The Eighth International Conference on Electronic Measurement and Instruments ICEMI’2007

A Timing Synchronization and Frequency Offset Estimation

for OFDM Systems Based on PN (pseudo-noise) Sequence

Wang Lin Chang Huan (School of Automation, Xi’ an University of Technology, Xi’ an 710048, China)

Abstract: Synchronization is a key problem of orthogonal

frequency division multiplexing (OFDM) systems. A method

of timing synchronization and frequency offset estimation for

OFDM systems based on PN sequence is proposed in this

paper, which utilizes one special training sequence to

overcome the shortcomings of the synchronization method

proposed by Schmidl & Cox[1]. Both theoretical analysis and

simulation show that the proposed method has a better

performance in timing synchronization and only a little

resource loss.

Keywords: OFDM; frequency offset estimation; timing

synchronization; PN Sequences

1 Introduction

The next-generation multimedia wireless systems have attracted worldwide attention for their broadband data transmission capacity and economical feature. The common problem in wireless communication systems is multi-path interference. With the increase of transmission rate, multi-path interference causes significant deterioration to the quality of communication. Thus, an ideal modulation scheme is desired to be efficient in multi-path environment. The orthogonal frequency division multiplexing (OFDM) modulation scheme is one of such schemes.

High data rate is achieved between the transmitter and the receiver once they are ideally synchronized. However, there usually exists a small timing and frequency offset, whose existence will dramatically degrade the performance of the whole OFDM systems. Hence, before signals can be

demodulated, OFDM symbols need to be time-synchronized and carrier frequency offset compensated. Many synchronization algorithms for OFDM systems have been proposed, which can be divided into three main categories: The first one is based on specific training sequences at the beginning of radio frame .For instance, schemes based on duplicate structures of training signals are introduced in refs. [1-3]; The second one is to maximize the average log likelihood function with the cyclic prefix inserted, as proposed in refs. [4]; The third one is of a hybrid close-loop structure exploiting training sequences and data-decision-feedback information, as discussed in refs. [5]. In this paper, we propose an effective synchronization scheme as a modification to Schmidl&Cox’s method[1]. This modified method can eliminate the symbol timing plateau, while avoids resource loss.

2 OFDM Systems Model

The base band model of OFDM systems is shown in Fig.1. In the transmitter, the N serial input symbols are first converted from serial to parallel to form a vector of N symbols. (N is the number of sub-carriers in OFDM systems). Then, the N symbols are modulated onto N sub-carriers by the IFFT, which are converted back from parallel to

serial (P/S) data symbols and a guard interval gN is

inserted before these data symbols. The resulting OFDM symbols are serially transmitted over various channels, whose duration of impulse response is

assumed to be less than gN . In the receiver, the

inverse operation is performed.

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The Eighth International Conference on Electronic Measurement and Instruments ICEMI’2007

In discrete form, the output of the N-point IFFT can be described as:

1

0

1 2exp , 0,1,2, , 1N

nn

j kns k X k NNN

1

where nX is the data symbol on the n-th sub-carrier,

N is the number of sub-carriers. Considering the unknown symbol arrival time and carrier frequency offset f , the received OFDM signals with additive Gaussian noise n(k) is given by:

2exp( ) ( )

fkr k s k j n k

N 2

3 Schmidl & Cox method

Schmidl & Cox’s synchronization algorithm was proposed in 1997 [1], which includes two PN sequences to finish synchronization. Table 1 illustrates the use of PN sequences (c1,k , c2,k ) in the training sequences for an OFDM symbol with nine sub-carriers with the points from a subset of a 256-QAM constellation.

3.1 symbol timing synchronization method The first training sequence in Table 1 contains two

identical halves in time domain after IFFT. According to

IFF

T

D/A C

hannel

A /D

Sync

S/P Remove

CP

FFT P/S bit stream

S/P P/S Insert cp (N)

r(k)

bit stream Xn s(k)

Fig. 1 Block Diagram of A Base Band OFDM System

the first training sequence where the first half is identical to the second half, expect for a phase shift caused by the carrier frequency offset. If the conjugate of a sample from the first half is multiplied by the corresponding sample from the second half, the effect of the channel should cancel. At the start of the frame, the products of each of these pairs of samples will have approximately the same phase, so the magnitude of the sum will be a large value, and let the sum of the pairs of products be:

/ 2 1

0

*( ) /2N

m

P d d m d m Nr r 3

The received energy for the second half-symbol is defined by:

/ 2 1

0/ 2

2( )

N

md m NR d r 4

The timing metric is given by:

2

2( )

( )( )

P dM d

R d 5

Where d is a time index corresponding to the first sample in a window of N samples. The timing metric reaches a plateau (Fig.3) which leads to some uncertainty as to the start of the frame.

Table 1 Illustrates of Use of PN Sequence for The Training Sequences

Freq.num.k -4 -3 -2 -1 0 1 2 3 4 c1,k 7+7j 0 -7+7j 0 7+7j 0 7-7j 0 7+7j c2,k 5-5j -5-5j -5-5j -5+5j -5-5j 5+5j -5+5j 5-5j 5+5j

-j j -1 -1 1 2,2

1,

c kvk c k

vk is the differentially-modulated PN sequence on the even frequencies of the second training symbol

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The Eighth International Conference on Electronic Measurement and Instruments ICEMI’2007

3.2 frequency offset estimation method Assume the frequency offset would be

f f o i f of f f ( ffof is fractional

frequency offset and ifof is integer frequency

offset),from the above symbol timing estimation shown, near the best timing point, the main difference between the two halves of the first training symbol

will be a phase difference of T f , then fraction

frequency offset estimation is / Tffof , after

the two symbols are frequency corrected by

/ T (by multiplying the samples by ),

Let their FFT’s be Y

2 /j t Te

1,k Y2,k .The PN sequence vk will appear at the output except it will be shifted by 2z

z is an integer positions because of the uncompensated frequency shift of 2z/T. Let X be the set of indices for the even frequency components: The number of even positions shifted can be

calculated by finding to maximize g

2* *

1, 2 2 , 2( )

2 22 ( )2 ,

Y v Yk g k k gk XB g

Y kk X

6

With integer g spanning the range of possible frequency offsets and W being the number of even frequencies with the PN sequence. Then the frequency offset estimate would be:

7 '

f / 2 /T g T

4 Modified Method

For eliminating the timing plateu caused by

Schmidl&Cox method, the samples of the modified training symbol(excluding cyclic prefix) are designed to be of the form(in the time domain):

Where A represent samples of length L=N/8 in the time domain. B is symmetry sequence of training sequence A, as shown in Fig.2. 4.1 symbol timing synchronization algorithm The timing metric of modified method is given by:

( )3( )3 2 ( )3

P dM d

R d8

/2( ) ( )( )3

0

NP d r d k d k

k9

2/ 2( ) ( )3

0

NR d r d k

k 10

4.2 frequency offset estimation algorithm From the above Schmidl&Cox method’s frequency

offset estimation shown, near the best timing point, the main difference between the first and the third parts of modified training symbol will be a phase

difference of /2T f , then Integer frequency

offset estimation can be gotten by

2 /f T and the main difference

between the first and the seventh parts of modified training symbol will be a phase difference of

3 /T f

WWWW

2, then Frequency offset coarse estimation

can 2 / 3f T .

X ,2,...,4,2,2,4,...,2,

Fig. 2 Training Sequence Structure of Modified Algorithm

a b c c a a b c c b a b c c b a a c c b a

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The Eighth International Conference on Electronic Measurement and Instruments ICEMI’2007

5 Results and Analysis

Performance of the modified algorithm in the paper has been carried by the computer simulation .In the simulation process, the system used is 1024 sub-carriers ,100 point guard interval, QAM modulation under AWGN channel of no intersymbol interference. We construct a Gaussian noise generator for analoging noise and use a random

generator for producing frequency offset f ( in

0 2/ TFFT) ,then we will add noise and frequency offset generated to the transmitted signal.

The timing metrics of Schimdl & Cox method and modified method are shown in Fig.3 the modified method eliminate the timing plateau and have steeper roll-off timing metric off the correct timing point .

Fig. 4 has given out the mean square error of the modified method in different signal-to-noise As Fig.4 shown ,the difference of received signals and transmitted signals is very small.It can accurately renew the original signal.

Fig.3 Timing Metric Curve of Schimd&Cox

and The Modified Method

Fig. 4 Mean Square Error of The Modified

Method in Different Signal-to-Noise

6 Conclusion

Based on the training sequence structure of Schmidl & Cox synchronization method, we design a proper training sequence structure in the modified method, which exists symmetry in the time domain and only uses a training symbol to achieve synchronization problems of OFDM systems. The modified method can eliminates the timing plateau caused by Schmidl&Cox synchronization method for OFDM systems and reduces the computation complexion and improves spectrum resources’ efficiency.

References

[1]. T.M.Schmidl and D.C.Cox, “Robust frequency and timing

synchronization for OFDM,”IEEE Trans .on

Comms.Vol.45,No.12,Dec 1997,pp.1613-1621.

[2]. PARK Byungjoon, “ A novel timing estimation method

for OFDM systems[J]. IEEE Communications Letter, 2003,

7(5):239-241.

[3]. P.H. MOOSE, “A Technique for Orthogonal Frequency

Division Multiplexing Frequency Offset Correction,”

[J].IEEE Trans. Commun . Vol.42, pp. 2908-2914, 1994.

[4]. J.-J.van de Beek, M. Sandell, P .O. Borjesson, “ML

estimation of timing and frequency offset in OFDM

systems,” IEEE Trans On Signal

Processing,vol.45,pp.1800-1805,Jul.1997.

[5]. BOLCSKEI H. Blind estimation of symbol timing and

carrier frequency offset in wireless OFDM systems[J].IEEE

Transactions on Communication,2001,49(6):988-996.

[6]. M.Luise and R.Reggiannini, “Carrier Frequency

Acquisition and Tracking for OFDM Systems,” IEEE

Trans.Commun.,

Author Biography

ChangHuan(1982-) was born in China. She received the

B.S.degree in electrical engineering from Xinjiang Normal

University. She is now a M.S. candidate at School of

Automation, Xi’an University of Technology. Her areas of

research interests include communication theory and statical

signal processing.

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