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.     

Blind carrier frequency offset estimation in SISO, MIMO, and multiuser OFDM systems

Relying on a kurtosis-type criterion, we develop a low-complexity blind carrier frequency offset (CFO) estimator for orthogonal frequency-division multiplexing (OFDM) systems. We demonstrate analytically how identifiability and performance of this blind CFO estimator depend on the channel's frequency selectivity and the input distribution. We show that this approach can be applied to blind CFO estimation in multi-input multi-output and multiuser OFDM systems. The issues of channel s, multiuser interference, and effects of multiple antennas are addressed analytically, and tested via simulations.     

Joint estimation of symbol timing and carrier frequency offset of OFDM signals over fast time-varying multipath channels

In this paper, we present a novel joint algorithm to estimate the symbol timing and carrier frequency offsets of wireless orthogonal frequency division multiplexing (OFDM) signals. To jointly estimate synchronization parameters using the maximum likelihood (ML) criterion, researchers have derived conventional models only from additive white Gaussian noise (AWGN) or single-path fading channels. We develop a general ML estimation algorithm that can accurately calculate symbol timing and carrier frequency offsets over a fast time-varying multipath channel. To reduce overall estimation complexity, the proposed scheme consists of two estimation stages: coarse and fine synchronizations. A low complexity coarse synchronization based on the least-squares (LS) method can rapidly estimate the rough symbol timing and carrier frequency offsets over a fast time-varying multipath channel. The subsequent ML fine synchronization can then obtain accurate final results based on the previous coarse synchronization. Simulations demonstrate that the coarse-to-fine method provides a good tradeoff between estimation accuracy and computational complexity.     

Complex efficient carrier frequency offset estimation algorithm in OFDM systems

A new carrier frequency offset estimation scheme in the orthogonal frequency division multiplexing (OFDM) system is proposed. The proposed algorithm is an extension of the Michele Morelli (M&M) algorithm. By dividing one training symbol into L>1 identical small blocks, the carrier frequency offset estimation range up to /spl plusmn/L/2 times subcarrier spacing can be obtained. The proposed algorithm can utilize the correlativity among all small blocks of a training symbol more sufficiently than the M&M algorithm, and thus it is more accurate and robust. Without increasing the estimation errors, the computational complexity of the proposed algorithm can be further reduced by increasing parameters H/sub l/ and H/sub h/ with a positive value simultaneously.     

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     

Blind carrier frequency offset estimation for noncircular constellation-based transmissions

We address the problem of nondata aided frequency offset estimation for noncircular transmissions over frequency-selective channels in a linear precoder-based communications context. Linear precoding is representative of a downlink direct-sequence code division multiple access (DS-CDMA) system or of an orthogonal frequency division multiplexing (OFDM) system. We observe that twice the frequency offset is a cyclic frequency of the received signal. We thus introduce an estimator relying on the maximization of the empirical cyclocorrelations. We analyze its asymptotic behavior and obtain a closed-form expression for the asymptotic covariance. This enables us to design relevant system parameters. Numerical illustrations are provided and confirm our theoretical assertions. Comparisons with existing methods are also reported.     

Modified nonlinear least square approaches to carrier frequency offset estimation in OFDM systems

Two modified nonlinear least square (NLS) estimators for carrier frequency offset (CFO) in orthogonal frequency-division multiplexing (OFDM) systems are proposed. In the modified NLS CFO estimators, slot elements in an OFDM block symbol are weighted in terms of their received energies. Simulation results show that the proposed new estimators outperform the original one especially in a low signal-to-noise ratio range.     

Blind channel and carrier frequency offset estimation usingperiodic modulation precoders

Previous results have shown that blind channel estimators, which are resilient to the location of channel zeros, color of additive stationary noise, and channel order overestimation errors, can be developed for communication systems equipped with transmitter-induced cyclostationarity precoders. The present paper extends these blind estimation approaches to the more general problem of estimating the unknown intersymbol interference (ISI) and carrier frequency offset/Doppler effects using such precoders. An all-digital open-loop carrier frequency offset estimator is developed, and its asymptotic (large sample) performance is analyzed and compared to the Cramer-Rao bound (CRB). A subspace-based channel identification approach is proposed for estimating, in closed-form, the unknown channel, regardless of the channel spectral nulls. It is shown that compensating for the carrier frequency offset introduces no penalty in the asymptotic performance of the subspace channel estimator. Simulations are presented to corroborate the performance of the proposed algorithms     

A new symbol timing and carrier frequency offset estimationalgorithm for noncoherent orthogonal M-CPFSK

We present a new joint symbol timing and carrier frequency offset estimation algorithm for noncoherent orthogonal continuous-phase M-ary frequency-shift keying (M-CPFSK). Our algorithm performs nondata-aided feedforward processing of finite-length observations, and it is suited for an all-digital modem implementation based on a DSP or an ASIC processor. The algorithm exploits phase continuity of M-CPFSK in order to generate both a spectral component at the carrier frequency offset and a timing error signal. This is obtained without nonlinear transformations of the received signal involving noise×noise products. Thus, our algorithm can operate at a very low input signal-to-noise ratio. We discuss the operating range of our algorithm, and we show that no additional overhead (training sequence) in excess of the standard overhead of FDMA/TDMA packet transmission is required to resolve timing and frequency ambiguities. Moreover, we show that by differentially preceding the transmitted symbols, it is possible to eliminate automatically frequency ambiguities, at the price of a slight increase in the bit-error rate. An approximate mean-square error analysis of the estimators and simulation results prove that our algorithm provides good performance, even with a relatively short observation block length and large carrier frequency offset. Computer simulations show also that our algorithm is extremely robust to phase noise. These features make our algorithm a good candidate for satellite FDMA/TDMA applications in the 20-30 GHz band, with a large number of users and bursty transmission     

一种零前缀OFDM系统的符号同步和载频估计算法

提出一种在零前缀正交频分复用(ZP-OFDM)系统中,估计符号定时和载波频偏的算法.算法根据ZP-OFDM系统的零前缀特性,利用双滑动窗口检测能量的分布来完成符号定时同步;同时,给出一种改进的平均法估计小数倍频率偏移.通过分析和仿真可以看出,无论是在白高斯噪声信道还是多径信道,具有一个训练符号的ZP-OFDM系统可以准确而有效的估计符号定时和频率偏差.     

Fast coarse estimator of carrier frequency offset for OFDM systems

A coarse carrier frequency offset estimation algorithm for orthogonal frequency division multiplexing (OFDM) systems is proposed. The algorithm exploits the phase difference of the adjacent subcarriers of the received signal, which is proportional to the frequency offset. The proposed scheme necessitates much lower computational load compared to the conventional correlation based methods, while it reveals similar estimation performance for practical OFDM systems.     

ML estimation of time and frequency offset in OFDM systems

We present the joint maximum likelihood (ML) symbol-time and carrier-frequency offset estimator in orthogonal frequency-division multiplexing (OFDM) systems. Redundant information contained within the cyclic prefix enables this estimation without additional pilots. Simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode     

一种改进的适用于分组传输的OFDM频偏估计方法

提出了一种改进的基于训练符号的频偏估计方法.该方法通过综合利用训练符号和循环前缀的信息得到时域的细频偏估计,通过峰值检测得到频域的粗频偏估计.仿真结果表明,在多径衰落信道下,在频偏估计范围达到整个信号带宽的同时,本算法的估计精度也有了明显的提高,并且当信噪比达到12dB时,可以使剩余频偏限制在子载波间隔的2％以内.     

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.     

Joint frame synchronization and frequency offset estimation in OFDM systems

A new joint frame synchronization and carrier frequency offset estimation scheme in orthogonal frequency division multiplexing (OFDM) systems is proposed in this paper, where both frame synchronization and carrier frequency offset estimation can be performed by using only ONE training symbol. Frame synchronization and carrier frequency offset acquisition are performed simultaneously in the proposed scheme. Reliable frame synchronization is obtained in the proposed scheme even in low SNR. The maximum carrier frequency offset acquisition range of the proposed scheme can be up to one half of the total signal bandwidth. The same training symbol can also be utilized to carrier frequency offset Fine Adjustment, which estimates the remaining carrier frequency offset after acquisition with higher accuracy. The performance comparison of the proposed Fine Adjustment algorithm and Schmidl's algorithm by using computer simulation illustrates and verify the superior performance of the proposed algorithm with regard to estimation accuracy.     

OFDM系统载频偏移的ESPRIT方法估计

分析了OFDM系统信号模型与经典ESPRIT方法所要求的观测向量之间的相合之处，给出了利用经典ESPRIT算法估计OFDM系统载频偏移的方法。然后尝试使用了一种经典ESPRIT算法（TLS—ESPVaT）估计载波频率偏移，仿真结果表明使用该方法比类ESPRIT算法具有更高的估计精度，证明了使用经典ESPRIT方法估计栽波频率偏移的可行性与有效性。     

OFDM blind carrier offset estimation: ESPRIT

In orthogonal frequency-division multiplex (OFDM) communications, the loss of orthogonality due to the carrier-frequency offset must be compensated before discrete Fourier transform-based demodulation can be performed. This paper proposes a new carrier offset estimation technique for OFDM communications over a frequency-selective fading channel. We exploit the intrinsic structure information of OFDM signals to derive a carrier offset estimator that offers the accuracy of a super resolution subspace method, ESPRIT