Three Timing Synchronization Methods Based on Two Same Preambles for OFDM Systems

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Procedia Engineering

ProcediaProcedia Engineering 00 (2011) Engineering 29 000–000 (2012) 1656 – 1661 www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Three Timing Synchronization Methods Based on Two Same Preambles for OFDM Systems Chao Chen*, Zhanxin Yang Engineering Center of Digital Audio and Video, Communication University of China 100024 Beijing, China

Abstract The purpose of this paper is to propose two fast timing synchronization methods of OFDM System which has two preamble symbols, the two preamble symbols are used for SNR estimation for OFDM systems. The synchronization techniques are examined in Multipath fading environments for comparison. The results of the performance comparison are presented in terms of mean obtained by simulations.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology Keywords:synchronization; OFDM; SNR estimation; two preambles;

1 Introduction There are two based ways for timing synchronization of general OFDM systems, the data-aided categories and the non-data-aided estimation. The data-aided category uses a training sequence or pilot symbols for estimation. It has high accuracy and low calculation, but loses the bandwidth and reduces the data transmission speed. The non-data aided category often uses the cyclic prefix correlation. It doesn’t waste bandwidth and reduce the transmission speed, but its estimation range is too small and the arithmetic is complex, not suitable for acquisition. In most successful cases, only the data-aided method was used. So in this paper, only the data-aided methods will be discussed. For the OFDM system which has only one preamble, there are many mature synchronization algorithms. In this section, 3 different timing offset estimation algorithms will be briefly described.

Chao Chen. Tel.: +86-9577-9082; E-mail address: [email protected].

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.01.190

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1.1 Schmidl’s Method Two training symbols are placed at the beginning of each frame as preamble [1]. The training symbol has two identical halves in the time domain. It has the following pattern: S s = [ A, A]

(1)

To detect the frame, the conjugate of a sample from the first half is multiplied by the corresponding sample from the second half, and then at the start of the frame, the products of each of these pairs of samples will have approximately the same phase and the magnitude of the sum will be peaked. The timing metric of this estimator is given by P (d )

M (d ) = L −1

∑ (r

= P (d )

2

( R ( d )) *

m =0

d +m

L −1

(2)

2

⋅ rd + m +l )

R ( d ) = ∑ rd + m + l

(3) (4)

2

m =0

Here L = N / 2 is the length of complex samples in one half of first training symbol (excluding Cyclic Prefix), rk is the received signal, and d is a time index corresponding to the first samples in a sliding window of 2L samples.

Figure 1. (a)Timing metric in Schmidl’s method

(b)Timing metric in Minn’s method

As show in Figure 1(a), in the range of CP, due to its circulation, M(d) had little difference, this phenomenon is called the ‘peak plateau phenomenon’. 1.2 Minn’s Method Based on Schmidl & Cox method, Minn et al [2] modified the training sequence’s pattern and timing metric’s definition and designed the first training symbol having four parts with following patterns: S M = [ A, A, − A, − A] (5) Where A represents samples of length L = N / 4 generated by N / 4 point IFFT modulated data of a PN sequence. The timing metric used in the evaluation of the technique is given by (2) where = P (d )

1

L −1

∑∑r

= k 0= m 0

1

*

d + 2 Lk + m

L −1

⋅ rd + 2 Lk + m + L

R ( d ) = ∑ ∑ rd + 2 Lk + m + L = k 0= m 0

2

(6) (7)

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Where rk is the received signal, and d is a time index corresponding to the first sample in a sliding window of 4L samples. Minn designed the new frame structure, increased the difference between adjacent time scales, and re-defined the time scale function. Thus it bring negative values for the correlation function near the correct, thereby this method can solve the ‘peak plateau phenomenon’ by Schmidl’s way. See figure 1(b). 1.3 Park’s Method Minn’s method reduces the timing metric plateau found in Schmidl’s method but the MSE is still large particularly in ISI channels. This is resulted from the timing metric values around the correct timing points in Minn’s method are almost the same. Park et al [3] proposed to increase the difference between the peak timing metric with respect to other metric values. The proposed method entails modifying the training sequence’s pattern and timing metric’s definition to maximize the different pairs of product between them. The first training symbol having four parts with the following patterns: (8) S P = ⎡⎣ A, B, A* , B* ⎤⎦

Where A represents samples of length L = N / 4 generated by IFFT of a PN sequence. B is designed to be symmetric with A ， A* and B * are conjugate of A and B respectively. The timing metric is given by (2), where = P (d )

N 2

∑r k =0

N 2

d −k

⋅ rd + k

R ( d ) = ∑ rd + k

(9)

2

(10)

k =0

where rk is the received signal.

Figure 2.

(a)Time metric in Park’s method

(b) Structure of two preambles

As figure 2(a), Park’s method can position uniquely. 2 Timing Synchronization for Two Preamble

In most OFDM systems, there is only one preamble as the synchronous symbol, the timing synchronous algorithms based one preamble perform accurately and fast. But in individual case, two same preambles are needed, such as the system which could conduct the SNR estimation mentioned by Boumard [5]. If the system includes noise estimation, then we must have two identical preamble symbols, as in figure 2(b). Considering the synchronization symbol 1 and synchronization symbol 2 have the same structure, so we can’t use the methods which have been introduced in previous section. We must re-adjust the time scale function.

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Next, according to the characteristics of the synchronous symbol, this paper introduces three schemes for the time synchronization. 2.1 Method 1 As shown above, we can put the two synchronization symbols and CPs together as two identical vectors which the length is TS = Tu + Tg .Where Tu is the length of the symbol and Tg is the length of CP. Thus, compared with Schimidl’s method, we can found that the two preambles have the similar structure. But in Schimidl’s method, the CP in front of the symbol is the same as the end of the symbol, so, leading the ‘peak plateau phenomenon’. If still in accordance with the Schimidl’s algorithm operation, but the operation method of measuring range is extended to include CP the synchronization symbol length, we can get L −1 (11) = P ( d ) ∑ ( r * d + m ⋅ rd + m + l ) m=0

R (d ) =

L −1

∑

m=0

rd + m + l

2

(12)

Where L is the sum of N points FFT and the cyclic prefix length. To calculate time scale function, we can get result as figure 3(a).

Figure 3. (a)Time metric in method 1 for two preambles

(b) Time metric in step 1 method 2

Comparison of Schimid’s method, due to extended sliding window, it can reach the maximum value in the correct position, and avoid the phenomenon of" peak value platform". But the method has two disadvantages. • Due to the extension of L, this method cause much more computation. With the increasing of N, the computing of complex multiplication and addition will increase 2N. • Because the value near the correct position changed slowly, so the method did not achieve good synchronous effect, it can’t get synchronization when the SNR is less than 8 dB. 2.2 Method 2 Considering the computation of the method 1 is too much to find the signal in time, we have to find a new method to reduce the computation. In the two synchronization symbol, there are four complete same zones. Zone 1, zone 2, zone 3 and zone 4. Due to the four zones, we could follow the next two steps to achieve synchronization.

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Figure 4.

Two preambles synchronization method 2

Figure 5.

(a) Time metric in step 2 method 2

5

(b) Time metric in Method 3

y

Step1 : In terms of the two same intervals, zone 1 and zone 3, combining with Schimidl’s way, we change the time scale as follow: = P ( d1)

L −1

∑ (r

*

m =0

d 1+ m

⋅ rd 1+ c + m + l )

L −1

R ( d1) = ∑ rd 1+ c + m + l

2

(13) (14)

m=0

Where L represents the length of CP, C is the length of FFT, thus we can coarsely find the starting position as Figure 3(b). y Step 2: In the first step, we can get two pulses by time scaling function. The first pulse is the starting point of the first symbol including CP. The second pulse is the starting point of the second symbol including CP. Nest step, with second pulse as the centre, we make the time range smaller to do Schimdl’s method to get fine synchronization. As follow = P ( d 2)

L' −1

∑ (r

m=0

*

d 2+ m

L' −1

⋅ rd 2 + c + m )

R ( d 2 ) = ∑ rd 2 + c + m

2

(15) (16)

m=0

'

Where L and c are all the length of CP. After the two steps, we could easily and accurately find the starting point of the OFDM symbol. And this method reduced the amount of computation greatly, total consumption of the two steps is the 2c/(c+N) of the first method. Where c is the length of CP and N is the FFT point. Generally speaking, N is as 4-16 times as c in OFDM system. 2.3 Method 3 In method 2, zone 2 and zone 3 are exactly the same and adjacent, as shown in figure 4. We can design the two zone as the following pattern:

S3 =[ A, − A, A, − A] Refer to Minn’s method, the time metric function is amended as follow:

(17)

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1

L −1

P (d ) = ∑∑ rd*+ Lk + m ⋅ rd + Lk + m + 2 L k =0 m =0 1 L −1

R (d ) = ∑ ∑ rd + Lk + m + 2 L

2

(18) (19)

k =0 m =0

Then we got figure 5(b):

Figure 6. (a) Synchronization error ratio in AWGN channel

(b) Synchronization error ratio in multipath

Method 3 is an ideal arithmetic with small computation quantity and precise positioning 3. Simulation and Conclusion The simulations are carried out to evaluate the above 3 methods, and the methods will be tested in AWGN channel and multipath fading channel. As shown in figure 6(a) and figure 6(b), in the AWGN condition, each methods has good performance, when the SNR is over 5dB, all of the methods have no error positioning. In the multipath fading channel, due to the effects of multipath and Doppler frequency shift, the positioning accuracy is not very high, and has ‘plateau effect’, which denote how to improve the SNR, we can’t get better performance. In fact, in the condition that exist multipath and Doppler shift, the frequency and the phase of the received signal were changed. So, for any kind of time synchronization there is the platform effect, which requires the use of frequency synchronization to adjust the capability. Acknowledgment

The author would like to thank the crew of Engineering Center of Digital Audio and Video, Communication University of China for hard works and Sponsor by Important National Science & Technology Specific Projects (2010ZX03005-001).M References [1]

Timothy M. Schmidl ， Donald C. Cox, “Robust Frequency and Timing Synchronization for OFDM”, IEEE

TRANSACTIONS ON COMMUNICATIONS, VOL. 45, NO. 12, DECEMBER 1997 [2]

Minn H, Bhargava V.K,“ A simple and efficient timing offset estimation for OFDM systems ”，Vehicular Technology

Conference Proceedings, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st ，2000 , Page(s): 51 - 55 vol.1 [3]

Byungjoon Park, Hyunsoo Cheon, Changeon Kang, Daesik Hong,“A novel timing estimation method for OFDM

systems ”, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE ,Volume: 1 2002 , Page(s): 269 - 272 vol.1. [4]

Fan Wu, Mosa Ali Abu-Rgheff，“Time and Frequency Synchronization Techniques for OFDM Systems operating in

Gaussian and Fading Channels: A Tutorial” [5]

Boumard, S.” Novel Noise Variance and SNR Estimation Algorithm for Wireless MIMO OFDM Systems”, Global

Telecommunications Conference, 2003. GLOBECOM '03. IEEE , Page(s): 1330 - 1334 vol.3, 2003.