JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 18

A NovelTechnique for Time Synchronization in OFDM Systems Akram Ramezani

Abstract-This paper presents a new method for time synchronization in OFDM systems. The method is based on exploiting the correlation caused by appending the cyclic prefix to OFDM symbols. According to the simulation results, the improvement in estimation accuracy is quite considerable comparing to similar methods. Index Terms- OFDM, time offset, cyclic prefix, maximum likelihood estimation

1 INTRODUCTION In communication systems based on OFDM (Orthogonal Frequency Division Multiplexing) digital data is divided into several parallel sub-channels where orthogonal subcarriers will be modulated by one of the common digital modulation schemes. Since the symbol duration in OFDM systems is much longer than conventional systems, the system is less sensitive to channel-induced dispersion and is robust against Inter Symbol Interference (ISI) and fading caused by multipath propagation. Fig. 1 shows the block diagram of a typical OFDM system. In order to increase the system’s robustness against ISI effects, a periodic copy of the end each symbol which is called the cyclic ____________________________________ AkramRamezani is with the Department of Electrical Engineering, Science & Research Branch Islamic Azad University, Tehran, Iran

Fig. 1. Block diagram of a typical OFDM system

prefix is added to the beginning of it. In addition to protecting the OFDM systemfrom ISI, the cyclic prefix also provides protection against time offset errors in the receiver. In spite of all that OFDM systems have to offer, one significant problem with these systems is their sensitivity to time and frequency offset. This is caused by the loss of the orthogonality between the subcarriers. Thus the accuracy of the frequency and timing error estimation is of a major

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JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 19

influence on the overall OFDM system performance. See [1,2]

be eliminated and we can model the received signal r(k) as :

The time offset estimation methods can be roughly divided to those that use pilot or training symbols and those that exploit redundancy inherent of the signals used in OFDM transmission.

(1) Where θ presents the unknown symbol time offset and n(k) is the additive white zero mean Gaussian noise with variance
 caused by the channel. As in [5] we consider s(k) to approximate a complex Gaussian process whose real and imaginary parts are independent. But it is not a white process due to the correlation caused by cyclic prefix. Based on the assumptions stated above we can say

It is a common belief that methods which use training pilot tones benefit from greater accuracy while suffering from lower bandwidth efficiency; however the method presented in this paper tends to prove the contrary, since the estimation error resulted by this technic which is based on the correlation caused by adding the cyclic prefix is much lower than those of similar technics which use pilot tones like [3,4].

r(k)=s(k-θ) + n(k)

    
 


(2)

3 ML ESTIMATION

In this paper we present a method that exploits the redundancy caused by adding cyclic prefix and estimates the symbol time offset using maximum likelihood estimation.

The ML estimator function of time offset θ as derived in [1] is

2 SYSTEM MODEL

if we drop the conditioning on θ we have

As shown in Fig. 1, the serial data is first divided into N parallel sub-channels and then modulated by one of the common digital modulation schemes such as QAM, QPSK, BPSK,… . The type of modulation used at this step determines the number of bits each sample will be carrying. After taking IFFT of the block of N modulated samples in order to avoid large number of sub-channel modems, the copy of the last L samples is added to the beginning of each OFDM symbol. Assuming a discrete time AWGN channel whose impulse response is shorter than L samples, the effect of ISI can

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(4)

from [5] we can rewrite (4) as   *  +,|- |. cos 212  3- ! 4 5Ф 7

(5)

Where

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(6) (7)

JOURNAL OURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 20

In order to estimate θ we have to maximize . A and B can be omitted since A has no role in the process and B is a positive constant, so θ can be estimated by maximizing (8).

of an AWGN channel, the system performance in dispersive channel is quite good too.

(8)

3 SIMULATION

We use Monte Carlo simulations to evaluate the performance of estimators. In each simulation imulation 125000 symbols are used, we evaluate the performance of estimator by means of the sample offset estimator estim mean squared error. Now if we use one value of β, preferably one corresponding to a low SNR value since estimation error naturally decreases while SNR increases, as it is illustrated in Fig. 4 the estimation error decreases considerably comparing to the other two estimators that use the same system model.It also illustrates that although we basedd the estimation on the assumption

Fig. 2.Optimal values of β for different SNR values

Fig. 3.. Optimum value of β for SNR=5 dB

10

10

MSE

In previous section we derived an ML estimation for symbol time offset θ. In (8) β is a positive constant which simulations show that estimation error varies significantly for it’s different values. Thus it has a key role in minimizing the estimation error and improving the system performance. In order to find the optimum value of β where re the estimation error is minimum, the simulation results show that in AWGN channels we should use different values of β for different SNR values as illustrated in Fig. 2.

10

10

10

4

Dispersive channel Reference estimator estimator in [3] estimator in [4] proposed estimator in AWGN channel

2

0

-2

-4

0

1

2

3

4

5 SNR (dB)

6

7

8

9

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Fig. 4. Estimator performance formance in AWGN and dispersive channel( time offset estimator in [[7] is mentioned as the reference estimator) estimator

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JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 21

4 CONCLUSION A new method based on [5] for time synchronization in OFDM systems was presented here. The estimation error is significantly low and the method is quite simple and bandwidth efficient since the need for adding pilot tones in order to increase the estimation accuracy is eliminated.

References [1] T. Polletand M. Moeneclaey, “Synchronizability of OFDM signals,” Proc. Globecom, vol. 3, Singapore, Nov. 1995, pp. 2054–2058. [2] J.-J. van de Beek, S. K. Wilson, P. O. Börjesson, and P.Ödling, “Orthogonal frequency-divisionmultiplexing (OFDM),” Review of Radio Science 1996–1999, R. Stone, Ed. Piscataway, NJ: IEEE Press, 1999. [3] DanielLandström, Sarah Kate Wilson, Jan-Jaap van de Beek, Per Ödling, and Per Ola Börjesson. “Symbol Time Offset Estimation in Coherent OFDM Systems”. IEEE Transactions on Communications, VOL. 50, NO.4, 2002. [4] Seo Bin Hong, Hyung-Myung Kim. “Pilot signal design algorithm for efficient symbol time offset estimation in an OFDM system”. Signal Processing 87,Elsevier B.V. 2007. [5] J. J. van de Beek, M. Sandell, P. O. Börjesson . “ML Estimation of Time and Frequency Offset in OFDM Systems”, IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol. 45, pp.1800-1805NO. 7, jul 1997.

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