Joint Frequency and Symbol Synchronization Schemes for an OFDM System

This paper proposes two multi-stage joint symbol timing and carrier frequency synchronization schemes for an orthogonal frequency division multiplex (OFDM) system. Simultaneous estimation of symbol timing and frequency offset is derived from the maximum likelihood (ML) principle, assuming a cyclic prefix (guard interval) is inserted in each OFDM symbol. One of the proposed algorithms derives an initial frequency estimate in the first stage that reduces the frequency uncertainty to only two or three sub-carrier spacings. The timing information and a finer frequency estimate that has a resolution of a sub-carrier spacing are obtained in the second stage. The third stage provides an estimation for the residual fractional frequency error. The other algorithm bypasses the first stage for one can use the second stage alone to search for the timing and frequency offsets. However, the computing complexity of the second stage is higher than that of the first stage, thus the three-stage algorithm is a preferred choice unless the frequency uncertainty is small. Simulation results show that both algorithms yield excellent performance not only in white Gaussian channels but also in multipath fading channels.     

Timing recovery for OFDM transmission

Orthogonal frequency division multiplexing (OFDM) is an effective modulation technique for high-rate and high-speed transmission over frequency selective fading channels. However, OFDM systems can be extremely sensitive and vulnerable to synchronization errors. In this paper, we present a scheme for performing timing recovery that includes symbol synchronization and sampling clock synchronization in OFDM systems. The scheme is based on pilot subcarriers. In the scheme, we use a path time delay estimation method to improve the accuracy of the correlation-based symbol synchronization methods, and use a delay-locked loop (DLL) to do the sampling clock synchronization. It is shown that by using this scheme, the mean square values of the symbol timing estimation error can be decreased by several orders of magnitude compared to the common correlation methods in both the AWGN and multipath fading channels. In addition, the scheme can track the symbol timing drift caused by the sampling clock frequency offsets     

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.     

采样时钟偏差对OFDM系统性能的影响

针对采样时钟同步偏差对正交频分复用（Orthogonal Frequency Division Multiplexing，OFDM）系统的影响，建立了数学模型，分别就采样定时偏差和采样频率偏差的影响进行详细分析；经过仿真，从星座图、误码率（Bit—Error—Rate，BER）及信噪比（Signal—to—Noise Ratio，SNR）损失等角度对采样频率偏差的影响做了揭示和验证。结果表明，采样频率偏差会引起信号幅度衰减和子载波间干扰（Inter—Carrier Interference，ICI），导致系统信噪比性能下降；这种影响与子载波位置有关，还会随着OFDM符号数的增多而加剧。     

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.     

Timing and frequency synchronization for the uplink of an OFDMA system

This paper deals with timing and frequency recovery for the uplink of an orthogonal frequency-division multiple access (OFDMA) system. The frequency estimator is derived from ad hoc reasoning, whereas the timing estimator is based on the maximum-likelihood criterion. Both schemes rely on the repetition of a fixed pilot symbol. Their main feature is that they provide feedforward estimates and allow synchronization in only two OFDM blocks. In contrast to other existing methods, they do not require that the subcarriers of a given user occupy adjacent positions in the signal bandwidth. This makes it possible to interleave subcarriers of different users so as to optimally exploit the frequency diversity of the channel. Theoretical analysis and computer simulations are used to assess the performance of the proposed synchronizers. It is found that the degradations due to residual frequency and timing errors are negligible at signal-to-noise ratios of practical interest.     

Residual Synchronization Error Elimination in OFDM Baseband Receivers

It is well known that an OFDM receiver is vulnerable to synchronization errors. Despite fine estimations used in the initial acquisition, there are still residual synchronization errors. Though these errors are very small, they severely degrade the bit error rate (BER) performance. In this paper, we propose a residual error elimination scheme for the digital OFDM baseband receiver aiming to improve the overall BER performance. Three improvements on existing schemes are made: a pilot‐aided recursive algorithm for joint estimation of the residual carrier frequency and sampling time offsets; a delay‐based timing error correction technique, which smoothly adjusts the incoming data stream without resampling disturbance; and a decision‐directed channel gain update algorithm based on recursive least‐squares criterion, which offers faster convergence and smaller error than the least‐mean‐squares algorithms. Simulation results show that the proposed scheme works well in the multipath channel, and its performance is close to that of an OFDM system with perfect synchronization parameters.     

Robust frequency and timing synchronization for OFDM

A rapid synchronization method is presented for an orthogonal frequency-division multiplexing (OFDM) system using either a continuous transmission or a burst operation over a frequency-selective channel. The presence of a signal can be detected upon the receipt of just one training sequence of two symbols. The start of the frame and the beginning of the symbol can be found, and carrier frequency offsets of many subchannels spacings can be corrected. The algorithms operate near the Cramer-Rao lower bound for the variance of the frequency offset estimate, and the inherent averaging over many subcarriers allows acquisition at very low signal-to-noise ratios (SNRs)     

Theoretical analysis of ICI self-cancellation in OFDM systems over Rayleigh flat-fading channels

Orthogonal frequency division multiplexing (OFDM) has been widely used for its robustness against multipath fading and low-complexity implementation. However, OFDM system, especially with large number of subcarriers and high modulation order, is severely affected by the phase noise of oscillators and carrier frequency offset (CFO). On the other hand, self-cancellation schemes have received a lot of attention due to their simple implementation and high efficiency to suppress inter-carrier interference (ICI) in OFDM systems. Among those ICI self-cancellation methods, symmetric conjugate symbol repetition (SCSR) has been proven to have the best bit error ratio (BER) performance for phase noise suppression. In this paper, the performance of OFDM systems with SCSR ICI self-cancellation in the presence of both phase noise (PHN) and CFO are investigated, and analytical expressions are derived to calculate error probability evaluated by symbol error ratio (SER) over additive white Gaussian noise (AWGN) and Rayleigh flat fading channels. An approach of second order approximation of PHN/CFO has been performed to estimate the residual ICI, which could provide more accurate results. Simulation results show perfect agreement with those obtained by theoretical analysis, which could be used to estimate OFDM system error probability, facilitating the design of the overall system.     

A novel non-data-aided symbol timing recovery technique for OFDM systems

A new highly efficient non-data-aided technique to recover symbol timing of orthogonal frequency-division multiplexing systems is proposed. The algorithm in the proposed work exploits the interference that results due to the loss of orthogonality between subcarriers, where the second-order statistics of the resulting interference is proportional to the offset from the optimum sampling point. The presented technique does not require prior fine carrier synchronization, and it is capable of extracting symbol timing at low E/sub s//N/sub 0/ values with large carrier frequency offsets (CFOs). The system performance was investigated in multipath fading channels with large CFOs and additive white Gaussian noise.     

Joint optimization of time and frequency synchronization based on polynomial sequences for OFDM systems

In orthogonal frequency division multiplexing (OFDM) systems, time and frequency synchronization are two critical elements for guaranteeing the orthogonality of OFDM subcarriers. Conventionally, with the employment of pseudo-noise (PN) sequences in preamble design, the preamble information is not fully utilized in both symbol timing offset acquisition and carrier frequency offset estimation. In this article, a new synchronization algorithm is proposed for jointly optimizing the time and frequency synchronization. This algorithm uses polynomial sequences as synchronization preamble instead of PN sequences. Theoretical analysis and simulation results indicate that the proposed algorithm is much more accurate and reliable than other existing methods.     

一种基于循环前缀的OFDM时频同步新算法

OFDM符号是由多个子载波信号叠加而成,为确保各子载波之间的正交性,就对载波间的同步有很严格的要求,否则将造成信道间干扰和符号间干扰,严重影响OFDM系统的性能。提出一种新的基于循环前缀的OFDM时频同步算法,通过仿真,将新算法和传统的ML算法及集相关算法相比较。仿真结果表明,新算法定时捕获更快,且能更准确地确定无IBI干扰的循环前缀采样部分,具有更好的频偏和定时估计性能。     

MIMO OFDM系统中同步和信道的联合估计

提出了一种MIMO OFDM系统的定时恢复、频率同步和信道估计的联合算法。为了减少算法的复杂度，算法分两步完成：首先利用接收信号的自相关函数进行粗同步和信道估计，得到时延和频偏的粗估计，然后在粗估计基础上采用最大似然准则进行精确的同步和信道估计。仿真结果表明，该算法能够达到很好的效果，系统误码率接近已知信道响应时的情况。     

非数据辅助的OFDM系统符号同步算法

该文中研究了OFDM系统中的非数据辅助符号同步问题。首先,假设OFDM相邻子载波信道的频域响应相同,建立了一种基于OFDM系统相邻子载波间功率差值平方的代价函数,通过对代价函数最小化得到了一种适用于基带调制为恒幅调制的OFDM系统的非数据辅助符号同步算法。然后,通过对信道进一步假设,得到了其它两种类似的代价函数,并对载波频偏及信道噪声对算法的影响和算法的运算量进行了分析和讨论。最后,通过计算机仿真对所得同步算法在不同代价函数及不同载波频偏时的性能进行了分析,并同其它两种已有同类算法进行了比较。仿真结果表明,所得算法的性能总体上优于其它两种已有同类算法。     

Interaction between Symbol Timing Offset and Channel Interpolation in OFDM Systems: BER Analysis and Performance Degradation

In orthogonal frequency division multiplexing (OFDM) systems, since the cyclic prefix (CP) is designed to be longer than the channel impulse response, there exists a certain range within the CP where symbol timing synchronization can be accomplished avoiding adjacent inter symbol interference. However, the appearance of a linear phase term across subcarriers in the frequency-domain due to symbol timing offset (STO) is known to affect the performance of channel interpolation. In this paper, we analyze the performance degradation due to the interaction between STO and channel interpolation in OFDM systems affected by multipath Rayleigh fading. Particularly, simple closed-form expressions for the bit error rate (BER) are obtained for different quadrature amplitude modulation constellations. Results show that there exists an irreducible BER floor due to STO and channel interpolation, which depends on the STO, the subcarrier index, the pilot spacing and the correlation between pilot subcarriers.     

一种无需导频的适用于差分OFDM系统的符号与采样钟联合同步方法

该文提出了一种适用于OFDM系统的联合符号和采样钟同步校正方法,其中同步校正是在数字域通过改变对接收过采样信号的插值(interpolation)和抽取(decimation)实现的。这种方法在发送端相邻载波间采用差分QPSK调制,在接收端利用QPSK的差分解调信号获得同步误差信号,从而获得关于OFDM符号同步和采样钟同步调整的算法,其特点是无需专门的同步导频信号。所提出算法的同步性能在高斯白噪声信道和多径衰落信道均得到验证。     

A general SER formula for an OFDM system with MDPSK in frequency domain over Rayleigh fading channels

A closed-form formula for symbol-error rate (SER) of an orthogonal frequency-division multiplexing (OFDM) system with M-ary differential phase-shift keying (MDPSK) in frequency domain over Rayleigh fading channels is obtained. It is found that, by MDPSK in frequency domain, identical SERs can be achieved on all subcarriers. However, both time and frequency dispersion in the channel will introduce error floors. A comparison between OFDM-MDPSK in frequency domain and that in time domain reveals that the former system offers superior SER performance in a fast fading environment, while the latter performs better if the channel is mainly frequency selective. Moreover, the former system has lower implementation complexity.     

Joint Synchronization and Channel Estimation for OFDM Systems

1Introduction Orthogonal Frequency Division Multiplexing(OFDM) has become a popular technique for transmis-sion of signals over wireless channels . OFDMhas beenadoptedinseveral wireless standards such as Digital Au-dio Broadcasting ( DAB) , Digital Video Broadcasting(DVB-T) ,the IEEE 802 .11a[1]Local Area Network(LAN) standard and high performance LAN type 2(HIPERLAN/2)[2]standard. OFDMis also being pur-sued for Dedicated Short-Range Communications(DSRC) for road side to …     

A Data-Aided Symbol Timing and Frequency Offset Estimation Algorithm for OFDM Systems

In this paper the problem of data-aided symbol timing and frequency offset estimation in OFDM systems is considered. A synchronization scheme based on a pilot symbol containing two identical parts obtained by transmitting BPSK data symbols on the even subcarriers and setting zero on the remaining subcarriers is proposed. In this case, if the number of subcarriers is sufficiently large, the pilot symbol can be modeled as a noncircular (NC) complex Gaussian random vector (CGRV). By exploiting the joint probability density function of NC-CGRVs, the joint maximum likelihood estimator for the parameters of interest is derived. Since its implementation complexity is high, a simpler synchronization scheme is obtained. Moreover, refined symbol timing and frequency offset estimators, that assure relevant performance in multipath channels, are proposed. T. Fusco was born in Naples, Italy, on March 22, 1977. She received the Dr. Eng. degree (summa cum laude) in electronic engineering from the Second University of Napoli in 2002. Since November 2002 she has been a Ph.D. student at the Department of Electronic and Telecommunication Engineering of the University of Napoli Federico II. Her current research and study interests lie in the area of statistical signal processing, with emphasis on parameter estimation problems in the context of OFDM communications. M. Tanda was born in Aversa, Italy, on July 15, 1963. He received the Dr. Eng. degree (summa cum laude) in electronic engineering in 1987 and the Ph.D. degree in electronic and computer engineering in 1992, both from the University of Napoli Federico II. Since 1995, he has been an Appointed Professor of Signal Theory an the University of Napoli Fe-de-ri-co II. Moreover, he has been an Appointed Professor of Electrical Communications (from 1996 until 1997) and Telecommunication Systems (from 1997) at the Second University of Napoli. He is currently Associate Professor of Signal Theory at the University of Napoli Federico II. His research activity is in the area of signal detection and estimation, multicarrier, and multiple access communication systems.     

Intercarrier interference self-cancellation scheme for OFDM mobilecommunication systems

For orthogonal frequency-division multiplexing (OFDM) communication systems, the frequency offsets in mobile radio channels distort the orthogonality between subcarriers resulting in intercarrier interference (ICI). This paper studies an efficient ICI cancellation method termed ICI self-cancellation scheme. The scheme works in two very simple steps. At the transmitter side, one data symbol is modulated onto a group of adjacent subcarriers with a group of weighting coefficients. The weighting coefficients are designed so that the ICI caused by the channel frequency errors can be minimized. At the receiver side, by linearly combining the received signals on these subcarriers with proposed coefficients, the residual ICI contained in the received signals can then be further reduced. The carrier-to-interference power ratio (CIR) can be increased by 15 and 30 dB when the group size is two or three, respectively, for a channel with a constant frequency offset. Although the redundant modulation causes a reduction in bandwidth efficiency, it can be compensated, for example, by using larger signal alphabet sizes. Simulations show that OFDM systems using the proposed ICI self-cancellation scheme perform much better than standard systems while having the same bandwidth efficiency in multipath mobile radio channels with large Doppler frequencies