OFDM Carrier Synchronization Based on Time-Domain Channel Estimates

Carrier frequency synchronization is critical to the quality of signal reception in OFDM systems. This paper presents an approximate maximum-likelihood (ML) carrier frequency offset (CFO) estimation scheme based on time-domain channel estimates which retain the CFO information in the form of phase rotation. The proposed ML CFO estimate is investigated under static as well as time-varying fading channels. Statistical properties of the estimator are examined and Cramer-Rao lower bound (CRLB) is derived. Theoretical analysis and numerical simulations show that the proposed CFO estimator renders excellent performance with lower computational complexity. The proposed CFO estimate also has an advantage of allowing for more flexible pilot patterns     

Non-data-aided carrier-frequency offset estimation for pulse-shaping OFDM/OQAM systems

In this paper we consider the problem of blind carrier-frequency offset (CFO) estimation for pulse-shaping orthogonal frequency-division multiplexing (OFDM) systems based on offset quadrature amplitude modulation (OQAM). In particular, under the assumption of low signal-to-noise ratio, three maximum-likelihood (ML) CFO estimators for non-dispersive channels are derived. Due to their significant computational complexity a more feasible closed-form CFO synchronization algorithm is considered. The performance of the derived blind estimators is assessed via computer simulations and compared with that of a blind CFO estimator previously proposed in the literature, exploiting the second-order cyclostationarity property of the OFDM/OQAM signal.     

高阶QAM调制下OFDM的载波与采样频偏联合纠正

采用高阶QAM (Quadrature Amplitude Modulation)调制的正交频分复用(OFDM,Orthogonal Frequency-Division Multiplexing)系统,相对于低阶调制来说,密集的星座点分布更容易受到载波频偏与采样频偏的影响.本文分析了高阶QAM OFDM系统对频率同步精度的要求,提出了一种载波与采样频偏联合纠正的方法,并分别针对时不变多径信道和块衰落多径Rician信道给出了频偏估计的均方误差解析表达式.均方误差的理论分析与计算机仿真结果吻合;误比特率性能仿真表明,频偏纠正后的误比特率性能与无频偏情况比较,差异小于1dB.     

Blind Frequency Synchronization in OFDM via Diagonality Criterion

In this paper, we address the problem of blind carrier frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems in the case of frequency-selective channels. CFO destroys the orthogonality between the carriers leading to nondiagonal signal covariance matrices in frequency domain. The proposed blind method enforces a diagonal structure by minimizing the power of nondiagonal elements. Hence, the orthogonality property inherent to OFDM transmission with cyclic prefix is restored. The method is blind since it does not require a priori knowledge of the transmitted data or the channel, and does not need any virtual subcarriers. A closed-form solution is derived, which leads to accurate and computationally efficient CFO estimation in multipath fading environments. Consistency of the estimator is proved and the convergence rate as a function of the sample size is analyzed as well. To assess the large sample performance, we derive the CramÉr–Rao bound (CRB) for the blind CFO estimation problem. The CRB is derived assuming a general Gaussian model for the OFDM signal, which may be applied to both circular and noncircular modulations. Finally, simulation results on CFO estimation are reported using a realistic channel model.     

RLS-Based Joint Estimation and Tracking of Channel Response, Sampling, and Carrier Frequency Offsets for OFDM

This paper proposes a pilot-aided joint channel estimation and synchronization scheme for burst-mode orthogonal frequency division multiplexing (OFDM) systems. Based on the received signal samples containing pilot tones in the frequency domain, a cost function that includes the carrier frequency offset (CFO), sampling clock frequency offset (SFO) and channel impulse response (CIR) coefficients is formulated and used to develop an accompanying recursive least-squares (RLS) estimation and tracking algorithm. By estimating the channel CIR coefficients instead of the channel frequency response in the frequency domain, the proposed scheme eliminates the need for an IFFT block while reducing the number of parameters to be estimated, leading to lower complexity without sacrificing performance and convergence speed. Furthermore, a simple maximum-likelihood (ML) scheme based on the use of two long training symbols (in the preamble) is developed for the coarse estimation of the initial CFO and SFO to suppress dominant ICI effects introduced by CFO and SFO and to enhance the performance and convergence of the fine RLS estimation and tracking. Simulation results demonstrate that, over large ranges of CFO and SFO values, the proposed pilot-aided joint channel estimation and synchronization scheme provides a receiver performance that is remarkably close to the ideal case of perfect channel estimation and synchronization in both AWGN and Rayleigh multipath fading channels.      

A time-frequency decision-feedback loop for carrier frequency offset tracking in OFDM systems

Acquisition and tracking are two crucial stages necessary to the carrier frequency synchronization in orthogonal frequency division multiplexing (OFDM) systems. In this letter, by employing the rotation property of OFDM data subcarriers, a simple time-frequency decision-feedback loop without the use of pilot subcarriers is proposed for the fine carrier frequency offset (CFO) tracking. Specifically, with proper loop parameters, a residual CFO less than 10% of the subcarrier spacing may be well tracked for quarternary phase-shift keying (QPSK) modulation in the presence of noise, while for systems using QPSK, 16-QAM, and 64-QAM modulation schemes, the bit-error rate (BER) performance very close to that of an offset-free system may be achieved in both additive white Gaussian noise (AWGN) and frequency selective fading channels. Moreover, a hardware implementation in a practical OFDM system is fulfilled which verifies the effectiveness of the proposed scheme.     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

Blind frequency-offset estimator for OFDM systems transmitting constant-modulus symbols

We address the problem of carrier frequency offset (CFO) synchronization in OFDM communications systems in the context of frequency-selective fading channels. We consider the case where the transmitted symbols have constant modulus, i.e., PSK constellations. A novel blind CFO estimation algorithm is developed. The new algorithm is shown to greatly outperform a previously published blind technique that exploits the fact that practical OFDM systems are not fully loaded. Further, the proposed algorithm is consistent even when the system is fully loaded. Finally, the proposed CFO estimator is obtained via a one-dimensional search, the same as with the existing virtual subcarrier-based estimator, but achieves a substantial gain in performance (10-dB SNR or one order of magnitude in CFO MSE).     

Joint low‐complexity equalization and CFO estimation and compensation for UWA‐OFDM communication systems

Frequency synchronization has a great importance in preserving the performance of the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems. The carrier frequency offset (CFO) estimation can be blind or data‐aided. In this paper, the Zadoff‐Chu (ZC) sequences are used for OFDM synchronization in UWA communications, and they are compared with different data‐aided algorithms. We propose a low‐complexity algorithm for CFO estimation based on ZC sequences. Also, a joint equalization and CFO compensation scheme for UWA‐OFDM communication systems is presented. Simulation results demonstrate that the proposed CFO estimation algorithm allows estimation of the CFO accurately with a simple implementation in comparison with the traditional schemes. Also, the performance of the UWA‐OFDM system can be preserved in the presence of frequency offsets.     

A New Data Rotation Based CP Synchronization Scheme for OFDM Systems

In this paper, a new data rotation scheme for improving the symbol timing and carrier frequency offset (CFO) estimation of orthogonal frequency-division multiplexing (OFDM) systems is proposed. The new data rotation scheme intentionally introduces a cyclic shift after the inverse fast Fourier transform (IFFT) in the transmitter so that a higher energy cyclic prefix (CP) is obtained. This cyclic shift will not impair the orthogonality among the subcarriers and will only results in phase shift in the demodulated signal at the receiver. To recover the cyclic shift and for data detection, the scheme makes use of double differential encoding and decoding at the transmitter and the receiver. We analyze the performance of the new data rotation scheme by using order statistics theory. Our results show that the new scheme can provide a 1.6 dB gain in the performance of the CFO estimator and a 6 dB gain for the timing estimator at 15 dB SNR over AWGN channel, as well as a 6 dB gain in lock-in probability and a 4 dB gain in CFO performance at 5 dB SNR over frequency selective fading channel.     

OFDM盲载波间干扰抑制与同步算法研究

针对载波频偏引起的子载波间干扰问题,提出一种基于独立分量分析的OFDM载波频率同步算法。本算法直接实现载波频率同步,可以避免基于导频机制的频偏估计和由频偏估计误差带来的频谱效率降低与性能损失。首先建立含频偏OFDM独立分量分析模型,然后从最大似然原则得到分离的代价函数,结合自然梯度优化得到OFDM源信号实现载波频率同步。理论分析表明,提出的算法不仅具有基于最大似然的频偏补偿性能而且提高了系统的输出信噪比。最后,仿真分析证明了算法的有效性。      

Improved time and frequency synchronization for dual-polarization OFDM systems

This article presents techniques for improved estimation of symbol timing offset (STO) and carrier frequency offset (CFO) for dual-polarization (DP) orthogonal frequency division multiplex (DP-OFDM) systems. Recently, quaternion multiple-input multiple-output OFDM has been proposed for high spectral efficiency communication systems, which can flexibly explore different types of diversities such as space, time, frequency, and polarization. This article focuses on synchronization techniques for DP-OFDM systems using a cyclic prefix, where the application of quaternion algebra leads to new improved estimators. Simulations performed for DP system methods show faster reduction of STO estimator variance with a double-slope line in the log-variance line versus signal-to-noise ratio (SNR) plot compared with single-polarization (SP) counterparts, and simulations for CFO estimates show a 3-dB gain of DP over SP estimates for same SNR values defined, respectively, for quaternion-valued or complex-valued signals. Cramer–Rao bounds for STO and CFO are derived for the synchronization methods, correlating with the observed gains of DP over SP OFDM systems.     

Parameter Optimization for OFDM Systems in Doubly-Selective Fading Channels with Line-of-Sight Components

In wireless communications, the channel can often be modelled as a time-selective frequency-selective fading channel with line-of-sight (LOS) component. Although orthogonal frequency division multiplexing (OFDM) systems are developed to cope with the frequency selectivity of the channel, they will suffer from interference caused by the time-varying character of the channel, present in particular in the LOS component, when the number of carriers increases. A proper selection of the system parameters, such as the number of carriers and the length of the cyclic prefix, can alleviate the effect of the doubly-selective channel on the system performance. In this paper, we investigate analytically the effect of the aforementioned system parameters on the performance, and determine the optimum values of the system parameters. Further, we study the effect of deviations from the optimum parameters on the system performance     

Robust and Efficient OFDM Synchronization for FPGA-Based Radios

Orthogonal frequency division multiplexing (OFDM) is a popular modulation technique that can combat impulsive noise, is robust to multipath fading, is spectrally efficient, and can allow flexible allocation of spectrum. It has become a key standard in cognitive radio systems as well as an enabling technology for mobile data access systems. An OFDM receiver’s performance is heavily impacted by the accuracy of its symbol timing offset (STO) and carrier frequency offset (CFO) estimation. This paper proposes a novel OFDM synchronization method that combines robust performance with computational efficiency. FPGA prototyping is used to explore the trade-off between the number of computations to be performed and computation word length with respect to both synchronization performance and power consumption. Through simulation, the proposed method is shown to provide accurate fractional CFO estimation as well as STO estimation in a range of channels. In particular, it can yield excellent synchronization performance in the face of a CFO that is larger than many state-of-the-art synchronization implementations can handle. The system implementation demonstrates efficient resource usage and reduced power consumption compared with existing methods, and this is explored as a fine-grained trade-off between performance and power consumption. The result is a robust method suitable for use in low-power radios, enabling less precise analog front ends to be used.     

Exploiting input cyclostationarity for blind channel identificationin OFDM systems

Transmitter-induced cyclostationarity has been explored previously as an alternative to fractional sampling and antenna array methods for blind identification of FIR communication channels. An interesting application of these ideas is in OFDM systems, which induce cyclostationarity due to the cyclic prefix. We develop a novel subspace approach for blind channel identification using cyclic correlations at the OFDM receiver. Even channels with equispaced unit circle zeros are identifiable in the presence of any nonzero length cyclic prefix with adequate block length. Simulations of the proposed channel estimator along with its performance in OFDM systems combined with impulse response shortening and Reed-Solomon coding are presented     

Blind frequency-offset estimator for OFDM with general symbol constellation

An efficient feedforward blind carrier frequency offset (CFO) estimator for orthogonal frequency division multiplexing (OFDM) systems with general symbol constellation is presented. The proposed estimator requires only one OFDM symbol period to blindly and accurately estimate the CFO in Gaussian and multipath fading channels.     

一种针对双衰落信道OFDM的新均衡算法

在OFDM系统中，子载波间的正交性是保证OFDM性能的重要保障。针对双选择性衰落信道下的OFDM系统，该文在分析载波间干扰（ICI）的基础上，提出了一种采用频域迭代消除ICI的均衡算法。分析和仿真结果表明此方法能有效地保证载波间的正交性和改善了OFDM系统的误码率（BER）性能。     

OFDM传输系统同步方案简介

本文研究数字地面电视DVB-T的OFDM传输系统接收端的同步。根据OFDM的原理特点和DVB-T标准,设计同步方案。该方案采用多载波(OFDM)系统时域插在循环保护间隔携带的冗余信息进行粗符号和分数频率偏移估计。该方案利用OFDM系统时域插入的保护间隔前缀所携带的冗余信息,进行粗符号同步和分数频率偏移估计。FFT后,再利用频域插入的连续导频进行整数频偏估计,及利用分散导频通过估计信道冲击响应,实现精符号同步。仿真表明,同步设计在加性高斯白噪声信道能达到最佳性能,在慢衰落Rayleigh信道下也有较好的性能。     

BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels

We perform bit-error-rate (BER) analysis of orthogonal frequency division multiplexing (OFDM) systems impaired by both direct current (DC) offset and carrier frequency offset (CFO) in multipath Rayleigh fading channels. Since the performance of OFDM systems is sensitive to the CFO, it is necessary to estimate and correct the CFO at the receiver. The existence of DC offset degrades the performance of CFO estimator and results in large residual CFO after compensation. Moreover, the process of CFO compensation spreads the DC offset energy and causes DC offset interference to all subcarriers. By deriving the BER formula for OFDM systems employing binary phase-shift keying modulation, the dependency of BER on the DC offset, CFO, and estimated CFO is accurately quantified. Simulation results validate the correctness of our theoretical analysis.     

基于累积量和循环相关值的OFDM信号联合检测方法

为了提高在复杂信道环境下正交频分复用(OFDM)信号检测方法的性能,根据OFDM信号的渐进高斯性、自相关性、循环平稳性等特性,提出了一种基于累积量和循环相关值的OFDM信号联合检测方法.在瑞利多径衰落信道下对此方法进行了仿真研究,研究表明此方法能够有效抑制噪声和频率选择性衰落的影响,且弥补了其他方法难以区分高斯信号和OFDM信号这一不足,提高了对OFDM信号的检测率.