On timing offset estimation for OFDM systems

Two timing offset estimation methods for orthogonal frequency division multiplexing (OFDM) systems as modifications to Schmidl and Cox's method (see IEEE Trans. Commun., vol.45, p.1613-21, 1997) are presented. The performances of the timing offset estimators in additive white Gaussian noise channel and intersymbol interference channel are compared in terms of estimator variance obtained by simulation. Both proposed methods have significantly smaller estimator variance in both channel conditions     

ML-based symbol timing and frequency offset estimation for OFDM systems with noncircular transmissions

This paper deals with the problem of joint symbol timing and carrier-frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems with noncircular (NC) transmissions. Maximum-likelihood (ML) estimators of symbol timing and CFO have been derived under the assumption of nondispersive channel and by modeling the OFDM signal vector as a circular complex Gaussian random vector (C-CGRV). The Gaussian assumption is reasonable when the number of subcarriers is sufficiently large. However, if the data symbols belong to an NC constellation, the received signal vector becomes an NC-CGRV, i.e., a CGRV whose relation matrix (defined as the statistical expectation of the product between the vector and its transpose) is not identically zero. Hence, in this case, previously mentioned estimators, termed MLC estimators, are not ML estimators. In this paper, by exploiting the joint probability density function for NC-CGRVs, ML estimators are derived. Moreover, since their implementation complexity is high, feasible computational algorithms are considered. Finally, refined symbol timing estimators, apt to counteract the degrading effects of intersymbol interference (ISI) in dispersive channels, are suggested. The performance of the derived estimators is assessed via computer simulation and compared with that of MLC estimators and that of modified MLC (MMLC) estimators exploiting only ISI-free samples of the cyclic prefix.     

带有时偏的MC-CDMA上行链路的盲信道估计

为了能在带有时偏的MC-CDMA上行链路中估计信道，提出了一种新的信道估计方法。该方法能消除时偏对信道估计产生的影响，从而无需系统同步就能准确估计出信道。另外，由于扩频序列的信息对接收端是已知的，因此该信道估计方法可以利用扩频码的信息来完成盲估计。最后的仿真结果显示，该信道估计方法有良好的性能。     

A novel estimation method of timing offset for OFDM based WLAN systems

The conventional timing synchronization methods based on time domain correlation have the problems of timing metric plateau in Additive White Gaussian Noise(AWGN) channel and estimation error in multipath fading channel. To resolve the problems, this paper proposes a novel timing metric using the characteristics of long training symbols in IEEE802.11a and a new timing recovery method based on the new timing metric for Orthogonal Frequency Division Multiplexing(OFDM)-based WLAN systems. The proposed timing metric is defined as a sum of absolute values of the imaginary parts of all the subcarrier samples. It exhibits a unique characteristic that is very sensitive to the true synchronization point since it has minimum value at the true synchronization point and maximum around the true synchronization point. The simulation results show that the performance of timing synchronization is significantly improved, as a result, the probability of error estimation is lower than 10^-4 when Signal-to-Noise Ratio(SNR) is more than 10dB.     

Analysis of pilots for residual frequency offset estimation in MIMO OFDM systems

This paper analyses the estimation of residual frequency offset in MIMO OFDM systems using pilot subcarriers embedded in the data payload. A closed-form expression for the MSE is derived and it shows how the frequency and spatial correlation influence performance. It is also shown that an orthogonal design ensures robust performance, which is independent of the frequency correlation of the channel.     

叠加训练序列OFDM系统的联合频偏与信道估计

频率偏移导致用于叠加训练序列系统中的一阶信道估计方法失效.文中提出一种利用叠加训练序列进行OFDM系统的联合频偏和信道估计的方案.在简单介绍所建立的OFDM系统后,文中利用训练序列的周期性推导出频偏特征向量,并根据阵列信号求子空间的原理,利用接收信号矩阵的奇异值分解求出上述向量所在的线性子空间,通过相关匹配求出频率偏移,最后获得时域信道参数.理论分析表明频偏估计范围反比于训练序列周期,因此算法具有估计范围大的优点,且适用于所有叠加周期训练序列系统.仿真分析表明了算法的有效性.     

Performance of diversity schemes for OFDM systems with frequency offset, phase noise, and channel estimation errors

We provide expressions for the bit error rate of various transmit and receive diversity schemes for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency offset, phase noise, and channel estimation errors. The derivations are also applicable for a general multiplicative distortion of the received signal. Our results show that with perfect channel estimates, practical values of the phase noise do not significantly degrade the performance of the various diversity methods for binary phase-shift keying modulation. In contrast, the transmit diversity schemes for OFDM are much more sensitive to channel estimation errors than maximal ratio combining receive diversity.     

Blind estimation of symbol timing and carrier frequency offset inwireless OFDM systems

Orthogonal frequency-division multiplexing (OFDM) systems are highly sensitive to synchronization errors. We introduce an algorithm for the blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems. The proposed estimator is an extension of the Gini-Giannakis (see IEEE Trans. Commun., vol.46, p.400-411, 1998) estimator for single-carrier systems. It exploits the cyclostationarity of OFDM signals and relies on second-order statistics only. Our method can be applied to pulse shaping OFDM systems with arbitrary time-frequency guard regions, OFDM based on offset quadrature amplitude modulation, and biorthogonal frequency-division multiplexing systems. We furthermore propose the use of different subcarrier transmit powers (subcarrier weighting) and periodic transmitter precoding to achieve a carrier frequency acquisition range of the entire bandwidth of the OFDM signal, and a symbol timing acquisition range of arbitrary length. Finally, we provide simulation results demonstrating the performance of the new estimator     

Joint carrier frequency offset and channel estimation for OFDM systems with two receive antennas

Carrier frequency offset (CFO) in OFDM systems results in loss of channel orthogonality and hence degrades the system's performance. In this paper, we propose a new method for joint CFO/channel estimation for OFDM systems with two receive antennas. Our method avoids the complexity of full search methods in one or two dimensions. Using one training OFDM symbol and utilizing the knowledge of the structure of the inter‐channel interference that results from CFO, we develop a two‐stage estimation procedure. The first stage derives an initial CFO/channel estimate based on a one shot minimization step. The second stage refines this joint estimate by conducting a small CFO search in the vicinity of the initial estimate. This procedure provides CFO estimates over a full range of −N /2–N /2, (N : number of subcarriers), as well as the channel estimates. Computer simulations show an excellent performance that is very close to the Cramer–Rao lower bound and superior to some existing methods. The effect of antenna correlation on performance is also investigated through computer simulations, showing small performance degradation even at medium correlation coefficients (0.3–0.6). Copyright © 2015 John Wiley & Sons, Ltd.     

基于前导序列的OFDM定时同步与信道估计算法

本文针对IEEE802.11a前导序列无法精确定时的缺点,设计了一种新的前导序列,能够通过平台检测实现数据到达预警,之后利用有尖锐峰值的共轭对称结构做精确定时,因此误捕获率低,且不受频率偏移的影响.针对LS算法未考虑噪声带来估计误差的缺点,改进算法将LS算法估计的频域信道传输函数转换到时域,在时域利用信道脉冲响应的有限性,消除一部分噪声,再将其变换到频域替代LS算法所估计的信道传输函数.仿真结果表明,改进算法的均方误差较LS算法约有8dB的性能增益.     

Joint weighted least-squares estimation of carrier-frequency offset and timing offset for OFDM systems over multipath fading channels

This work presents an algorithm for joint estimation of carrier-frequency offset and timing offset for orthogonal frequency-division multiplexing (OFDM) systems in the tracking mode. The proposed weighted least-squares algorithm derives its estimates based on phase differences in the received pilot subcarrier signals between two symbols. Moreover, the optimal weights in two different channel conditions are derived. Both analysis and simulation show that the weighted least-squares algorithm can effectively and accurately estimate the carrier-frequency offset as well as the timing offset of OFDM signals in multipath fading channels.     

Enhanced MMSE channel estimation using timing error statistics for wireless OFDM systems

Estimation and tracking of the frequency-selective time-varying channel response is a challenging task for wireless communication systems incorporating coherent OFDM. In pilot-symbol-assisted (PSA) OFDM systems, the minimum mean-square-error (MMSE) estimator provides the optimum performance based on the channel statistics (channel correlation function and SNR). In OFDM systems, FFT-block timing error introduces a linear phase rotation to data modulated on individual subcarriers. An MMSE channel estimator designed only using the wireless channel statistics performs only sub-optimally when subcarrier phase rotations due to block timing errors are present. In this paper, we show that by using the block timing error statistics of the OFDM time-synchronizer the performance of the MMSE channel estimation can be significantly improved. Numerical results show that the bit-error-probability (BEP) performance degradation due to timing errors can be almost completely recovered by the proposed technique.     

无线信道中OFDM系统的频偏估计

OFDM技术作为一种适用于高速无线传输的调制技术近年来越来越受到关注。但 OFDM系统的显著问题是对频率偏移十分敏感。针对OFDM信道传输系统,提出了一种频率 偏移估计算法。该估计器采用内插技术,通过频域来实现,与传统的最大似然估计器相比,该 算法具有良好的性能和较简单的结构。     

A frequency offset estimation algorithm for OFDM systems

A new fine carrier frequency offset estimation algorithm in Orthogonal Frequency Division Multiplexing （OFDM） system is proposed. The correlation item is the training sequence instead of the received signal in the new algorithm. Simulation results show that the performance of the new algorithm is 4dB-9dB better than that of Schmidl＇s algorithm. Coarse frequency offset estimation is also discussed in this paper, which is the improvement of Zhang＇s method. The estimation range using the improvement method is twice as that using the Zhang＇s method. Based on the hardware of the receiver and the improved algorithm, a method using Fast Fourier Transform （FFT） is proposed to implement the coarse frequency estimation. The chip area of OFDM system can be reduced by using the proposed method.     

Improved preamble-aided timing estimation for OFDM systems

An improved method for estimating the frame/symbol timing offset in preamble-aided OFDM systems is presented. It uses a conventional preamble structure and combines autocorrelation techniques with restricted crosscorrelation to achieve a near-ideal timing performance without significant increase in complexity. Computer simulations show that the method is robust in both AWGN and fading multipath channels, achieving better performance than the existing methods.     

Sensing OFDM systems with timing and frequency offset for cognitive radio networks

In this paper, we consider the detection of orthogonal frequency division multiplexing with timing and frequency offset for cognitive radio over fast time‐varying multipath channels. By making different assumptions on the availability of the timing and frequency offset at the secondary user, we derive two algorithms based on likelihood ratio test and generalized likelihood ratio test, respectively and theoretically obtain the detection performances of them. The proposed algorithms jointly utilize energy of observations and correlation of the cyclic prefix (CP) data. The extensive simulations show that the two algorithms outperform the other CP‐based methods, perform well at very low signal to noise ratio (SNR) and are robust to the CP ratio. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel frequency offset estimation method for OFDM systems with large estimation range

In this paper, we proposed a novel frequency synchronization method which has larger estimation range than conventional method proposed by Tufvesson. A two steps frequency offset estimation method is performed in the new method. In the first step the received signal is correlated with local training sequence to eliminate the influence of training sequence which makes the estimation range of frequency offset is independent of period of the repeated data in the training sequence. The received signal is correlated with its delay in the second step to obtain the fine estimation of frequency offset. Precise estimation can be achieved in the proposed method than Tufvesson's method. The period of the repeated data in the training sequence determines the estimation range of the frequency offset in the conventional method, while in the new method they are irrelevant. Tens of subcarriers spacing can be estimated by the new method. The new method can be used in other cases as long as a known sequence is transmitted, which will introduce valuable flexibility in training sequence design. The validity of the algorithm is verified in AWGN channel and multipath fading channel.     

Carrier frequency offset estimation for OFDM systems using subcarriers

Carrier frequency offset (CFO) in orthogonal frequency-division multiplexing(OFDM) systems, which can induce the loss of orthogonality among subcarriersand result in significant performance degradation, is critical to be estimatedand compensated for. In this paper, a suboptimal scheme is proposed to estimatethe CFO using subcarriers. In the proposed scheme, the CFO is dividedinto the fractional part and the integer part, with the fractional CFO estimatedfollowed by the integer CFO estimation. Compared with previous work using subcarriers and exhaustive search, the implementation complexity of theproposed scheme is significantly lower due to the fact that the main componentrequired is a simple correlator. Furthermore, with only one trainingOFDM symbol and proper subcarrier allocation, the estimation range ofthe proposed scheme can be the inverse of the sampling duration. In contrast,conventional schemes with the same estimation range and complexity require two OFDM symbols. To achieve good performance,it will be shown that the subcarrier allocation should be based uponsome specific binary sequences such as the proposed extended m-sequences. It willalso be shown by simulations that the same subcarrier allocation criterionshould be employed for optimal maximum-likelihood CFO estimation.     

OFDM整数倍频偏ML估计方法的性能分析

提出了一种新的基于最大似然(ML)估计理论的OFDM整数倍频偏估计方法。讨论了新的和传统的整数倍频偏估计方法的均值和方差特性，分析比较了两种方法的错误估计概率。通过计算机仿真进行了验证，仿真结果和讨论分析结果相一致。