An Efficient Maximum Likelihood Carrier Frequency Offset Estimator for OFDM Using Null Subcarriers and Cyclic Prefix

Accurate estimation of carrier frequency offset (CFO) is an important requirement in orthogonal frequency-division multiplexing (OFDM) based wireless communication systems. In this paper, we propose a hybrid procedure to accomplish this task efficiently. One of the key importance of the approach is the judicious combination of two independent estimators so as to reduce the bandwidth overhead and computational complexity over many conventional methods. It employs the cyclic prefix and a few null subcarriers, respectively, for the fractional and integer frequency offset estimations. We also propose a novel null subcarrier allocation scheme based on Fibonacci series. The range of frequency offset that can be estimated by the proposed technique is equal to the full OFDM bandwidth. Furthermore, performance of the proposed CFO estimator is mathematically analyzed by deriving an expression for the bit error probability of the receiver under Rayleigh fading channel and the Cramer-Rao lower bound for the mean square estimation error. For moderate SNRs, our approach is shown to greatly outperform some recently published methods in terms of BER performance, bandwidth overhead and receiver complexity.     

OFDM Carrier Frequency Offset Estimation Methods With Improved Performance

Orthogonal frequency division multiplexing (OFDM) systems are highly sensitive to carrier frequency offset and symbol timing error. This paper deals with estimation method of integer frequency offset (IFO) without the aid of pilot symbols. The proposed IFO estimator exploits two consecutive identical OFDM data symbols with only change of phase. In order to improve the accuracy of the IFO estimator, receive diversity is adopted. To demonstrate the efficiency of the proposed IFO estimators, comparisons are made with other existing estimators in terms of error performance, estimation range, and complexity.     

Joint carrier frequency synchronization and channel estimation for OFDM systems via the EM algorithm

A joint carrier frequency synchronization and channel estimation scheme is proposed for orthogonal frequency-division multiplexing (OFDM) system. In the proposed scheme, carrier frequency synchronization and channel estimation are performed iteratively via the expectation-maximization (EM) algorithm using an OFDM preamble symbol. Moreover, we analytically investigate the effect of frequency offset error on the mean square error (MSE) performance of channel estimator. Simulation results present that the proposed scheme achieves almost ideal performance for both channel and frequency offset estimation.     

Performance analysis of channel estimation for OFDM systems with residual timing offset

The authors present an analysis of the effect of timing offset on channel estimation for comb-type pilot-aided orthogonal frequency division multiplexing (OFDM) systems. Residual timing offset does not negatively affect the channel estimation of the pilot subcarrier, but does corrupt the channel information obtained via interpolation. This paper provides the mean square error (MSE) channel estimation performance when a linear interpolation technique is used in a comb-type pilot-aided OFDM system. Analysis shows that the performance degradation of the channel estimator due to imperfect frame synchronization is dependent on the frequency correlation of the channels and the amount of timing offset     

Estimation of Integer Carrier Frequency Offset in OFDM Systems Based on the Maximum Likelihood Principle

An algorithm is derived for the estimation of the integer part of the carrier frequency offset in OFDM systems. The algorithm employs correlation of consecutive OFDM symbols in the frequency domain, is formulated for the general case of a system using data subcarriers and/or pilots and approximates the Maximum Likelihood (ML) correlation-based estimator for the AWGN channel. The cases of pseudo-pilots, boosted pilots and virtual subcarriers are also examined. It is shown that, compared to previous approaches based on symbol correlation, the algorithm makes better use of the information contained in the correlated symbols, leading to a more accurate, approximate ML estimate of the integer carrier frequency offset at operating signal-to-noise ratios. Simulations indicate that, even in the case of multipath channels, the proposed algorithm is very likely to outperform other techniques.      

Maximum likelihood method for integer frequency offset estimation of OFDM systems

A novel method for integer frequency offset estimation of OFDM systems is derived, which is based on the maximum likelihood (ML) technique and exploits the differential information between two consecutive blocks of OFDM data symbols in the frequency domain. The reason why the proposed ML method has better performance than the conventional method is analysed.     

利用CAZAC序列共轭对称性的OFDM时频同步算法

符号定时和载波频率偏差将严重影响OFDM系统的性能。基于具有重复结构的CAZAC序列,提出了一种仅利用一个CAZAC符号实现符号定时、整数倍频偏与小数倍频偏估计的同步算法。首先,所提算法在完成粗定时同步的同时得到整数倍频偏估计。然后根据整数倍频偏估计值对定时估计进行修正,最后完成小数倍频偏估计。分析与仿真结果表明,该算法相比于传统PARK算法,不仅完成了定时估计,而且得到了频偏估计;相对于经典SC算法,不但提高了传输效率,还显著改善了OFDM系统的定时与频偏估计性能;相比于利用CAZAC序列的同步算法,提高了算法的估计精度以及对多径信道的适应性。      

Robust and fast frequency offset estimation for OFDM based satellite communication

A pilot-aided Orthogonal Frequency Division Multiplexing (OFDM) frequency offset estimator designed for satellite communication system is proposed in the paper. The estimator focuses on the acquisition of the integer part of carrier frequency offset and the acquisition range is as large as the whole signal bandwidth. Making full use of the phase difference between received pilot and local referential pilot, a fast estimation is obtained. Compared with existing method, our method can also work well even in SNR as low as 0dB. Simulations verify the good performance of our method.     

Symbol time offset estimation in coherent OFDM systems

This paper presents a symbol time offset estimator for coherent orthogonal frequency division multiplexing (OFDM) systems. The estimator exploits both the redundancy in the cyclic prefix and available pilot symbols used for channel estimation. The estimator is robust against frequency offsets and is suitable for use in dispersive channels. We base the estimator on the maximum-likelihood estimator for the additive white Gaussian noise channel. Simulations for an example system indicate a system performance as close as 0.6 dB to a perfectly synchronized system     

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO–OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO–OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator.     

Robust channel estimation and ISI cancellation for OFDM systems with suppressed features

A feature-suppressed orthogonal frequency-division multiplexing (OFDM) system and the corresponding channel estimation and intersymbol interference (ISI) mitigation techniques are investigated in this paper. Cyclic prefix (CP) and pilot tones, which are commonly used in civilian OFDM systems for ISI mitigation and channel estimation, create distinctive waveform features that can be easily used for synchronization and channel estimation purposes by intercepting receivers. As a result, CP and pilot tones are eliminated in the proposed feature suppressed OFDM system to reduce the interception probability. Instead, a set of specially designed OFDM symbols, driven by different pseudorandom sequences, are employed as preambles to avoid unique spectral signature. These preambles are inserted into the OFDM data symbol stream periodically and in a round-robin manner. In addition, a random frequency offset is introduced to each preamble to further mask the multicarrier signature. New challenges arising from these feature suppression efforts are studied, including robust channel estimation and demodulation techniques in the presence of frequency offset and severe interference. Based on our interference analysis, an iterative ISI and intercarrier interference (ICI) estimation-cancellation-based technique is proposed for both channel estimation and OFDM data demodulation. Our channel estimator performs joint frequency offset and channel impulse response estimation based on the maximum-likelihood (ML) principle. To reduce its complexity, we employ a number of techniques, which include approximation of the ML metrics, as well as fast Fourier transform pruning. The performances and feasibility of the proposed feature suppressed OFDM system and the channel estimator are analyzed and verified through numerical simulations.     

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 channel response, frequency offset, and phase noise in OFDM

Accurate channel estimates are needed in orthogonal frequency-division multiplexing (OFDM), and easily obtained under the assumption of perfect phase and frequency synchronization. However, the practical receiver encounters nonnegligible phase noise (PHN) and carrier frequency offset (CFO), which create substantial intercarrier interference that a conventional OFDM channel estimator cannot account for. In this paper, we introduce an optimal (maximum a posteriori) joint estimator for the channel impulse response (CIR), CFO, and PHN, utilizing prior statistical knowledge of PHN that can be obtained from measurements or data sheets. In addition, in cases where a training symbol consists of two identical halves in the time domain, we propose a variant to Moose's CFO estimation algorithm that optimally removes the effect of PHN with lower complexity than with a nonrepeating training symbol. To further reduce the complexity of the proposed algorithms, simplified implementations based on the conjugate gradient method are also introduced such that the estimators studied in this paper can be realized efficiently using the fast Fourier transform with only minor performance degradation. EDICS: SPC-MULT, SPC-CEST, SPC-DETC.     

Low complexity joint time offset and frequency offset estimations for LTE uplink system

The orthogonal frequency division multiplexing (OFDM) is currently used in long term evolution (LTE) system. The time offset estimation (TOE) and frequency offset estimation (FOE) of OFDM is essential in mobile communication base. According to the conventional cross correlation TOE and FOE algorithms, a new cross correlation computation was proposed to estimate the time offset and frequency offset for LTE uplink system, so that the time offset and frequency offset can be estimated simultaneously with low complexity. Compared with the conventional TOE and FOE algorithms, the simulation show that the proposed can reduce complexity and improve performance for FOE with good performance for TOE in additive white Gaussian noise (AWGN) and multipath channel.     

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。     

Frequency and Timing Offset Estimation Using Single Reference Symbol

In this paper we will investigate the performance of an estimator employing single OFDM reference symbol for timing and frequency offset estimation. We will show how both coarse and fine frequency offset estimation can be performed with this single OFDM reference symbol. The performance of this estimator will be compared with the ML estimator employing OFDM reference symbols of different length for coarse and fine frequency offset estimation. It will be shown that, unlike ML estimator, the estimation range of the analyzed estimator is not constrained.     

OFDM系统频率和时间估计的循环平稳实现

提出了一个用于频率选择性衰落信道中传输的正交频分多路(OFDM)的定时和频率联合估计的算法。这种估计器利用了接收信号的二阶循环特性,而且不需要信道冲激响应的信息。计算机仿真表明,采用所提出的方案能显著地提高估计器的性能。     

多径衰落信道下的OFDM时频联合同步算法

符号定时和载波频率偏差将严重影响OFDM系统的性能。基于具有重复结构的CAZAC序列,提出了一种仅利用一个CAZAC符号实现符号定时、整数倍频偏与小数倍频偏估计的同步算法。这种算法在完成粗定时同步的同时得到整数倍频偏估计,然后根据整数倍频偏估计值对定时估计进行修正,最后完成小数倍频偏估计。分析与仿真结果表明,该算法相对经典算法,不但提高了传输效率,还显著改善了OFDM系统的定时与频偏估计性能,相比CAZAC序列算法,提升了多径信道下的同步性能。     

Joint Frequency Offset and Channel Estimation for OFDM Systems Using Pilot Symbols and Virtual Carriers

We consider joint estimation of carrier frequency offset and channel impulse response (CIR) for orthogonal frequency division multiplexing (OFDM) systems with pilot symbols and virtual subcarriers (VCs). We derive the receive-signal correlation structure due to the pilots and VCs, give the evidence of joint multivariate Gaussian distribution of the received samples, and derive an approximate maximum likelihood (ML) frequency offset estimator. We also derive the asymptotic mean-square error (MSE) and an approximate Cramer-Rao bound (CRB) and establish the asymptotic unbiasedness. Without pilots, in high signal-to-noise ratio, our estimator is equivalent to Liu and Tureli's estimator with N_v virtual carriers. When the pilot number (Np) is greater than the channel length L, our estimator acts as a subspace-based estimator with N_v + N_p - L virtual carriers. A decision-directed joint ML estimator is derived to iteratively update the estimates of frequency offset, data symbols and CIR. The optimal pilot and virtual carrier placement strategies are also discussed. The resulting decision-directed joint estimator performs within 0.8 dB of the ideal case even when the frequency offset is as large as 20%     

Fast Synchronization and Channel Estimation for OFDM Systems

A joint synchronization and channel estimation scheme is proposed for orthogonal frequency division multiplexing (OFDM) system. In the proposed scheme, the integer frequency offset, fine timing offset and channel estimation are estimated based on the characteristics of the chirp signals. The main contributions of the paper are: the more robust ability to find the actual first path instead of the strongest path on the assumption of repeated chirp waveforms in the timing synchronization approach, and the lower computational complexity with high performance in the channel estimation approach. Moreover, we analyze the performance of the proposed method and check it via Monte Carlo simulations. The simulation results show that the proposed method can achieve good performance for both synchronization and channel estimation in frequency selective channels.