- Research
- Open Access
Semiblind frequency-domain timing synchronization and channel estimation for OFDM systems
- Te-Lung Kung1Email author and
- Keshab K Parhi1
https://doi.org/10.1186/1687-6180-2013-1
© Kung and Parhi; licensee Springer. 2013
- Received: 12 October 2012
- Accepted: 4 December 2012
- Published: 2 January 2013
Abstract
In this article, we propose unit vectors in the high dimensional Cartesian coordinate system as the preamble, and then propose a semiblind timing synchronization and channel estimation scheme for orthogonal frequency division multiplexing (OFDM) systems. Due to the lack of useful information in the time-domain, a frequency-domain timing synchronization algorithm is proposed. The proposed semiblind approach consists of three stages. In the first stage, a coarse timing offset related to the delayed timing of the path with the maximum gain in multipath fading channels is obtained. Then, a fine time adjustment algorithm is performed to find the actual delayed timing in channels. Finally, the channel response in the frequency-domain is obtained based on the final timing estimate. Although the required number of additions in the proposed algorithm is higher than those in conventional methods, the simulation results show that the proposed approach has excellent performance of timing synchronization in several channel models at signal-to-noise ratio (SNR) smaller than 6 dB. In addition, for a low-density parity-check coded single-input single-output OFDM system, our proposed approach has better bit-error-rate performance than conventional approaches for SNR varying from 3 to 8 dB.
Keywords
- Timing synchronization
- Fine time adjustment
- Channel estimation
- Orthogonal frequency division multiplexing (OFDM)
- Unit vectors
- Frequency-domain processing
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is a promising technology to support high-rate wired and wireless applications due to its robustness to multipath delay spread[1–3]. However, in OFDM systems, synchronization errors can destroy the orthogonality among the subcarriers and result in performance degradation. Thus, timing synchronization in OFDM systems becomes much more challenging due to the increase in the amount of inter-carrier interference (ICI) and inter-symbol interference (ISI)[1]. Although the soft decoders employing error correction code can improve the system performance at low signal-to-noise ratio (SNR), perfect timing synchronization is necessary for the decoder to operate correctly. Therefore, in order to improve the system performance, it is important to find the actual delayed timing in multipath fading channels at the receiver. In addition, channel estimation also plays a crucial role in providing the channel information to the soft decoder and compensating the signal during the demodulation process[4]. Without the knowledge of timing offset and channel information at the receiver, the system will have a poor performance during the entire data transmission.
Various synchronization techniques for orthogonal frequency division multiplexing (OFDM) systems have been developed using well-designed preambles[5–14]. Although accurate timing estimation can be achieved, the bandwidth efficiency is also inevitably reduced. In order to reduce the waste of bandwidth, non-data aided synchronization algorithms based on the cyclic prefix (CP) have been proposed[15, 16]. However, in some multipath fading channels with non-line-of-sight (NLOS) propagation, both data-aided and non-data-aided synchronization methods frequently lead to the delayed timing in channels where the delayed path has larger gain than the first path. In this case, the resulting ICI and ISI would degrade the system performance. Also, the channel coding would not perform well because of the synchronization errors. Therefore, in order to solve this problem, a fine time adjustment is needed to modify the frequently delayed timing to the actual delayed timing in channels. In[15], the proposed timing estimator performs well only for the additive white Gaussian noise (AWGN) channels. While the system operates in the multipath fading channels, the proposed algorithm exhibits significantly large fluctuation in the estimated timing offset. In[16], the modified blind timing synchronization method has a good performance in the multipath fading channels with line-of-sight (LOS) propagation only when the SNR is greater than 20 dB. In[14], a well-designed time-domain training sequence is utilized to perform joint timing synchronization and channel estimation. Although the proposed timing estimator has excellent performance at low SNR[14], the power consumption of the proposed preamble is still too large to be adopted in some low-power wireless applications.
For wireless implantable medical devices, low-power consumption is necessary in order to prolong the battery operating time. This article develops a semiblind timing synchronization and channel estimation algorithm based on unit vectors, and demonstrates that this algorithm is suitable for multipath fading channels with both LOS and NLOS propagation. Due to the use of unit vectors as the preamble, the power consumption of this preamble at the transmitter is approximately equal to zero. Therefore, the proposed preamble is suitable for any low-power wireless implantable medical device. In addition, we utilize only one nonzero sample in the training sequence to perform the timing synchronization, and this training sequence definitely lacks useful information at the receiver. Compared with the existing preamble-based methods[5–9, 11, 12, 14], the number of nonzero elements in the proposed training sequence is the lowest. Thus, the proposed joint approach is called a semiblind method. In this article, we first obtain a coarse timing offset using the cross-correlation function outputs in the frequency-domain. Then, a fine time adjustment algorithm based on these outputs is applied. Finally, the channel response in the frequency-domain is obtained. Simulation results are represented to verify the effectiveness of our proposed algorithm. This article is an extended version of[13].
This article is organized as follows. Section 2. describes the system and the problem. In Section 3., the proposed semiblind timing synchronization and channel estimation algorithm is presented. Simulation results are provided in Section 4., respectively. Finally, Section 5. concludes this article.
2 Problem statement
2.1 System description
The training-sequence-based single-input single-output OFDM system architecture. Figure1 represents the proposed training-sequence-based single-input single-output OFDM system.
Timing synchronization in the time-domain
3 The proposed approach
3.1 Coarse timing synchronization
However, by using both real part and imaginary part of the cross-correlation function output, more information can be utilized to obtain a better coarse timing estimate.
From Equation (10), although M 1( d 1) gives a maximum value when d 1is at the delayed timing of the path with the largest gain in multipath fading channels, the actual delayed timing cannot be obtained.
3.2 Fine time adjustment
the length of the SOV is V , and Ω v ={0,1,…,V−1}. If M 1(v(i + 1))>β· M 1(v(i)) and M 1(v(i + 2))<β· M 1(v(i + 1)), the final timing estimate () is v(i + 1), where β is a threshold and i∈ Ω v . The detailed procedure of fine time adjustment is described in Algorithm 1
Algorithm 1.
Fine time adjustment. Initial Inputs: M 1(v(i)), v
- 1:
for i = 0 to V-1do
- 2:
if M 1(v(i + 1))>ß· M 1(v(i))then
- 3:
u=i + 1
- 4:
else
- 5:
break
- 6:
end if
- 7:
end for
- 8:
The power profiles of different channel models
CH I (NLOS) | CH II (NLOS) | CH III (LOS) | |
---|---|---|---|
| 0.3432 | 0.1885 | 0.5211 |
| 0.6211 | 0.3223 | 0.4338 |
| 0.0329 | 0.48 | 0.0420 |
| 0.0015 | 0.0079 | 0.0023 |
where the k ″ th tap has the second-largest power in the channel.
Channel estimation
where is the estimated channel response on the m th subcarrier.
4 Simulation results
A packet-based low-density parity-check (LDPC) coded single-input single-output (SISO) OFDM system was used for simulations, where each codeword is encoded with code (1600,800)[17] and each packet consists of a training sequence followed by 17 random OFDM data symbols. The structure of OFDM data symbols follows the IEEE 802.11a standard defined in[9], where N=64 and N CP =16. The training sequence of each packet is an unit vector with unit amplitude in the time-domain, where c=31 and the power of the training sequence is 1/64. Quaternary phase-shift keying modulation was adopted in simulations. For each packet transmission, the residual CFO was modeled as a random variable that is uniformly distributed within ±0.1 OFDM subcarrier spacing. In addition, the phase tracker based on the pilots in the frequency-domain is utilized to compensate the phase error[9].
We evaluate the proposed approach and other related schemes[7, 9, 15] under 6-path Rayleigh channels, where the power profiles of their first four taps are described in Table1 and represents the i + 1th tap power in the channel. A delayed timing offset (τ) is given by 65 samples. Channel Models I and II (CH I and CH II) represent multipath fading channels with NLOS propagation, and Channel Model III (CH III) is a typical multipath fading channel with LOS propagation. For CH I, the power of second tap dominates all channel taps. As for CH II, the third tap has the strongest power in the channel, and it is the worst channel model to evaluate the performance of timing synchronization in this article. Moreover, assume all channels are quasi-stationary during each packet transmission.
The Probability of perfect timing synchronization. Figure5 represents the probability of perfect timing synchronization,, where prob(·) is the probability function and is the estimated timing offset.
The Bias of timing estimator. Figure6 represents the bias of timing estimator,, where E[·] is the expectation function
The root mean squared error of timing estimator. Figure7 represents the root mean squared error of timing estimator,.
BER comparisons with[7]in all channel models.
BER comparisons with[9]in all channel models.
5 Conclusion
In this article, we have developed a semiblind timing synchronization and channel estimation scheme for OFDM systems based on unit vectors. We also developed a fine time adjustment algorithm to find the actual position of the first arrival path in LOS and NLOS channel models. Based on a simple threshold without any pre-simulation and theoretical derivation, the proposed fine time adjustment algorithm outperforms conventional schemes even at very low SNR. Simulation results show that there are no timing errors in our proposed time estimator when SNR exceeds 6 dB. In addition, zero BER is also achievable for a LDPC coded SISO OFDM system when SNR exceeds 8 dB.
Declarations
Authors’ Affiliations
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Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.