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.     

Analysis and design of joint CFO/channel estimate techniques for a cooperative STBC‐OFDM system

This paper studies the joint estimation technique of carrier frequency offset (CFO) and channel information for a distributed decode‐and‐forward (DF) cooperative space‐time block‐coded (STBC) orthogonal frequency division multiplexing (OFDM) system. For the considered relay system, we provide theoretical analysis of the effects upon the output signal‐to‐noise ratio (SNR), which is caused by the CFO/channel estimation error. Based on the provided analytical results, a joint CFO/channel estimation scheme is then developed, where the CFO estimate is achieved by a multiple‐dimensional linear search algorithm. Furthermore, we propose an alternative estimation solution with iteration approach being designed for the CFO estimation prior to the channel estimation. In contrast to the former estimator, the iterative method enjoys the advantage of the substantially reduced implementation complexity without sacrificing the estimate performance. The conducted computer simulation results verify the effectiveness of the proposed schemes.     

Iterative Carrier Frequency Offset and Channel Estimation for Underwater Acoustic OFDM Systems

This paper presents a practical low-density paritycheck (LDPC) coded OFDM system designed for the underwater acoustic channel with its attendant sparse multipath channel and Doppler effects. The carrier frequency offset (CFO) and channel state information (CSI) are assumed unavailable to both to the transmitter and the receiver. Several different receiver structures are considered, all of which perform CFO/channel estimation, detection and decoding in an iterative manner. The convergence behavior of the iterative receivers and their asymptotic performance are evaluated using the extrinsic information transfer (EXIT) chart method. OFDM receiver performance is further evaluated through simulations and field tests in shallow water.     

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.      

Multimedia transmission in MC-CDMA using adaptive subcarrier power allocation and CFO compensation

Multicarrier code division multiple access (MC-CDMA) system is one of the most effective techniques in fourth-generation (4G) wireless technology, due to its high data rate, high spectral efficiency and resistance to multipath fading. However, MC-CDMA systems are greatly deteriorated by carrier frequency offset (CFO) which is due to Doppler shift and oscillator instabilities. It leads to loss of orthogonality among the subcarriers and causes intercarrier interference (ICI). Water filling algorithm (WFA) is an efficient resource allocation algorithm to solve the power utilisation problems among the subcarriers in time-dispersive channels. The conventional WFA fails to consider the effect of CFO. To perform subcarrier power allocation with reduced CFO and to improve the capacity of MC-CDMA system, residual CFO compensated adaptive subcarrier power allocation algorithm is proposed in this paper. The proposed technique allocates power only to subcarriers with high channel to noise power ratio. The performance of the proposed method is evaluated using random binary data and image as source inputs. Simulation results depict that the bit error rate performance and ICI reduction capability of the proposed modified WFA offered superior performance in both power allocation and image compression for high-quality multimedia transmission in the presence of CFO and imperfect channel state information conditions.     

基于可变遗忘因子RLS在OFDM系统的载波频偏估计

在时变信道下正交频分复用（OFDM）系统中,通过导频辅助,提出基于可变遗忘因子RLS（VFF-RLS）的载波频偏（CFO）估计改进算法。针对传统RLS（CFF-RLS）算法中遗忘因子无法同时满足CFO估计收敛速度和收敛精度的缺陷,本文设计了线性变化遗忘因子(LFF)和非线性变化遗忘因子(NLFF) 两种可变遗忘因子方案来提升CFO估计性能。仿真结果显示：在低信噪比的情形下,基于VFF-RLS算法的CFO估计性能明显优于基于CFF-RLS算法的CFO估计性能。     

Scattered Pilots and Virtual Carriers Based Frequency Offset Tracking for OFDM Systems: Algorithms, Identifiability, and Performance Analysis

In this paper, we propose a novel carrier frequency offset (CFO) tracking algorithm for orthogonal frequency division multiplexing (OFDM) systems by exploiting scattered pilot carriers and virtual carriers embedded in the existing OFDM standards. Assuming that the channel remains constant during two consecutive OFDM blocks and perfect timing, a CFO tracking algorithm is proposed using the limited number of pilot carriers in each OFDM block. Identifiability of this pilot based algorithm is fully discussed under the noise free environment, and a constellation rotation strategy is proposed to eliminate the c-ambiguity for arbitrary constellations. A weighted algorithm is then proposed by considering both scattered pilots and virtual carriers. We find that, the pilots increase the performance accuracy of the algorithm, while the virtual carriers reduce the chance of CFO outlier. Therefore, the proposed tracking algorithm is able to achieve full range CFO estimation, can be used before channel estimation, and could provide improved performance compared to existing algorithms. The asymptotic mean square error (MSE) of the proposed algorithm is derived and simulation results agree with the theoretical analysis.     

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     

BER analysis and interference mitigation for GO‐OFDMA transmission

Carrier frequency offset (CFO) results in multiaccess interference and intersymbol interference and degrades the bit error rate performance. Mitigating the effects of CFO always burdens the receiver with respect to architecture and power. This disadvantage increases with increase in number of users. In the present work, bit error rate analysis of multiuser group orthogonal–orthogonal frequency division multiple access scheme for variable rate and single rate over pedestrian channel in the presence of CFO is presented. Through analysis, it is proved that by incorporating carrier interferometry codes in the scheme, CFO effects can be removed without burdening receiver. It is also shown by analysis that effect of CFO is rate dependent. Finally, simulation results are provided to confirm the analytical results.     

Blind and Semiblind Channel and Carrier Frequency-Offset Estimation in Orthogonally Space-Time Block Coded MIMO Systems

In this paper, the problem of joint channel and carrier frequency offset (CFO) estimation is studied in the context of multiple-input multiple-output (MIMO) communications based on orthogonal space-time-block codes (OSTBCs). A new blind approach is proposed to jointly estimate the channel matrix and the CFO parameters using a relaxed maximum likelihood (ML) estimator that, for the sake of simplicity, ignores the finite alphabet constraint. Although the proposed technique can be applied to the majority of OSTBCs, there are, however, a few codes that suffer from an intrinsic ambiguity in the joint channel, CFO, and symbol estimates. For such specific OSTBCs, a semiblind modification of the proposed approach is developed that resolves the aforementioned estimation ambiguity. Our simulation results demonstrate that although the finite alphabet constraint is relaxed, the performance of the proposed techniques approaches that of the informed (fully frequency-synchronized and coherent) receiver, provided that a sufficient number of data blocks is available for each channel realization.     

UFMC系统在多径衰落信道中的干扰消除

通用滤波多载波(UFMC)是5G通信系统中的关键技术,能够降低带外泄露.但是在多径衰落信道下UFMC系统会受到符号间干扰(ISI)和多普勒效应产生的载波频率偏差的影响,从而使系统的性能下降.为了消除系统中的干扰,提出了一种迭代最大似然算法.该方法主要通过迭代最大似然算法(ML)计算出载波频率偏差,把估计出的结果作为初始值并运用迭代的方法得到最终的载波频率偏差,当达到收敛区间时,迭代结束;最后利用相位旋转的概念补偿载波频率偏差并运用最小二乘算法更新信道响应信息,减少该系统干扰.仿真结果表明,在信噪比大于10 dB时,随着信噪比的增大,算法能够有效地抑制系统中的干扰,提高UFMC系统的性能.     

Recursive maximum likelihood estimation of time‐varying carrier frequency offset for orthogonal frequency‐division multiplexing systems

A recursive maximum likelihood carrier frequency offset (CFO) estimator is proposed in this work, where redundancy information contained in the cyclic prefix of multiple consecutive orthogonal frequency‐division multiplexing (OFDM) symbols is exploited in an efficient recursive fashion. Because the estimator is based on multiple OFDM symbols, the time‐varying CFO must be considered. We investigate the effect of time‐varying CFO on the performance of the estimator and the trade‐off between fast tracking ability and low estimation variance. We show that, without channel noise, the mean squared error (MSE) of estimation due to CFO estimation variation increases approximately quadratically with n, where n is the number of OFDM symbols used for CFO estimation (estimation window size), whereas the MSE due to channel noise decreases proportionally to 1/n (approximately) if the CFO is constant. A closed‐form expression of the optimal estimation window size (approximately) is derived by minimizing the MSE caused by both time‐varying CFO and channel noise. For wireless systems with time‐varying rate of change for CFO, the proposed estimator can be implemented adaptively. In addition, typical optimal estimation window sizes for WiMAX, DVB‐SH and MediaFLO systems are evaluated as an example. Copyright © 2011 John Wiley & Sons, Ltd.     

一种改进的OFDM盲同步算法

研究了OFDM系统中的最大似然估计(ML)算法,并使用数据循环移位以及多符号联合估计等技术对ML算法进行了改进,随后提出了一个综合性的新方案。仿真结果显示,在AWGN和瑞利多径衰落信道中,该方案可以有效提高符号定时偏差(STO)和载波频率偏移(CFO)的估计性能。     

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.     

Parameter estimation and error reduction for OFDM-based WLANs

We consider parameter estimation and error reduction for orthogonal frequency-division multiplexing (OFDM) based high-speed wireless local area networks (WLANs). We devise or select algorithms that can provide benefit to the overall system performance and can be efficiently implemented in real-time. In particular, first, we give a channel model which is especially useful for assessing the channel parameter estimation methods devised for OFDM-based WLANs. Second, we provide a sequential method for the estimation of carrier frequency offset (CFO), symbol timing, and channel response by exploiting the structure of the packet preamble specified by the IEEE 802.11a standard. Finally, to correct the residue CFO induced phase error using the pilot tones, we consider maximum-likelihood phase tracking and least-squares phase fitting approaches; to improve the channel estimation accuracy using the decoded data, we present a semiblind channel estimation method; to mitigate the sampling clock induced time delay error, we provide a sampling clock synchronization approach that obviates the need of an automatic frequency control clock recovery circuit. The overall system performance of using our algorithms is demonstrated via several numerical examples.     

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.     

基于差分空时调制的OFDM系统中的载波频率偏差估计算法

最近兴起的基于差分空时调制的正交频分复用系统可以采用非相干接收，从而避免了对时变多径信道状态信息的复杂估计，但存在的载波频率偏差会导致系统性能的下降。本文充分利用差分空时调制和循环前缀的特点，提出了的一种高效率高精度的频率偏差估计算法。该算法不需要任何辅助信号和信道估计，经过捕获和一次跟踪，解决了频率偏差的估计问题。理论分析表明，本文提出的算法能有效估计系统中存在的小数频率偏差。此外，仿真结果显示新算法在较低Eb／N0时，较常规算法有一个数量级以上的精度提高，而在高Eb／N0时可以有超过3个数量级的精度改善。     

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.     

RLS-Based Estimation and Tracking of Frequency Offset and Channel Coefficients in MIMO-OFDM Systems

In this paper, we investigate the problem of carrier frequency-offset (CFO) synchronization and channel estimation in multiple-input multiple-output orthogonal frequency-division multiplexing systems operating over unknown frequency-selective fading channels. We first propose a novel joint CFO and channel estimator, assuming time-domain training blocks are available. The proposed joint estimator consists of two recursive least-square (RLS) algorithms which iterate their estimated CFO and CIR values. We then derive a more precise pilot-aided RLS algorithm to estimate the residual frequency synchronization errors or track small CFO changes. With this, the accuracy of channel estimation is also enhanced. The analysis and simulation results show that, the proposed estimation and tracking scheme which is fully compatible with the existing standards is able to attain fast convergence, high stability, and ideal performances as compared with relevant Cramer–Rao bounds in all ranges of signal-to-noise ratio. Moreover, it can work well for wide tracking range up to ±0.5 of the subcarrier spacing.     

Low-complexity block double-differential design for OFDM with carrier frequency offset

Carrier frequency offset (CFO) estimation for orthogonal frequency-division multiplexing (OFDM) has caught attention as OFDM systems have become widely adopted in recent years. In this paper, we design a novel double-differential (DD) codec with low computational complexity. Our design bypasses CFO and channel estimation, and is easy to implement at both transmitter and receiver. It also guarantees full multipath diversity, and reduces the peak-to-average power ratio from the number of subcarriers to the channel order. In addition, it is robust to CFO drifting. The closed form of the performance for our design is derived for OFDM transmissions over frequency-selective channels with CFO. Thorough simulation results corroborate our claims.