 11, NO.2, FEBRUARY 2004
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A Blind OFDM Synchronization Algorithm Based on Cyclic Correlation Byungjoon Park, Student Member, IEEE, Hyunsoo Cheon, Eunseok Ko, Student Member, IEEE, Changeon Kang, Senior Member, IEEE, and Daesik Hong, Member, IEEE
Abstract—Future wireless systems will need to employ blind estimation to achieve better spectral efficiency. In this letter, we introduce a blind synchronization algorithm for jointly estimating timing and frequency offset in orthogonal frequency division multiplexing (OFDM) systems. The proposed estimator exploits the second-order cyclostationarity of received signals and then uses the symbol-timing and carrier frequency offset information appearing in the cyclic correlation. Because it is a blind estimator, no channel impulse response information is required. Simulations demonstrate that the proposed estimator performs at a sufficiently high level, thus indicating its suitability for use over fading channels. Index Terms—Blind synchronization, frequency offset estimation, orthogonal frequency division multiplexing (OFDM), timing offset estimation.
I. INTRODUCTION
B
OTH DATA-AIDED and non-data-aided synchronization methods have been proposed for orthogonal frequency division multiplexing (OFDM) synchronization. Most OFDM synchronization algorithms use training symbols [1]–[3]. However, the use of training symbols is not bandwidth-efficient. Therefore, non-data-aided algorithms are more desirable if we wish to avoid reducing the data rate. Generally, these kinds of synchronization algorithms make use of the redundancy introduced by cyclic prefixes [4]. The scheme for blind joint estimation of symbol timing and frequency offset in single carrier systems was first proposed by Gini [5]. That estimator makes use of the cyclostationarity of the received signals. For multicarrier applications, Bolcskei introduced the blind algorithm for estimating symbol timing and frequency offset [6]. However, Bolcskei’s algorithm requires that the channel impulse response be known. In this letter, we propose a non-data-aided synchronization algorithm for the estimation of symbol-timing and carrier frequency offset. This synchronization algorithm exploits the second-order cyclostationarity of entire received OFDM signals. No channel status information is required to estimate the symbol timing and frequency offset. Our approach can
Manuscript received November 14, 2002; revised February 6, 2003. This work was supported by the Basic Research Program of the Korea Science and Engineering Foundation under Grant R01-2000-000-00271-0(2002). The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Monir Ghogho. The authors are with the Information and Telecommunications Laboratory, Department of Electrical and Electronics Engineering, Yonsei University, Seoul 120-749, Korea (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/LSP.2003.819347
be viewed as an extension of Gini’s algorithm, which was proposed for single carrier systems. This letter is organized as follows. Section II describes our model for the received OFDM signals. In Section III, we propose a blind estimator based on cyclic correlation of the received signals. Section IV describes the performance of the proposed estimator, and Section V contains our conclusions. II. OFDM SYSTEM DESCRIPTION An OFDM signal transmitted through a frequency-selective fading channel can be expressed as (1) is the channel impulse response, and where is order. The transmitted signal
is the channel
(2) where is the transmitter pulse shaping filter, is the sub, and ’s are the carrier number, is defined as complex information symbols. At the receiver, the timing offset is modeled as a delay in the received signal, and the frequency offset is modeled as a phase distortion of the received data in the time domain. These two uncertainties and the additive white Gaussian noise yield the received signal (3) where is the integer-valued unknown arrival time of a symbol, is the frequency offset, and is the initial phase. For the sake of simplicity, the following points are assumed in this letter. • is a zero-mean independent and identically distributed (i.i.d.) sequence with values drawn from a finite-alphabet complex constellation, with variance . • For , each is zero-mean independent . Gaussian random variable with variance is uncorrelated with and . • III. BLIND SYNCHRONIZATION ALGORITHM The goal of synchronization is to estimate and . The algorithm we are proposing is based on the cyclostationarity of the received OFDM signals caused by the pulse-shaping filter.
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IEEE SIGNAL PROCESSING LETTERS, VOL. 11, NO.2, FEBRUARY 2004
To ascertain the cyclostationarity of the received signal, we must derive the time-varying correlation of the received signal
(4) is variance of and . where is periodic in with period . Thus, it For a fixed , has cyclostationarity with period and discrete Fourier series coefficients, which is called cyclic correlation. From (4), the cyclic correlation turns out to be
Fig. 1.
(5) where . To show the dependence of delay which was absorbed in
MSE for symbol-timing estimator in multipath fading channel.
To avoid the effects of noise, let us consider only cases where . For , we can retrieve from the cyclic correlation phase shown in (8) as follows:
on the time , we can rewrite using Parseval’s theorem
Given timing offset
for
(9)
, the frequency offset
can be derived
as (10) (6)
where denotes Fourier transform of Let Inserting (6) into (5), then we obtain
. .
(7) can be compensated for by multiThe effect of with (7). Once we have defined plying , we can rewrite (7) as
(8) As seen in (8), the timing offset and frequency offset appear as cyclic correlation phase, and the channel impulse redoes not affect the cyclic correlation phase. Theresponse fore, no channel information is required for the proposed estimator. Moreover, since frequency offset appears as the phase of cyclic correlation with respect to the lag , frequency offset has no influence on the timing estimator.
Since we cannot have access to ensemble cyclic quantity, we must estimate it from finite data samples. We obtain from the dataset . If the number of data is large enough, then should be asymptotically unbiased and consistent in a mean-square sense, i.e., . As a consequence, the estimator of and is asymptotically unbiased and consistent in the mean-square sense. The effect of imperfection in cyclic correlation can potentially be reduced by averaging. However, there is a trade-off involved in the selection of averaging number. The most reasonable value may be selected by simulations so as to minimize the complexity and mean-square error (MSE) of the estimator. IV. SIMULATION RESULTS We conducted Monte Carlo simulations to evaluate the performance of the estimators. We considered OFDM system with 64 subcarriers and used a raised cosine pulse filter for the transmitter pulse-shaping filter in the simulations. We evaluated the performance of the estimator by means of the MSE, and we compared the performance of the proposed estimator with that of Bolcskei’s. Fig. 1 shows the MSE of the symbol-timing estimator versus increases. As mentioned the SNR as the frequency offset above, it is observed that the MSE of the proposed symboltiming estimator is almost equal irrespective of the frequency offset, and the symbol-timing estimator is hardly affected by the noise.
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the proposed synchronization algorithm is better suited for the initial synchronization of OFDM systems over fading channels. V. CONCLUSION We presented a blind estimation algorithm for symbol timing and frequency offset for use in OFDM systems. The proposed estimator uses cyclic correlation of the received OFDM signal. Because it is a blind estimator, channel status information and training symbols are not required. Simulation results show that the proposed estimator demonstrates almost the same performance as Bolcskei’s estimator, which requires the use of channel information. REFERENCES
Fig. 2. MSE for frequency offset estimator in multipath fading channel.
The MSE for the frequency offset estimator is depicted in Fig. 2. As seen in the figure, the MSE is not varying with the SNR. Therefore, more reliable estimation can be achieved independent of SNR. However, the performance of the frequency offset estimator is degraded in relation to the frequency offset. The simulation results clearly show that the MSE performance of the proposed estimator is close to the MSE performance for Bolcskei’s estimator as proposed in [6]. However, the estimator proposed here requires no channel information, whereas Bolcskei’s estimator does. Therefore,
[1] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol. 45, pp. 1613–1621, Dec. 1997. [2] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun., vol. 42, pp. 2908–2914, Oct. 1994. [3] T. Kim, N. Cho, J. Cho, K. Bang, K. Kim, H. Park, and D. Hong, “A fast burst synchronization for OFDM based wireless asynchronous transfer mode systems,” in Proc. Globecom, 1999, pp. 543–547. [4] J. J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Processing, vol. 43, pp. 761–766, Aug. 1997. [5] F. Gini and G. B. Giannakis, “Frequency offset and symbol timing recovery in flat-fading channels: A cyclostationarity approach,” IEEE Trans. Commun., vol. 46, pp. 400–411, Mar. 1998. [6] H. Bolcskei, “Blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems,” IEEE Trans. Commun., vol. 49, pp. 988–999, June 2001.
