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 estimation of OFDM carrier frequency offset via oversampling

Blind deterministic estimation of the orthogonal frequency division multiplexing (OFDM) frequency offset via oversampling is proposed in this paper. This method utilizes the intrinsic phase shift of neighboring sample points incurred by the frequency offset that is common among all subcarriers. The proposed method is data efficient - it requires only a single OFDM symbol to achieve reliable estimation, hence making it more suitable to systems with stringent delay requirement and mobility-induced channel variation. The proposed scheme is devised to perfectly retrieve frequency offset in the absence of noise. Quite remarkably, we show that in the presence of channel noise, this intuitive scheme is indeed the maximum likelihood estimate of the carrier frequency offset. The possible presence of virtual carriers are also accommodated in the system model, and some interesting observations are obtained. The Cramer-Rao lower bound is derived for the oversampling-based signal model, and we show through numerical simulation that the proposed algorithm is efficient. Practical issues such as identifiability, the front-end filter bandwidth, and the possible presence of correlated noises are also carefully addressed.     

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.     

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.     

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.     

一种高效的OFDM载波频偏盲估计方法

针对正交频分复用（OFDM）系统,提出了一种低复杂度、高性能的载波频偏盲估计 方法。该方法充分利用载波频偏估计代价函数在一定区间内的单谷特性,采用黄金分割法搜 索载波频偏估计代价函数极值,从而大大降低其计算复杂度。最后对该方法和Tureli′s MU SIC-like(TML)载波频偏估计方法在加性高斯白噪声信道和多径信道环境下进行了仿真,结 果表明, 在同等条件下该方法的计算复杂度大大低于TML载波频偏估计方法。     

Propagator based closed-form blind carrier frequency offset estimation for OFDM systems

Most of the blind Orthogonal Frequency Division Multiplexing （OFDM） Carrier Frequency Offset （CFO） estimators necessitate large number of samples to ensure the estimation accuracy. However, the number of samples can not be selected too large because of the carrier offset drift. In this letter, a new closed form algorithm for blind OFDM CFO estimation in frequency-selective channel is proposed. This method utilizes the propagator obtained from data matrix and the diagonal loading technique, thus it has better performance even only using one or two OFDM blocks. Furthermore, the range of the CFO estimation which can be handled is overall transmission spectral. Simulation results confirm its effectiveness.     

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     

新的MIMO-OFDM 系统盲频偏估计算法

针对瑞利衰落信道,提出了一种新的基于加权循环前缀(CP,cyclic prefix)的MIMO-OFDM系统频偏估计算法及其简化实用算法。根据最大比合并原理,降低了MIMO-OFDM系统符号间干扰和高斯白噪声对频偏估计性能的影响。然后,利用无线信道统计信息,得到其简化算法。仿真结果表明,此算法在瑞利衰落信道中可以取得良好的频偏估计性能并优于其他同类算法。     

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 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.     

Joint estimation of carrier frequency offset, dc offset and I/Q imbalance for OFDM systems

Orthogonal frequency division multiplexing (OFDM) systems with direct-conversion receiver (DCR) are vulnerable to carrier frequency offset (CFO), dc offset (DCO) and in-phase/quadrature (I/Q) imbalance. In this paper, we propose blind estimator for joint estimation of CFO, DCO and I/Q imbalance in OFDM systems with DCR. Simulation results show that performance of proposed estimator approaches Cramér-Rao lower bound (CRLB) asymptotically, which demonstrates its effectiveness.     

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.     

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     

Blind symbol timing offset estimation for offset‐QPSK modulated signals

In this paper, a blind symbol timing offset (STO) estimation method is proposed for offset quadrature phase‐shift keying (OQPSK) modulated signals, which also works for other linearly modulated signals (LMS) such as binary‐PSK, QPSK, π/4‐QPSK, and minimum‐shift keying. There are various methods available for blind STO estimation of LMS; however, none work in the case of OQPSK modulated signals. The popular cyclic correlation method fails to estimate STO for OQPSK signals, as the offset present between the in‐phase (I) and quadrature (Q) components causes the cyclic peak to disappear at the symbol rate frequency. In the proposed method, a set of close and approximate offsets is used to compensate the offset between the I and Q components of the received OQPSK signal. The STO in the time domain is represented as a phase in the cyclic frequency domain. The STO is therefore calculated by obtaining the phase of the cyclic peak at the symbol rate frequency. The method is validated through extensive theoretical study, simulation, and testbed implementation. The proposed estimation method exhibits robust performance in the presence of unknown carrier phase offset and frequency offset.     

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.     

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.