En Zhou, Xiaolin Hou, Zhan Zhang, and Hidetoshi Kayama. Innovative Radio Transmission Lab. DoCoMo Beijing Communication Laboratories Co., Ltd. Beijing ...
A Preamble Structure and Synchronization Method based on Central-Symmetric Sequence for OFDM Systems En Zhou, Xiaolin Hou, Zhan Zhang, and Hidetoshi Kayama Innovative Radio Transmission Lab DoCoMo Beijing Communication Laboratories Co., Ltd Beijing, P.R. China Email: {zhou, hou, z.zhan, kayama}@docomolabs-beijing.com.cn
Abstract—This paper proposes a novel preamble structure and a synchronization method based on central-symmetric sequence for OFDM systems. The preamble structure can be easily constructed in frequency domain and is spectrum efficient which can afford time and frequency synchronization, channel estimation, SNR estimation. And a new timing estimator is also proposed according to the preamble structure, which combined the merits of delayed and symmetric correlation based methods. The proposed timing estimator can well suppress interferences and get better timing performance. Compared to the typical Park’s method, proposed method is super in low SNR environment and almost the same in high SNR environment.
I. I NTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) is an effective technique to combat multipath fading. In OFDM system, the insertion of a guard interval between symbol blocks called cyclic prefix (CP) mitigates inter-symbol interference (ISI). OFDM has been adopted as the modulation scheme for DAB (Digital Audio Broadcasting) system, ADSL (Asymmetry Digital Subscriber Loop), 3GPP LTE (Long Tern Evolution) specifications, and IEEE802.11n, IEEE802.16 standards. And it is also the core technique of future broadband mobile communication systems (IMT-advanced). Synchronization is important for OFDM systems. Till now, a lot of methods [1]-[10] have been proposed, in which large amount of methods are based on preambles. Such preamble based methods have satisfied and robust synchronization performances with low computational complexity. Generally, they can be further divided into two categories, category I: delayed correlation based methods [1]-[3]; category II: symmetric correlation based methods [4]-[6][10]. The typical cyclic prefix based methods [2] and repetition preamble based methods [1][3] belong to category I. The principal merit of category I methods is that it is easy for real implementation and can perform time and frequency synchronization simultaneously. However, the obtained timing metric is triangle-like shape, which is hard to get accurate timing performances. As to the methods of category II, the principal merit is that it can obtain pulse-like timing metrics, which is advantageous for accurate timing performances. However, the computational complexity will be much larger than that of category I.
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And the preambles they employed are not very suitable for frequency offset estimation. In order to obtain satisfied timing performance, methods of category II are considered. Literature [5] has addressed the synchronization preamble structure and method using symmetric identical preamble. The preamble has two identical symmetric parts and the timing metric is constructed using symmetric correlation profile. However, its construction of timing metric has not eliminated the effect of frequency offset. Hence, its timing performance will be heavily deteriorated by the system frequency offset. Furthermore, there have two side peaks in the obtained timing metric. And it just uses maximum operation to detect the desired position, which is not practical. Park [4] has also proposed one timing synchronization method using central-symmetric sequences. It can obtain pulse-like timing metric shape and very satisfied timing performance. Furthermore, Park’s preamble structure and timing metric construction has removed the effect of frequency offset. Hence, its timing performance has no relationship with system frequency offset. However, Park’s preamble structure can only perform time synchronization, not support frequency offset estimation and channel estimation. As to the mentioned two methods, both preamble structures can’t be constructed in frequency domain. Hence, they are not flexible and virtual subcarrier friendly. In this paper, symmetric correlation based synchronization method will be addressed. A spectrum efficient preamble structure will be proposed, which can be easily constructed in frequency domain. According to the preamble structure, a new timing estimator will be proposed which combines the merits of delayed correlation based methods and symmetric correlation based methods. The rest of the paper is organized as follows: The proposed preamble structure and related timing estimator is described in Section II. Our simulation results are discussed in Section III and the field experiment test are briefly introduced in Section IV. Finally, Section V gives the conclusion. II. P ROPOSED P REAMBLE S TRUCTURE AND R ELATED T IMING E STIMATOR The desired synchronization preamble should have central symmetric property which will be used to get accurate timing
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Fig. 1.
Central-symmetric sequence (basic element)
Fig. 3.
Fig. 2.
Central-symmetric sequence (basic element)
synchronization performance. To generate the desired preamble sequence, the following constrains are made: 1) Preamble can be constructed in frequency domain 2) Frequency pilots have two discrete phase states (ϕ and ϕ ) Thus, if ϕ and ϕ has the relationship of ϕ = π + ϕ, the corresponding time domain signal will have central-symmetric structure as shown in Fig. 1, in which notation C represents ˜ represents its reverse version. Sequence C will a sequence, C have a length of N/2 − 1, where N is the whole sequence’s length. And the symmetric correlation profile will have a constant phase 2ϕ. This can be easily proved using the property of Inverse Discrete Fourier Transform (IDFT) operation. Denote a length N frequency domain sequence by X(k) and the corresponding conjugate version by X ∗ (k). Transform sequence X(k) using IDFT, the obtained time domain signal is denoted by x(n), and x(n) = IDF T [X(k)]. According to the definition of IDFT, we can easily obtained that IDF T [X ∗ (k)] = x∗ (N − n), 0 ≤ n ≤ N − 1 (1) x(N ) = x(0) ¯ If X(n) is a real sequence with length N , rotate sequence ¯ ¯ X(n) with a phase ϕ and denote by X(n) = exp(jϕ)X(n), sequence X(n) would have two discrete phases ϕ and π + ϕ. ¯ Since X(n) is a real sequence, hence ∗ ¯ ¯ X(k) = (X(k)) ⇒ exp (−jϕ) X(k) = exp(jϕ)(X(k))∗
serially denoted as C, D, C, D. Sequence D is the rotated reversed conjugated version of sequence C. If sequence C is defined as C = {x(n)}, the corresponding sequence D is ˜ ∗. defined as exp(j2ϕ){x∗ (N − n)}, hence D = exp(j2ϕ)C The preamble structure has a series merits and is also spectrum efficient. If we call the structure of Fig. 1 as a basic element, proposed preamble structure is just the two repetitions version of basic element. It can be obtained directly by transforming the frequency signal that only has pilots on even subcarriers. Equal energy pilot signals can be used to construct the preamble. Thus it can afford channel estimation function. Furthermore, pilot signals are assigned on even subcarriers and odd subcarriers are set to be zeros. This feature can be used to estimate the average received SNR. The second half part is the repetition of the first half part, Moose scheme [1] can be used for frequency offset estimation. And the preamble has delayed and symmetric correlation properties, which both can be used for timing synchronization. Because the other functions are similar with the conventional method, timing synchronization will be focused on in the following description. A new timing metric will be proposed which combines the merits of delayed and symmetric correlation profile. The only drawback is that it has two side peaks. However, the error detection caused by the side peaks can be easily avoided. Symmetric correlation profile is calculated as
N/2−2
Γs (d) =
r(d + N/2 − 1 − n)r(d + N/2 + 1 + n) (3)
n=0
where r(n) is the received preamble signal. And the delayed correlation profile can be calculated as
∗
⇒ exp (−jϕ) IDF T [X(k)] = exp(jϕ)IDF T [(X(k)) ] ⇒ x(n) = exp(j2ϕ)x∗ (N − n)
Central-symmetric sequence (basic element)
(2) The proposed preamble structure is shown in Fig. 2. Preamble with one OFDM symbol length is divided into four parts,
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N/2−1
Γd (d) =
k=0
r∗ (d + k)r(d + N/2 + k)
(4)
(a) Large threshold
(b) Small threshold Fig. 4.
Schematic diagram of timing decision
The received signal power is
N/2−1
Pd (d) =
|r(d + k)|2
(5)
k=0
A novel timing metric is defined as M (d) =
|Γs (d)| · |Γd (d)| (P (d))2
(6)
Here, the proposed timing metric is the production of the symmetric correlation profile and delayed correlation profile. The product operation at least has the following merits: 1) The interference caused by the neighbored data signals can be well suppressed; 2) The side peaks can be further reduced and the timing metric becomes sharper; 3) the dynamic range of timing metric will be reduced compared to the conventional squared operation [4][5]. Fig. 3 gives an example of the proposed timing metric in multipath channel environment, from which we can see that the final timing metric has better property and advantage for timing synchronization. For conventional timing estimators, most of the published methods [2][4][5] make decisions according to the maximum values of the obtained timing metrics. However, maximum operation is not practical in real systems. In other words, position of the first path should be located when in multipath environment, not the strongest path. So, practical situation is that the desired position is always detected according to a well designed threshold. As shown in Fig. 3, the obtained timing metric has two side peak areas. When the threshold is much low, there would make error decision. So, a new detection algorithm should be designed to solve this ambiguity caused by side peaks. And the threshold should also be carefully designed and adaptively varied to meet different environment. To solve the ambiguity problem caused by side peaks, one possible detection method is illustrated in Fig. 4. After timing metric is obtained, the position where the timing metric
Fig. 5.
Schematic diagram of timing estimator
is firstly larger than the threshold can be detected as d0 . If the timing metric only has one peak, position d0 is the desired position. However, there have two sided peaks in the timing metric, apart from the main peak with distance N/4 samples from both directions. Hence, the correct position must be in the two candidates d0 and d0 + N/4. Theoretically, the value of side peak is about 1/4 of that of the main peak. And they will vary in the same direction because the observation signal sequence is identical. Hence, there is no probability of the side peak larger than the main peak. According to the obtained position d0 , two unoverlapped areas can be defined, area 1: d0 + [−D0 , · · · , 0, 1, D1 ] and area 2: d0 + N/4 + [−D0 , · · · , 0, 1, D1 ], where D0 and D1 are the forward and backward search depth compared to the first path respectively. To obtain robust detection performance, D0 should be about several samples and larger than or close to the maximum channel delay. If the maximum value of the timing metric in area 1 is larger than that in area 2, the desired timing position can be decided as d0 , otherwise d0 +N/4. The schematic diagram of the detection method is shown in Fig.
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4(a) and Fig. 4(b) when threshold is large or low respectively. Fig. 5 gives the schematic diagram of the proposed timing estimator. The received signals pass through two channels, one calculates the timing metric and another calculates the received signal power. The production result of the signal power and coefficient β is as the threshold and compare with the timing metric delayed of N/4 samples. If the delayed timing metric is larger than threshold, limited area maximum search operations are triggered for the timing metric and the delayed timing metric respectively. The larger one of the obtained two maximum values corresponding two unoverlapped areas will help to make the correct decision. Adaptive threshold design is also important for real application. The absolute value of the obtained timing metric will vary much large in different channel model and different SNR environment. Hence, the threshold should also be varied adaptively to track the variety of channel. Considering the value of timing metric has integrated all effects and the strong correlation between two neighbored frames, the value of side peak in current frame can be used to construct the threshold for the following frame. Thus, the threshold coefficient can be designed as βn = max{βmin , |Mn−1 (dˆ − N/4)|} (7) β0 = βmin
Fig. 6.
where Mn (d) is the timing metric value on position d in the nth frame and dˆ is the obtained timing decision. The threshold coefficient is mainly determined by the value of timing metric side peak in the fore frame. However, when SNR is very low and the number of multipath is very large, the value of timing metric would become very small. Thus, the minimum value of the threshold coefficient βmin should be bounded. The value of βmin could be set according to simulation results.
Fig. 7.
Performance of detection method
Timing performance comparison (threshold detection)
III. S IMULATION R ESULTS Simulations are performed to evaluate the superiority of the proposed timing estimator. System bandwidth is assumed to be 12.5MHz, and the corresponding sample interval is 80 ns. The total bandwidth is divided into 1024 subcarriers with subcarrier space of 12.2kHz. The length of cyclic prefix is 96 samples and typical urban (TU) channel model is employed. For the threshold, βmin should be optimized in advanced according to the channel environment. In our simulation, βmin is optimized by simulations and set to be 0.1 for the following evaluations. Fig. 6 gives the performance of detection method. The horizontal axis is the timing offset compared to the first path and the vertical axis is the corresponding probability. The top sub-figure shows the obtained result using the conventional detection algorithm that is just according to a threshold. From it we can see that the obtained timing decisions are mainly centered on two areas, which are around the main peak and the fore side peak respectively. However, when using the proposed detection method depicted in Fig. 4, all the obtained timing decisions are around the main peak area. Thus, the ambiguity problem is overcome by the proposed detection method.
Fig. 7 compares the timing performance of the proposed method and Park’s method [4] when using threshold detection method. As shown in Fig. 7, the proposed method is better than Park’s method in low SNR environment while almost the same in high SNR environment. Fig. 8 further compared the performance when using maximum operation to detect the desired position. In this case, side peaks have no effect to the timing performance. The only factor that will affect the timing performance is the different timing metric. As shown in Fig. 8, the performance of proposed method is much better than Park’s method in low SNR environment while almost the same in high SNR environment. This is because that the proposed timing metric can suppress the interference caused by the data signal and the preamble signal. This effect is especially obvious in low SNR environment for the existence of large interference. Fig. 9 gives the probability distribution function (PDF) performance comparison when using threshold detection. Timing estimator’s PDF performances are mainly affected by channel environment (channel model). Timing shifts compare to the
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Fig. 8.
Timing performance comparison (maximum value detection)
Fig. 9.
PDF performance comparison
first path only have several discrete values, which are mainly determined by the channel model. When the energy of the first path is not very weak, the position of the first path can be located. However, if the energy of the first path is too week and lower than threshold, the position of the second path would be located, and so on. Only all the fore paths’ energies are lower than threshold, the timing estimator would locate on the position of back paths. In this case, it would not introduce inter-symbol interference and degrade system performance because the energies of fore multipaths are very low and can be ignored.
combines the symmetric and delayed correlation profiles. The timing metric can well suppress interferences caused by data signal and preamble signal itself. Considering real application, threshold based timing detection is adopted. A timing detection method is proposed to solve the ambiguity decision problem caused by side peaks. And an adaptive threshold is also designed. Simulation results demonstrate that proposed timing estimator can get accurate timing performance. Compared to the typical Park’s method, proposed method is super in low SNR environment and almost the same in high SNR environment.
IV. F IELD E XPERIMENT E VALUATION
R EFERENCES
To further verify the performance and the feasibility of the proposed method, FPGA hardware testbed has been implemented. The OFDM baseband signal is generated by transmitter FPGA board which has multiplexed the synchronization preamble signal. Then the baseband signal is modulated to RF signal by signal generator. The wireless channel is emulated by channel emulator in RF mode. And synchronization method is implemented in receiver FPGA board. To reduce hardware resource, the signal is one bit quantized when performing symmetric correlation operation. This quantization would not affect the final synchronization performance much while can greatly reduce the consumed hardware resource. The obtained field test results are well in accordance with the theoretical simulation results. And it can work well in high mobility environment even up to 120km/h.
[1] P.H. Moose, ”A technique for orthogonal frequency-division multiplexing frequency offset correction,” IEEE Trans. on Commu., vol.42, no.10, pp.2908-2914, Oct. 1994. [2] J.J. van de Beek, M.Sandell, and P.O. Borjesson, ”ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. on Signal Processing, vol.45, pp.1800-1805, July 1997. [3] T.M Schmidl, D.C.Cox, ”Robust frequency and timing synchronization for OFDM,” IEEE Trans. on Commu., vol.45, pp.1613- 1621, Dec. 1997. [4] Byungjoon Park, Hyunsoo Cheon, and Daesik Hong, ”A novel timing estimation method for OFDM systems”, IEEE commun. letters, vol.7, no.5, pp. 239-241, May 2003. [5] Kwang-chul Kim, ”Method for creating symmetric-identical preamble and method for synchronization symbol and frequency of orthogonal frequency division multiplexed signals by using symmetric-identical preamble”, SAMSUNG ELECTRONICS CO., LTD., US patent, Pub. No.: US 2003/0072256 A1, Pub. Date: Apr. 17, 2003. [6] M. Morelli, ”Timing and frequency synchronization for the uplink of an OFDMA system,” IEEE Trans. on Commu., pp.296-306, Feb. 2004. [7] En Zhou, Xing Zhang, Hui Zhao, and Wenbo Wang, ”Synchronization algorithms for MIMO OFDM systems,” IEEE WCNC 2005, vol.1, pp.1822, March 2005. [8] En Zhou, Hui Zhao, and Wenbo Wang, ”Timing Synchronization for Interleaved OFDMA Uplink System,” IEEE ICCCAS 2006, vol.2, pp.11471152, June 2006. [9] En Zhou, Yuyu Yan, and Wenbo Wang, ”A Novel Timing Synchronization Method for Localized OFDMA Uplink System,” IEEE ICC 2006, vol.11, pp.5086-5090, June 2006. [10] Zhongshan Zhang, Hidetoshi Kayama, and C Tellambura, ”Joint Frame Synchronization and Carrier Frequency Offset Estimation in Multicarrier Systems,” IEEE GLOBECOM 2006, pp.1-6, Nov. 2006.
V. C ONCLUSION In this paper, a novel preamble structure and synchronization method has been proposed, which combines the merits of symmetric and delayed correlation based methods. The preamble structure can be easily constructed in frequency domain and is also spectrum efficient. In addition to time and frequency synchronization, it can also afford channel estimation, SNR estimation. According to the novel preamble structure, a new timing metric has been proposed, which
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