An alternative blind feedforward symbol timing estimator using two samples per symbol

Recently, S.J. Lee proposed a blind feedforward symbol timing estimator that exhibits low computational complexity and requires only two samples per symbol (see IEEE Commun. Lett., vol.6, p.205-7, 2002). We analyze Lee's estimator rigorously by exploiting efficiently the cyclostationary statistics present in the received oversampled signal; its asymptotic (large sample) bias and mean-square error (MSE) are derived in closed-form expression. A new blind feedforward timing estimator that requires only two samples per symbol and presents the same computational complexity as Lee's estimator is proposed. It is shown that the proposed new estimator is asymptotically unbiased and exhibits smaller MSE than Lee's estimator. Computer simulations are presented to illustrate the performance of the proposed new estimator with respect to Lee's estimator and existing conventional estimators.     

A new non-data-aided feedforward symbol timing estimator using twosamples per symbol

A new non-data-aided feedforward symbol timing estimator is proposed, which can apply to two samples per symbol. Numerical results show the proposed estimator is approximately unbiased. Computational complexity of the new estimator is even simpler than conventional estimators with two samples per symbol. Estimation accuracy of the new estimator is similar to that of the conventional estimator with four samples per symbol presented by Oerder and Meyr in 1988, which is the simplest among the estimators using four samples per symbol. While some conventional estimators have better estimation accuracy than the proposed, this estimator has an attractive advantage over the formers from an implementation point of view     

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.     

Analysis of a serial symbol timing recovery technique employingExclusive-OR circuit

An analysis is presented of the performance of a serial symbol timing recovery (STR) circuit which employs an Exclusive-OR circuit for conventional coherent digital modulated communication systems. The output of the timing circuit is a nearly sinusoidal wave whose zero crossings indicate the appropriate sampling instants for extraction of the data. Assuming that the data pulses entering the timing path are even symmetric, exact analytical expressions for the mean and mean-squared values of the timing wave and for the RMS phase jitter are derived as a function of various system parameters such as channel band limiting, postfiltering, delay element, and power spectral density of noise. Numerical results, also checked by computer simulations, show that considerable improvement can be obtained in jitter performance, in addition to the advantages over other STR techniques of lower cost and simpler hardware implementation     

The performance of two symbol timing recovery algorithms for PSKdemodulators

A statistical analysis of a decision-directed symbol timing algorithm for phase shift keyed modems is presented. The timing detector uses only one sample per symbol period and is suitable for high speed modems which employ discrete-time synchronization methods. Expressions for the timing detector's mean value and variance, as a function of timing offset, are derived and compared to simulation results. The analysis includes the effects of decision errors which occur at low signal-to-noise ratios and eventually limit the useful operating range of the decision-directed methods. A modification is described so that the need for prior phase recovery is avoided. These algorithms are compared to a popular two-sample-per-symbol nondecision-directed timing detector. A method of examining the relative performance of the various algorithms is presented and results are given for a range of signal-to-noise ratios and channel bandwidths     

Optimal Farrow coefficients for symbol timing recovery

The Farrow structure provides an efficient way to implement interpolation filters. Such filters are often required in digital modems to allow symbol timing recovery. A method for generating Farrow filter coefficients that minimize the mean square error (MSE) at the symbol decision instants is presented. Minimizing the MSE at the symbol decision instants is nearly equivalent to minimizing the symbol error rate (SER) but is more mathematically convenient. The MSE at times other than the symbol decision instants does not affect the SER and is not considered in the optimization. Example coefficients are tabulated and performance is illustrated using SER results generated by computer simulation     

DVB-C中可变速率符号的定时恢复

介绍了一种在DVB-C接收机中应用的基于非同步采样用内插技术实现的符号同步方法,完成了可变速率的符号同步,用Matlab实现其仿真性能,并在QAM/BPSK解调器中成功实现.     

Optimization of symbol timing recovery for QAM data demodulators

This paper describes an effective technique for the optimization of the clock recovery circuit in an all-digital modem for linearly modulated signals. Starting from the concept of prefiltering of the data signal (already pursued by these authors in the context of analog data receivers), it is shown how to design an optimum digital prefilter for the minimization of jitter due to both Gaussian and pattern noise in the closed-loop clock recovery scheme by Gardner (1986). The numerical results of the theoretical analysis, obtained after iterative resolution of a constrained-minimum problem via the Lagrange multiplier method, are checked by simulation and can be nicely justified by the consideration of the frequency response of the optimum prefilter. The key outcome of such an approach is the demonstration of a substantial performance improvement in terms of steady-state clock jitter, even with remarkably simple FIR prefilters with a small number of taps     

Iterative symbol timing recovery for short burst transmission schemes

This paper presents a novel iterative symbol timing recovery (STR) scheme for short burst transmission formats, a paradigm commonly found in modern wireless systems, like, for instance, time division multiple access (TDMA) schemes and future wireless packet data networks. Both data-aided (DA) and decision-directed (DD) solutions are considered and performance is pursued by means of an iterative burst-by-burst scheme which exploits the Farrow structure for the polynomial interpolation filter. The convergence of the algorithm is discussed according to the expectation maximization (EM) framework. Performance is evaluated by simulating 4-QAM and 16-QAM transceivers and simulations results are compared under different modulation orders and channel conditions, for both the decision-directed and data-aided cases.     

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     

New technique for timing recovery

We describe a simple, new timing recovery technique in which an antiparallel diode pair is used to detect the phase difference between a data stream and a locally generated timing wave. Our 274 Mbit/s demonstration circuit provides dependable synchronisation even when the input signal/noise ratio is only 6 dB.     

可变速率符号定时恢复在QAM解调器中的实现

随着数字通信技术的发展,不同速率业务的相继推出,传统的符号定时恢复方法已不能满足要求,提出了一种基于非同步采样,用内插技术实现的符号同步方法,完成了可变速率的符号同步,并在QAM解调器中成功实现.     

A combined code acquisition and symbol timing recovery method for TDS-OFDM

A novel timing recovery method which combines code acquisition and symbol timing recovery for TDS-OFDM (time domain synchronous OFDM) is developed. The method is based on the searching and tracking of the correlation peaks of the PN sequences embedded in the signals. Simulations show that this algorithm has very good performance for both AWGN and multipath channels, even when a small frequency offset exists in the sampling clock of the receiver.     

A modified Gardner detector for symbol timing recovery of M-PSK signals

In this letter, we propose a modified version of the Gardner detector for symbol timing recovery of M-ary phase-shift keying (M-PSK) signals. Simulation results show that the proposed modification leads to significant performance improvement when M-PSK signals are highly bandlimited and M is small. Specifically, the reduction in the level of self-noise due to the modification amounts to 10.7 dB for quaternary phase-shift keying signals with the rolloff factor of 0.25 and the normalized noise-equivalent loop bandwidth of 0.005. In terms of computational complexity involved, the proposed method has an advantage over the known self-noise reduction methods for M-PSK signals with small M.     

Low-complexity feedforward symbol timing estimator using conditional maximum-likelihood principle

A low complexity feedforward symbol-timing estimator based on the conditional maximum-likelihood principle is proposed. An approximation is applied to the Fourier series expansion of the conditional maximum-likelihood function such that implementation complexity is greatly reduced. It is shown that the proposed estimator can be viewed as a generalization of the well-known square nonlinearity estimator proposed by Oerder and Meyr in 1988. Simulation results show that the performance of the proposed estimator is very close to the conditional Cramer-Rao bound and is better than that of the square nonlinearity estimator.     

Adaptive MAPSD algorithms for symbol and timing recovery of mobileradio TDMA signals

Dual-mode adaptive algorithms with rapid convergence properties are presented for the equalization of frequency selective fading channels and the recovery of time-division multiple access (TDMA) mobile radio signals. The dual-mode structure consists of an auxiliary adaptive filter that estimates the channel during the training cycle. The converged filter weights are used to initialize a parallel bank of filters that are adapted blindly during the data cycle. When the symbol timing is known, this filter bank generates error residuals that are used to perform approximate maximum a posteriori symbol detection (MAPSD) and provide reliable decisions of the transmitted signal. For channels with timing jitter, joint estimation of the channel parameters and the symbol timing using an extended Kalman filter algorithm is proposed. Various methods are described to reduce the computational complexity of the MAP detector, usually at the cost of some performance degradation. Also, a blind MAPSD algorithm for combining signals from spatially diverse receivers is derived. This diversity MAPSD (DMAPSD) algorithm, which can be easily modified for the dual-mode TDMA application, maintains a global set of MAP metrics even while blindly tracking the individual spatial channels using local error estimates. The performance of these single-channel and diversity MAPSD dual-mode algorithms are studied via computer simulations for various channel models, including a mobile radio channel simulator for the IS-54 digital cellular TDMA standard     

Coarse recovery of carrier frequency and symbol timing in multibeam satellite channels

A multibeam concept under full frequency reuse is a major prerequisite for high throughput satellite systems. The resulting interference problems might be tackled by appropriately designed precoding or multiuser detection schemes. However, before such powerful techniques are applicable, the most important transmission parameters have to be recovered successfully. In the context of this paper, a feedback structure for joint control of carrier frequency and symbol timing is investigated for a multibeam scenario, which has been developed in some previous work by the authors for a single user link. It is to be noticed that we describe a recovery method for a multibeam satellite network with suitably selected interference mitigation techniques; as a consequence, all cochannels are assumed to be aligned in frequency and time to the reference beam; other signal models are out of scope and not addressed in this contribution.     

Frequency offset and symbol timing recovery in flat-fadingchannels: a cyclostationary approach

Two open-loop algorithms are developed for estimating jointly frequency offset and symbol timing of a linearly modulated waveform transmitted through a frequency-flat fading channel. The methods exploit the received signal's second-order cyclostationarity and, with respect to existing solutions: (1) they take into account the presence of time-selective fading effects; (2) they do not need training data; (3) they do not rely on the Gaussian assumption of the complex equivalent low-pass channel process; and (4) they are tolerant to additive stationary noise of any color or distribution. Performance analysis of the proposed methods using Monte Carlo simulations, unifications, and comparisons with existing approaches are also reported     

16QAM symbol timing recovery in the upstream transmission of DOCSIS standard

This paper investigates the performance of the digital symbol timing recovery schemes for 16QAM upstream transmission of the DOCSIS standard. Two forms of nonlinearity are considered: the magnitude square operation and the delay multiplication operation, both of which generate the output signal that contains the symbol timing information. The detailed analysis for the magnitude square timing recovery is given in the digital domain, and consequently the symbol timing estimate can be directly obtained by the discrete Fourier transform. The simulation results show that the magnitude square timing recovery and delay multiplication timing recovery algorithms suffer from the same problem that the estimation error is reduced slowly at high signal-to-noise ratios due to the effect of self-noise. To this end, the third scheme, which is the magnitude square timing recovery with prefilter, is examined. This scheme shows a superior performance and a comparison with the results of the other two schemes is made.