An Improved Sampling Frequency Offset Estimator for OFDM-Based Digital Radio Mondiale Systems

After coarse synchronization in orthogonal frequency division multiplexing (OFDM) systems, there might still be a residual frequency offset (RFO) and a sampling clock frequency offset (SFO), which seriously degrade the performance of the systems. This paper suggests a simple way of estimating the SFO in OFDM-based digital radio mondiale (DRM) system. To demonstrate the efficiency of the proposed SFO estimator, comparisons are made with other existing estimators in terms of mean square error (MSE) performance, estimation range, and complexity.     

OFDM系统的两种频率跟踪算法的性能比较

本文分析了残余频偏对OFDM系统性能的影响,针对OFDM系统中常见的两种频率跟踪算法,比较了它们在加性高斯白噪声信道、SUI- 2和SUI- 5信道环境下的性能。仿真表明,采用计算相位旋转的频率跟踪算法比基于循环前缀的频率跟踪算法的估计精度高。在信道最大多径时延较循环前缀长度小时,两种算法对系统性能影响均较小;在信道最大多径时延接近循环前缀长度时,基于循环前缀的频率跟踪算法的估计误差的标准偏差通常超过子载波间隔的1 %,系统会有明显的信噪比损失     

基于星座点特征的OFDM残留频偏跟踪算法

残留频偏会导致星座点发生旋转,而且这种旋转与时间有关,时间越长,旋转越大。若残留频偏长时间得不到校正,将会使星座点旋转到其他象限从而出现判决错误,使系统的性能急剧恶化。针对这个问题,提出了一种基于星座点特征的残留频偏跟踪算法。该算法要求在信道估计之后完成,并假定一个OFDM帧内的信道频率响应保持不变。该算法包括三个步骤,首先将每个OFDM符号的星座点划分为四个子集,然后对每个子集的均值求相位角获得相位误差,最后经环路滤波器输出一个校正量补偿时域频偏。由于残留频偏估计值的提取充分利用了所有数据子载波信息,并对每个子集进行了求均值处理,所以有效的改善了环路的输入信噪比。它适用于子载波为QPSK或QAM调制的OFDM系统,不同的子载波调制方式跟踪范围不同,最大跟踪范围为±0.05个子载波间隔。仿真表明:新算法性能要优于基于循环前缀的算法,与基于导频的跟踪算法性能相当。      

A Robust SFO Estimation Scheme for OFDM-Based DRM with Non-Symmetric Distributed Pilots

This paper proposes a robust sampling frequency offset (SFO) estimation scheme in an orthogonal frequency division multiplexing based digital radio mondiale system with non-symmetrically distributed pilots. In particular, a post fast Fourier transform SFO estimation method is suggested to provide an unbiased estimate of SFO in the presence of frequency selectivity of the channel as well as non-symmetrically distribution of pilot symbols. In order to verify the performance of the proposed frequency-offset estimation scheme, a closed-form expression for the mean square error (MSE) is derived. We show via simulations that the proposed estimation scheme achieves a remarkable robustness against frequency selectivity fading and the theoretical MSE analysis is proven accurate.     

Cramér-Rao Bound for SAGE-based Residual Frequency Offset Estimation Algorithm in OFDM Systems

The Cramér-Rao bound (CRB) is a powerful tool in estimation theory as it gives a performance lower bound for parameter estimation problems. In this paper, a much tighter CRB for Lee’s residual frequency offset (RFO) estimation method (IEEE Transactions on Communications 54:765, 2006) is first given. The tighter low bound is obtained by considering the ICI that affects the performance of space-alternating generalized expectation-maximization (SAGE) based RFO estimator. It can be concluded that the performance of SAGE based RFO estimation method decreases as the normalized RFO increases and increases with the increasing of signal-to-noise (SNR). Simulation results show that the proposed CRB of SAGE based RFO estimator is extremely tight. It approximates closely the MSE performance obtained by Monte Carlo simulation.     

Inter-Frame, Fine Frequency/Phase Synchronization forSimple Space-Time-Coded OFDM Receivers

This paper proposes an enhanced receiver (Rx) configuration for multiple-input, multiple-output (MIMO) OFDM systems, operating under the composite effect of phase noise (PHN), residual frequency offset (RFO) and the transmission channel, herein modeled as quasi-static but unknown. The proposed Rx identifies the different impairments by exploiting their different time constants and compensates for each one accordingly. It includes a novel inter-frame fine frequency synchronization (FFS) scheme, which is closely coupled to an intra-frame adaptive phase synchronizer/channel estimator. The proposed scheme is evaluated for a 2 times 2, Alamouti space-time code (STC), and is shown to provide significant performance gain. The theory can be employed with any other STC scheme.     

The effect of diversity on a burst-mode carrier-frequency estimatorin the frequency-selective multipath channel

This paper describes a carrier-frequency offset estimator derived using maximum-likelihood techniques. The estimator is designed for a digital space-diversity receiver, operating in a wide-band frequency-selective multipath fading channel. The estimator is suited to a burst-mode time-division-multiple-access system, because the estimate is formed in an open-loop manner, and relies on a training sequence normally used in burst-mode systems. The main advantage is that it does not require channel state information; rather, it only requires knowledge of the auto-correlation of the channel. Simulation results show the estimator to be unbiased over a wide frequency range. The normalized error standard deviation is shown to be 0.0015 across the frequency offset range for a receiver with four diversity branches, when the normalized channel delay spread is 0.1, the signal-to-noise ratio (SNR) is 10 dB, and the training sequence length is 23 symbols. It is found that, for most parameter configurations, there is approximately a factor of two improvement in the estimate error standard deviation when the antenna diversity is doubled     

MSE Analysis of Sampling Frequency Offset Estimation Scheme for OFDM-Based Digital Radio Mondiale (DRM) Systems

A precise estimation and compensation of sampling frequency offset (SFO) is an important issue in an orthogonal frequency division multiplexing (OFDM) system because of its time-variant behavior. This paper considers the problem of SFO estimation for OFDM-based digital radio mondiale (DRM) systems. In this study, we develop expressions for the mean square error (MSE) of the conventional SFO estimators used in the OFDM-based DRM system. Their low-complexity variants and computation complexity are reported. The theoretical MSE analysis for different algorithms are validated by Monte-Carlo simulations within the framework of the OFDM parameter and pilot pattern defined in the DRM specification. It is also shown that the computation complexity of the low-complexity variants is significantly reduced, compared with that of original versions.     

一种基于二倍钟采样的OFDM载波偏差估计算法

本文从OFDM信号的二倍钟采样出发,给出了一种载波偏差估计算法,该算法直接利用时域信号的采样来估计载波偏差,克服了频域实现算法受载波偏差影响大的缺点,使得算法在不同的载波偏移下具有相同的估计精度,载波偏差估计范围大,同时该算法充分利用信号的有效能量,估计精度高,优于采用循环前缀的算法;论文同时给出了算法性能的理论分析和计算机仿真结果.     

Residual frequency offset compensation using the approximate SAGE algorithm for OFDM system

In this letter, we propose an iterative detection scheme in the presence of residual frequency offset (RFO) for orthogonal frequency-division multiplexing systems using an approximate application of the space-alternating generalized expectation-maximization (SAGE) algorithm. In the proposed scheme, the expectation step intends to divide the received signal into the desired signal and the interference signal. In the maximization step, the desired signal is used to estimate required parameters (i.e., RFO, data symbols, and channel state information) sequentially. Simulation results present that the proposed scheme shows almost ideal performance as long as the normalized RFO value is within 0.2.     

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.     

REDUCED COMPLEXITY FREQUENCY ESTIMATOR FOR BURST TRANSMISSION

In burst transmission, carrier recovery is a critical point for synchronization systems. With a feedforward carrier phase recovery algorithm, a small frequency offset can significantly increase the cycle slip rate and then the phase error variance. Therefore, in order to obtain an accurate carrier phase estimation, a precise frequency correction is required. For M-states phase shift keying (M-PSK) modulated signals an unbiased feedforward reduced complexity frequency estimator (RCFE), operating in the non-data aided mode (NDA) is derived from the maximum likelihood (ML) principle. A compromise is realized between noise filtering and estimation slip probability by minimizing the estimator variance. It is optimized to operate at a low signal-to-noise ratio and short bursts. Its performance is compared to that of the ML estimator. The estimator is applied to an all-feedforward synchronization structure with QPSK modulated signals. Global performance of the modem synchronization structure is supplied. © 1996 by John Wiley & Sons, Ltd.     

Decision-directed fine synchronization in OFDM systems

A new decision-directed (DD) synchronization scheme is proposed for joint estimation of carrier frequency offset (CFO) and sampling clock frequency offset (SFO) in orthogonal frequency-division multiplexing (OFDM) systems. By exploiting the hard decisions, we report accurate estimators of residual CFO and small SFO. The performance analysis and simulation results indicate that the proposed novel DD scheme achieves much better performance than the conventional pilot-based schemes in both additive white Gaussian noise and frequency-selective channels.     

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.     

Performance Evaluation of Timing Estimation Technique Using Extended Cyclic Prefix for Correlation Sequence for OFDM Systems

This paper presents an analysis of symbol timing offset (STO) estimation method for orthogonal frequency division multiplexing systems. The proposed method does not require any preamble and with the use of available cyclic prefix (CP) samples we have proposed an extended CP. The extended CP is used to exploit more number of correlation products in correlation sequence so that a more accurate starting point of any symbol can be estimated. A simplified maximum likelihood estimation process for proposed timing estimation technique is given which enables us much more accurate timing estimate due to decreased error variance. The performance of the proposed method is evaluated in terms of mean square error of timing estimator against different signal to noise ratio values and in terms of error distribution of the estimators with and without the effect of carrier frequency offset in various channel scenarios such as AWGN, HIPERLAN/2A and HIPERLAN/2E. Simulation results shows that proposed method has significantly better performance compared to the CP based method for STO estimation.     

Cramer–Rao bound and minimum variance unbiased estimator for joint sampling clock offset and channel taps in MC‐CDMA systems

Exact closed‐form expressions of the Cramer–Rao bound (CRB) for joint sampling clock offset and channel taps are obtained in multi‐carrier code division multiple access systems. CRB is undoubtedly the most well known variance's bound to determine. It provides a benchmark against which we can compare the performance of any unbiased estimator. Furthermore, minimum variance unbiased (MVU) estimator for these parameters is proposed. Moreover, maximum likelihood (ML) and least‐squares estimators for joint sampling clock offset and channel taps are presented. Best linear unbiased estimator is also introduced just for channel taps. The performances of the estimators are compared through simulation results with the proposed CRB. Our results show the better performances of MVU and ML estimators with more computational complexity compared with the others. Copyright © 2008 John Wiley & Sons, Ltd.     

Sampling Frequency Offset Estimation for Pilot-Aided OFDM Systems in Mobile Environment

In orthogonal frequency division multiplexing (OFDM) systems, most of the conventional sampling frequency offset (SFO) estimation methods work under the assumption of time-invariant or slow time-variant channels. In mobile environment, the time-variant channel significantly degrades the accuracy of SFO estimation. To solve the problem, we first analyze the properties of time-variant channels. If terminal moves within some tens of the wavelength of radio frequency (RF) signal, channel path delay almost remains unchanged. For most practical OFDM systems, our analysis indicates that channel path delay can be regarded as unchanged during the interval of some tens of OFDM symbols in time-variant channels. Based on the analysis, we propose a novel SFO estimation method for pilot-aided OFDM systems. Different from the conventional methods, the proposed method estimates SFO by detecting the variation of the symbol timing error caused by SFO. The detection is finished by implementing correlation between the channel impulse responses (CIRs) estimated by different OFDM symbols. Performance of the proposed method is simulated and compared with that of two conventional post-FFT methods. Numerical results show that, the proposed SFO estimation method performs better than the conventional methods not only in time-variant channels, but also at low SNRs and large residual carrier frequency offsets (CFOs).     

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     

超奈奎斯特信号载波频偏估计的梯度下降算法

超奈奎斯特（Faster-than-Nyquist, FTN）传输技术是一种基于时域压缩的信号调制技术，具有更高的传输速率及频带利用率，但是却引入了无限长的码间串扰（inter-symbol interferences , ISIs），这对载波频偏估计提出了新的挑战。对于FTN信号的频偏估计，传统算法在门限和精度等方面都有所下降。本文将梯度下降算法应用到载波频偏估计中，通过迭代搜索的方式，获得对频偏的精确估计。估计过程中直接通过数据部分进行估计，不需要借助额外的导频序列。仿真结果表明，梯度下降法与传统算法在性能上相比有了较好的改善，虽然具有较多的迭代次数和运算量，但是却能够较好地适应FTN信号的特性。梯度下降法不仅在门限范围内更靠近克拉美罗界（Cramer-Rao bound，CRB），而且在整个频段上具有更稳定的性能。      

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.