Blind symbol timing offset estimation for offset‐QPSK modulated signals

In this paper, a blind symbol timing offset (STO) estimation method is proposed for offset quadrature phase‐shift keying (OQPSK) modulated signals, which also works for other linearly modulated signals (LMS) such as binary‐PSK, QPSK, π/4‐QPSK, and minimum‐shift keying. There are various methods available for blind STO estimation of LMS; however, none work in the case of OQPSK modulated signals. The popular cyclic correlation method fails to estimate STO for OQPSK signals, as the offset present between the in‐phase (I) and quadrature (Q) components causes the cyclic peak to disappear at the symbol rate frequency. In the proposed method, a set of close and approximate offsets is used to compensate the offset between the I and Q components of the received OQPSK signal. The STO in the time domain is represented as a phase in the cyclic frequency domain. The STO is therefore calculated by obtaining the phase of the cyclic peak at the symbol rate frequency. The method is validated through extensive theoretical study, simulation, and testbed implementation. The proposed estimation method exhibits robust performance in the presence of unknown carrier phase offset and frequency offset.     

Design of optimal interpolation filter for symbol timing recovery

We propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog-to-digital (A-D) conversion sampling clock is not synchronized to the transmitter symbol clock. The optimal filter is designed by minimizing the mean-square error (MSE) at the output of the receiver, assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given. The MSE minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients. We also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter. Although the proposed optimal filter is designed assuming the availability of the correct timing difference, we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal, we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4. Simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter     

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.     

A Bayesian maximum-likelihood sequence estimation algorithm for apriori unknown channels and symbol timing

It is shown that the optimum demodulator for the case of an a priori unknown channel and symbol timing can be approximated using a modified Viterbi algorithm (VA), in which the branch metrics are obtained from the conditional innovations of a bank of extended Kalman filters (EKFs). Each EKF computes channel and timing estimates conditioned on one of the survivor sequences in the trellis. It is also shown that the minimum-variance channel and timing estimates can be approximated by a sum of conditional EKF estimates, weighted by the VA metrics. Simulated bit error rate (BER) results and averaged-squared channel/timing error trajectories are presented, with estimation errors compared to the Cramer-Rao lower bound. The BER performance of the modified VA is also shown to be superior to that obtained using a decision-directed channel/timing estimation algorithm     

一种零前缀OFDM系统的符号同步和载频估计算法

提出一种在零前缀正交频分复用(ZP-OFDM)系统中,估计符号定时和载波频偏的算法.算法根据ZP-OFDM系统的零前缀特性,利用双滑动窗口检测能量的分布来完成符号定时同步;同时,给出一种改进的平均法估计小数倍频率偏移.通过分析和仿真可以看出,无论是在白高斯噪声信道还是多径信道,具有一个训练符号的ZP-OFDM系统可以准确而有效的估计符号定时和频率偏差.     

High-precision symbol timing algorithm for specific emitter identification

The existing symbol timing algorithms have the problems that the method of delay estimation is improper and the calculation precision of the interpolation is insufficient for the pretreatment of specific emitter identification.A high-precision symbol timing algorithm was proposed to solve these problems.Aiming at the former problem,a two-step estimation method was adopted,rough estimation of delay was firstly obtained by the forward algorithm,and then the accurate value was acquired through local search with the demodulated symbols.For the latter problem,a window-based approach was used to design an interpolating filter which could optimize the anti-aliasing characteristics and improve the calculation accuracy.Simulation results show that the proposed algorithm can effectively solve the above problems and achieve better recognition results in the radiation source recognition compared with the conventional symbol timing algorithm.     

Blind estimation of symbol timing and carrier frequency offset inwireless OFDM systems

Orthogonal frequency-division multiplexing (OFDM) systems are highly sensitive to synchronization errors. We introduce an algorithm for the blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems. The proposed estimator is an extension of the Gini-Giannakis (see IEEE Trans. Commun., vol.46, p.400-411, 1998) estimator for single-carrier systems. It exploits the cyclostationarity of OFDM signals and relies on second-order statistics only. Our method can be applied to pulse shaping OFDM systems with arbitrary time-frequency guard regions, OFDM based on offset quadrature amplitude modulation, and biorthogonal frequency-division multiplexing systems. We furthermore propose the use of different subcarrier transmit powers (subcarrier weighting) and periodic transmitter precoding to achieve a carrier frequency acquisition range of the entire bandwidth of the OFDM signal, and a symbol timing acquisition range of arbitrary length. Finally, we provide simulation results demonstrating the performance of the new estimator     

Joint parameter estimation and symbol detection for linear ornonlinear unknown channels

We present an iterative method for joint channel parameter estimation and symbol selection via the Baum-Welch algorithm, or equivalently the Expectation-Maximization (EM) algorithm. Channel parameters, including noise variance, are estimated using a maximum likelihood criterion. The Markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward-backward algorithm. The calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability. The proposed receiver can be used for both linear and nonlinear channels. It improves the system throughput by making saving in the transmission of known symbols, usually employed for channel identification. Simulation results which show fast convergence are presented     

Joint symbol timing and channel estimation for OFDM based WLANs

The orthogonal frequency-division multiplexing access technique has been attracting considerable interest especially for wireless local area networks (WLANs). We consider the joint estimation of the symbol timing, the channel length and the channel-impulse response. A novel estimation algorithm based on maximum-likelihood principles and the generalized Akaike information criterion are proposed. We provide simulation results to illustrate the performance of our proposed algorithm     

Periodic variation method for blind symbol rate estimation

In order to obtain unknown symbol rate of incoming signal at a receiver, in this paper, cyclostationary features of linear digitally modulated signals are exploited by proposed periodic variation method. A low complexity but highly accurate symbol rate estimation technique is obtained. The proposed method is based on a superposed epoch analysis over autocorrelations obtained blindly in different sampling frequencies. The obtained autocorrelations are analyzed in the frequency domain, and it is seen that there are large oscillations when the autocorrelation is obtained around the symbol rate. Then, a superposed epoch analysis is developed in order to estimate symbol rate based of the periodic variations on the frequency responses of autocorrelations. The proposed algorithm is quite accurate in the noisy environment because the noise is having no frequency component after taking Fourier transform of autocorrelations in all sampling rates, and this feature is also valid for the offset frequency that the purposed estimation is not affected by offset frequency. Thus, a successful blind symbol rate estimation algorithm is obtained, and it performs much better error performance than those using the well‐known cyclic correlation based symbol rate estimations, as it is proven by the obtained performances presented in the paper. Copyright © 2013 John Wiley & Sons, Ltd.     

瑞利衰落信道下改进的OFDM符号定时算法

对相干OFDM系统中结合循环前缀和导频信息的传统符号定时同步算法进行了分析和研究,提出了一种改进的符号定时同步算法.此算法相对于传统算法由于更加有效的利用了观察样本信息,具有更大的定时同步范围.同时考虑时间偏移参数在若干OFDM符号区间内不变,给出了一种利用连续多个OFDM符号的算法,以提高定时同步的准确度.仿真验证了所提出算法在瑞利衰落信道下可以有效地改进传统算法的定时性能.     

OFDM数字接收机的符号定时同步算法研究与仿真

同步技术是OFDM的关键技术之一,同步实现方案优劣对OFDM性能有举足轻重的影响,而符号的时间同步偏差则会导致码间干扰(ISI).OFDM系统的符号定时同步又可以分为粗估计和细估计两个阶段.主要对基于循环前缀的符号同步粗估计及基于频域导频符号细估计算法进行了深入的研究及仿真分析.     

一种多进制连续相位调制信号的符号定时跟踪方法

针对多进制连续相位调制信号(MCPFSK)的传输系统,提出一种在相位上提取定时误差的符号定时跟踪方法,并分析定时跟踪环路的特性。根据MCPFSK信号特性,接收端将信号差分、鉴相后,利用多进制信号特性提取定时误差。Matlab仿真结果表明,在加性高斯白噪声信道上,该方法能准确地估算出定时偏差,适用于MCPFSK信号的非相干差分解调系统。     

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.     

Timing error detector design and analysis for orthogonal space-time block code receivers

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.     

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.     

大频偏低信噪比条件下OFDM系统中的符号定时估计

符号定时估计是OFDM系统中的关键问题之一,该文就此问题提出了一种新的基于训练符号的定时估计算法。研究表明,新算法的性能基本不受载波频偏的影响,且具有很强的抗噪特性。通过采用这种算法可将定时误差缩小到只有抽样时间间隔的一半。并且,还可利用这个频域训练符号来进行载波频偏的估计,从而只需一个训练符号就能完成符号定时和载波频偏的联合捕获。     

Closed-form blind symbol estimation in digital communications

We study the blind symbol estimation problem in digital communications and propose a novel algorithm by exploiting a special data structure of an oversampled system output. Unlike most equalization schemes that involve two stages-channel identification and channel equalization/symbol estimation-the proposed approach accomplishes direct symbol estimation without determining the channel characteristics. Based on a deterministic model, the new method can provide a closed-form solution to the symbol estimation using a small set of data samples, which makes it particularly suitable for wireless applications with fast changing environments. Moreover, if the symbols belong to a finite alphabet, e.g., BPSK or QPSK, our approach can be extended to handle the symbol estimation for multiple sources. Computer simulations and field RF experiments were conducted to demonstrate the performance of the proposed method. The results are compared to the Cramer-Rao lower bound of the symbol estimates derived in this paper     

Joint channel and symbol estimation by oblique projections

The problem of simultaneous blind channel and symbol estimation of a single-input multiple-output (SIMO) communication channel is considered. It is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finite sample convergence property. Furthermore, this estimator can be obtained by the use of oblique projections. An order detection algorithm that avoids the use of subjective thresholding is also proposed. Applications to multiuser detection are also considered     

一种新的SC-FDE系统粗定时同步算法

定时同步是单载波频域均衡(SC-FDE)系统的一项关键技术,其中的粗定时同步算法决定着同步收敛速度,由Schmidl和Cox提出的传统算法中出现的测度峰值平台影响着粗同步的精度与速度。通过训练符号格式的重新设计,利用其中4个相同部分良好的相关特性,提出了一种基于特殊训练符号的粗同步算法。仿真结果表明,在高斯白噪声信道和多径衰落信道条件下,新算法定时偏差估计的方差和均值接近于理论值,粗定时同步能够精确地完成,较好解决了测度峰值平台问题。