 Research Article
 Open Access
Blind Coarse Timing Offset Estimation for CPOFDM and ZPOFDM Transmission over Frequency Selective Channels
 Vincent Le Nir^{1, 2}Email author,
 Toon van Waterschoot^{1},
 Jonathan Duplicy^{3} and
 Marc Moonen^{1}
https://doi.org/10.1155/2009/262813
© Vincent Le Nir et al. 2009
 Received: 9 May 2009
 Accepted: 15 December 2009
 Published: 19 January 2010
Abstract
We present a blind coarse timing offset estimation technique for CPOFDM and ZPOFDM transmission over frequency selective channels. The technique exploits the cyclic prefix or zeropadding structure to estimate the starting position of the OFDM symbols without requiring any additional pilots. Simulation results are performed on various channel models with timing and frequency offsets. The presented technique is compared with the autocorrelationbased technique and various techniques in frequency selective channels. Our algorithm shows better performance results than those of the autocorrelationbased technique in NLOS channels, where the most predominant channel path is usually not the first arrival path.
Keywords
 Orthogonal Frequency Division Multiplex
 Root Mean Square Deviation
 Minimum Mean Square Error
 Carrier Frequency Offset
 Cyclic Prefix
1. Introduction
In this paper, we describe a technique to blindly estimate the timing offset in digital communications systems employing orthogonal frequency division multiplexing (OFDM). The starting position of the OFDM symbols is estimated using the cyclic prefix (CP) or zeropadding (ZP) structure of the transmitted signal without requiring any additional pilots. The aim of the paper is to provide an alternative coarse timing offset estimation technique to the autocorrelationbased technique [1–3] which does not perform well in nonlineofsight (NLOS) frequency selective channels as well as for ZPOFDM transmission.
The literature on timing offset estimation and carrier frequency offset (CFO) estimation can be divided in two categories: dataaided and nondataaided techniques. Dataaided techniques use additional pilot symbols known at the receive side to estimate the timing and frequency offsets based on autocorrelation and other features [4–6]. Nondataaided techniques do not require additional pilot symbols and can exploit the cyclic prefix structure of the transmitted signal in an autocorrelation metric [1, 3] (which is a simplified version of the maximum likelihood (ML) algorithm requiring the knowledge of the received signaltonoise ratio (SNR) [2]). However, these techniques fail when the channel exhibits strong multipath components. Other nondataaided techniques require the knowledge of the pulse shaping filter and exploit the cyclostationarity of the OFDM signal by a cyclic autocorrelation metric [7, 8], use bellpatterns to detect the symbol energy variations of the first subcarrier [9], require the knowledge of the maximum delay spread [10], or perform symbol timing and frequency offset estimation jointly [11].
In this paper, we propose a new nondataaided approach for timing offset estimation which does not require the knowledge of the SNR [2], the pulse shaping filter [7, 8] or the maximum channel delay spread [10] and works well for CPOFDM and ZPOFDM transmission when the channel exhibits strong multipath components. For the mathematical derivations, we assume that the cyclic prefix duration or zeropadding duration is larger than the channel impulse response ; however we will show that the algorithm still exhibits good performance when (or ). Moreover, we assume the knowledge of the symbol duration , the cyclic prefix duration (or the zeropadding duration ) and the number of subcarriers which can indeed be estimated blindly with the algorithms described in [12]. The timing offset estimation technique exploits the cyclic prefix or zeropadding structure of the OFDM signal and tracks time domain symbol energy variations based on a transition metric. Contrary to the autocorrelation metric [1–3], the transition metricbased technique is able to estimate the timing offset in frequency selective channels with strong multipath components.
The paper is organized as follows. In Section 2, we present the OFDM signal model, we review the technique for timing offset estimation based on the autocorrelation metric, and then the techniques based on the transition metric are presented for CPOFDM and ZPOFDM transmission. In Section 3, simulation results are presented with realistic channels models. Finally, conclusions are drawn in Section 4.
2. Description of the Algorithm
The nondataaided technique presented in this paper has been developed in the context of radio surveillance and cognitive radio systems for multicarrier modulations. The wideband received signal may contain multiple OFDM signals of interest. Therefore, the received signal is sampled in a large bandwidth to include existing and future OFDM standards, such as Wifi (2.4 GHz or 5 GHz), WiMAX (3.5 GHz), LongTerm Evolution (LTE), or WiMedia (ECMA368) signals. The carrier frequencies, bandwidths, and average powers of the detected signals are estimated. After downconversion to baseband and lowpass filtering, each signal of interest is processed through a feature detection block to determine whether or not it is an OFDM signal and to estimate blindly its symbol duration , its cyclic prefix duration (or its zeropadding duration ) and its number of subcarriers [12]. Each signal of interest can be modeled as a received sequence of length such that
where is the transmitted signal vector oversampled by the ratio between the cutoff frequency of the lowpass filter and the transmitter maximum frequency, the 's are the oversampled multipath channel coefficients with the number of channel taps, is the vector of Additive White Gaussian Noise (AWGN), the receiver phase offset, the receiver frequency offset, and the receiver timing offset.
2.1. Timing Offset Estimation Techniques for CPOFDM Transmission
However, maximizing the autocorrelation metric over a window of length will rather provide a timing offset estimate of the most predominant channel path than a timing offset estimate of the starting position for the OFDM symbols. Indeed, only a duration of is fully correlated between the received sequence and the conjugated received sequence shifted by the symbol duration . Therefore, the autocorrelation metric is expected to work well in lineofsight (LOS) scenarios where the most predominant channel path is the first arrival path, but it will fail in NLOS scenarios where the most predominant channel path is usually not the first arrival path.
Instead of using an autocorrelation metric, we propose to use a metricbased on the difference between the received sequence and the same sequence shifted by the symbol duration (see also Figure 2). The correlated duration of the cyclic prefix is cancelled out in this operation. In this way, the cyclic prefix structure of the OFDM signal is exploited by tracking time domain symbol energy variations based on a transition metric between the end of the fully correlated duration and the beginning of a new OFDM symbol. Contrary to the autocorrelation metric [2, 3], the transition metricbased technique is able to estimate the timing offset in frequency selective channels even with strong multipath components. The received sequence of length is also divided into blocks of size where the transition metric is performed on the available blocks except the last block. The proposed transition metric is given by
One can see that the modulus operation is used outside the difference operation. This formula is especially suited for small CFOs. However, one can apply the modulus operation to each component of the formula to make the algorithm insensitive to large CFOs. An algorithm that minimizes the difference metric between the received sequence and the same sequence shifted by the symbol duration over a window duration has been presented in [4]. The authors use prolonged guard intervals assuming a quite large ISI free period and known pilot symbols to provide finetiming synchronization. In this paper, the ratio between two consecutive averaged difference metrics is calculated which require only one ISI free symbol to estimate the true timing offset (or even no ISI free symbol when as long as the largest ratio index corresponds to the true timing offset). Moreover, it can be shown that averaging over several symbols in the same block has a negative impact on the timing offset estimate because this time smoothing will create an uncertainty on the starting position of the OFDM symbol [4].
The transition metric can be evalued for each index according to Figure 2 and ranging from to . As the transition metric is the ratio between two consecutive averaged metrics, we define the difference metric . When applying the signal model (1) to the difference metric (with ), it can be shown that
The transition metric can be rewritten as
The detection of the transition corresponding to (4) is given at delay :
while for other delays, the ratio can be considered very small especially at high SNR (ratio between two successive elements of (4)). In the case , the detection of the transition is also given at delay by
This proves that the proposed transition metricbased technique can exhibit good performance when as long as the channel has smaller power components for delays larger than the cyclic prefix duration than the first tap (which can be considered valid for an exponentially decreasing power delay profile). For low SNR, the performance of the algorithm can be improved by considering multiple ratios of the difference metric
The detection of the transition is also given at delay . As increases, the performance of the algorithm improves as long as the denominator falls in the correlated duration (ISI free part) .
2.2. Timing Offset Estimation Techniques for ZPOFDM Transmission
A similar algorithm which tracks time domain symbol energy variations can be used for ZPOFDM signals, where the autocorrelation metric also fails. We assume that the symbol duration and the zeropadding duration have been estimated blindly according to the algorithm described in [12]. We also assume that the zeropadding duration is larger than the channel impulse response . In this case, the zeropadding structure of the received OFDM signal is exploited by tracking time domain symbol energy variations (transition metric) between the end of the duration (noise only) and the beginning of a new OFDM symbol (the time domain symbol energy variations are not averaged over several symbols in the same block because this time smoothing has a negative impact on the timing offset estimate). The transition metric is performed on the available blocks except the last block and is given by
For ZPOFDM signal, we define the difference metric . When applying the signal model (1) to the difference metric, it can also be shown that
The transition metric and the detection value at delay are also given by (5), (6). For the case , the detection value at delay is given by (7). Multiple ratios of the difference metric can also be considered to improve the performance at low SNR. The performance of the algorithm improves as long as the denominator falls in the ISI free part . In the next section, simulation results compare the autocorrelation metric and the transition metric for CPOFDM signals. For ZPOFDM signals, the transition metric can also be compared to a correlation metricbased on a power mask in the time domain. Indeed, knowing the symbol duration and the zeropadding duration , the power correlation metric finds the power mask of length that maximize the correlation with the received power in the time domain. Assuming that the received power has been normalized to unity, the power correlation metric is given by
with
3. Simulation Results
SUI channel models.
SUI 1 channel  

Tap 1  Tap 2  Tap 3  
Delay ( s)  0  0.4  0.9 
Power (dB)  0 


factor  4  0  0 
Doppler (Hz)  0.4  0.3  0.5 
SUI 4 channel  
Tap 1  Tap 2  Tap 3  
Delay ( s)  0  1.5  4 
Power (dB)  0 


factor  0  0  0 
Doppler (Hz)  0.2  0.15  0.25 
OFDM signal parameters.
Parameters  WiMAX  WiMedia 

Bandwidth  10 MHz  528 MHz 
 256  128 
Number of samples in  64  37 
 25.6 s  242.42 ns 
 6.4 s  70.07 ns 
Nb symbols  10  10 
Channels  SUI1 4  CM1 
 0.9 4 s  113.63 ns 
Number of samples in  9 40  60 
The coefficient variation shows the dispersion of the timing offset parameter from its true value normalized to the mean of the observed value at a particular SNR threshold. One can see that the autocorrelation metricbased technique [1, 3] and the MMSE metricbased technique [4] give better results than the transition metricbased technique for SUI1 channels, with 3 dB difference at a lockin probability of 0.8. As demonstrated in Section 3, for LOS channels the most predominant channel path is the first arrival path and the transition metric is averaged over 10 blocks while the autocorrelation metric is averaged over 10 blocks times the cyclic prefix duration. Although we have considered multiple ratios for the transition metric , the autocorrelation metricbased technique performs better than the transition metricbased technique owing to the exploitation of a larger number of symbols in the same OFDM block. Considering the knowledge of the channel delay spread , the performance of the MC1 and MMSE1 metricbased techniques [17] improves the SNR of the autocorrelation and MMSE metricbased techniques by 1 dB at a lockin probability of 0.8. The derivative metricbased technique achieves the lowest SNR ( dB) at a lockin probability of 0.8. However, the right figure shows that the derivative metricbased technique [18] gives the highest CV(RMSD) compared to the MC1 and MMSE1 metricbased techniques. The autocorrelation and MMSE metricbased techniques have lower CV(RMSD) than the derivative metricbased technique. The minimum CV(RMSD) is given by the transition based technique for SNR larger than 8 dB. For SUI4 channels, the autocorrelation and MMSE metricbased techniques have similar performance compared to the transition metricbased technique for low SNRs. However, the transition metricbased technique gives significantly better results than the autocorrelation and MMSE metricbased techniques when the SNR is larger than 3 dB (we have considered multiple ratios for the transition metric ). In fact, the autocorrelation and MMSE metricbased techniques cannot exceed a lockin probability of 0.5 even at high SNR because the most predominant channel path is usually not the first arrival path. The MC1, MMSE1 (considering the knowledge of the channel delay spread ), and derivative metricbased techniques achieve very good performance compared to the transition metricbased technique for SNRs lower than 13 dB. However, for higher SNRs, the transition metricbased technique outperforms the MC1, MMSE1, and derivative metricbased techniques which cannot exceed a lockin probability of 0.8. The right figures show that the transition based technique gives closer estimates to the true value of the timing offset than the autocorrelation, MMSE, MC1, MMSE1, and derivative metricbased techniques at almost all SNR ranges for SUI4 channels.
4. Conclusion
In this paper, we have described a technique to blindly estimate the timing offset in digital communications systems employing orthogonal frequency division multiplexing (OFDM). The starting position of the OFDM symbols has been estimated without any additional pilots using the cyclic prefix or zeropadding structure of the transmitted signal. This paper has provided an alternative coarse timing offset estimation technique to the autocorrelationbased technique which does not perform well in nonlineofsight (NLOS) frequency selective channels as well as for ZPOFDM transmission. The results confirm that the transition metricbased technique is able to estimate the timing offset in frequency selective channels with strong multipath components for CPOFDM and ZPOFDM transmission.
Declarations
Acknowledgment
This research work was carried out in the frame of the European FP7 UCELLS project. The scientific responsibility is assumed by its authors.
Authors’ Affiliations
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