A fully digital noncoherent and coherent GMSK receiver architecturewith joint symbol timing error and frequency offset estimation

We propose a fully digital noncoherent and coherent Gaussian minimum shift keying (GMSK) receiver architecture with joint frequency offset compensation and symbol timing recovery. Carrier phase offset can be estimated if the coherent demodulation mode is adopted. The converted base-band complex signal is first frequency discriminated and then passed through a digital filter which performs a fast Fourier transform (FFT). The frequency offset can be estimated from the DC component of the FFT, and the symbol timing error can be estimated from the phase angle of the FFT at a specified frequency which is equal to an integral multiple of half the bit rate. These two estimated parameters are then used for frequency offset compensation and symbol timing recovery during a preamble period. Coarse carrier phase can be estimated by averaging sampled in-phase and quadrature-phase signals and finding its phase angle within the preamble period after carrier frequency offset is estimated and compensated. The bit error rate (BER) performance of this GMSK receiver architecture is assessed for an additive white Gaussian noise (AWGN) channel by computer simulation     

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     

一种用于调制识别的盲码元定时估计算法

针对通信信号调制识别中的同步分类问题提出一种盲码元定时估计算法,对于调制方式未知的信号,可以估计未知信号的定时同步,得到最佳采样点信息,实现数字信号的同步分类。仿真结果表明本文的算法对于各种信号具有良好的同步效果。     

ML-based symbol timing and frequency offset estimation for OFDM systems with noncircular transmissions

This paper deals with the problem of joint symbol timing and carrier-frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems with noncircular (NC) transmissions. Maximum-likelihood (ML) estimators of symbol timing and CFO have been derived under the assumption of nondispersive channel and by modeling the OFDM signal vector as a circular complex Gaussian random vector (C-CGRV). The Gaussian assumption is reasonable when the number of subcarriers is sufficiently large. However, if the data symbols belong to an NC constellation, the received signal vector becomes an NC-CGRV, i.e., a CGRV whose relation matrix (defined as the statistical expectation of the product between the vector and its transpose) is not identically zero. Hence, in this case, previously mentioned estimators, termed MLC estimators, are not ML estimators. In this paper, by exploiting the joint probability density function for NC-CGRVs, ML estimators are derived. Moreover, since their implementation complexity is high, feasible computational algorithms are considered. Finally, refined symbol timing estimators, apt to counteract the degrading effects of intersymbol interference (ISI) in dispersive channels, are suggested. The performance of the derived estimators is assessed via computer simulation and compared with that of MLC estimators and that of modified MLC (MMLC) estimators exploiting only ISI-free samples of the cyclic prefix.     

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     

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.     

Burst demodulation of QAM with unknown carrier phase

A new algorithm for the burst demodulation of QAM with unknown carrier phase is presented. This algorithm utilises sequence detection and the Viterbi algorithm and does not require estimation of the carrier frequency and phase. Its applications can be widely found in broadband wireless access and other systems that use burst transmission     

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     

ML estimation of symbol timing and carrier phase for CPM in Walshsignal space

An algorithm to estimate jointly the symbol timing and carrier phase for continuous-phase modulation (CPM) is described. It is designed to optimize the steady-state performance of the CPM synchronizer and exhibits excellent performance, very close to the optimum maximum-likelihood estimate. The algorithm is simple and practical and may be employed with any CPM scheme. It is based on a signal space decomposition of the CPM signal in the Walsh signal space     

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.     

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to the problem of nondata aided symbol-timing estimation for linear modulations. The study is performed under the unconditional maximum likelihood framework where the carrier-frequency error is included as a nuisance parameter in the mathematical derivation. The second-order moments of the received signal are found to be the sufficient statistics for the problem at hand and they allow the provision of a robust performance in the presence of a carrier-frequency error uncertainty. We particularly focus on the exploitation of the cyclostationary property of linear modulations. This enables us to derive simple and closed-form symbol-timing estimators which are found to be based on the well-known square timing recovery method by Oerder and Meyr. Finally, we generalize the OM method to the case of linear modulations with offset formats. In this case, the square-law nonlinearity is found to provide not only the symbol-timing but also the carrier-phase error.     

Improvement of delay spread immunity by using symbol timing synchronisation based on maximum likelihood estimation for 16 QAM/TDMA diversity receivers

Symbol timing synchronisation (STSYNC) based on maximum likelihood estimation and a receiver configuration in which each branch independently estimates optimum STSYNC timing are proposed to improve delay spread immunity for I6 QAM/TDMA diversity receivers. Computer simulation confirms that the proposed STSYNC and receiver configuration can improve delay spread immunity by approximately 30%.<>     

On the true Cramer-Rao lower bound for data-aided carrier-phase-independent frequency offset and symbol timing estimation

In this letter we present new and simple closed form expressions for the true Cramer-Rao lower bound (CRB) for data-aided (DA) joint and individual carrier frequency offset and symbol timing estimation from a linearly modulated waveform transmitted over an AWGN channel. The bounds are derived under a carrier-phase-independent (CPI) estimation strategy wherein the carrier phase is viewed as a nuisance parameter and assumed to have a worst-case noninformative uniform distribution over [-ππ]. The computation of these CRBs requires only a single numerical integration. In addition, computationally simpler yet highly accurate asymptotic lower bounds are presented. As particularizations, new bounds for individual CPI frequency estimation with known symbol timing from M-PSK and continuous wave (CW) signals are also reported.     

Multiple symbol differential detection with diversity reception

In this letter we first consider the maximum-likelihood sequence estimator for multiple symbol differential detection (MSDD) over the slow fading diversity channel. Since this optimum decision metric results in a complex receiver implementation whose average bit-error probability (BEP) performance is difficult (if not impossible) to obtain analytically, we then focus our attention on evaluating the average BEP for MSDD with diversity reception in the form of postdetection equal-gain combining (EGC) giving emphasis to its ability to bridge the gap between EGC of conventional differentially detected M-PSK and maximal-ratio combining of coherently detected M-PSK with differential encoding     

自适应QAM解调及频偏估计方法研究

提出了一种新型的基于自适应滤波的QAM解调算法和频偏估计方法.以最小均方误差自适应算法(LMS)为例,讨论了采用本解调算法解调的过程及其性能.本解调算法无需自适应滤波器完成收敛,从而降低了对采样频率和处理速度的要求.仿真结果表明:本解调算法的误码率理论值与仿真结果一致性好.同时,基于本解调算法的频偏估计,能方便地给出频偏大小.     

A combined timing and frequency synchronization and channel estimation for OFDM

This letter addresses training-signal-based combined timing and frequency synchronization and channel estimation for orthogonal frequency-division multiplexing systems. The proposed scheme consists of two stages. At the first stage, coarse timing and frequency-offset estimates are obtained. Based on these estimates, a (coarse) channel response estimate is obtained. The timing and frequency-offset estimates at the second stage are obtained by maximum-likelihood (ML) realization based on a sliding observation vector. Then ML channel estimation is performed. A means of complexity reduction by an adaptive scheme is also presented. The simulation results show that the proposed combined approach performs quite well, and circumvents the problem of mismatch among individual synchronization tasks.     

Bit error rate floors in coherent optical systems with delay demodulation

Reports the results of an accurate analysis of the effect of filtering on phase noise, appropriate to coherent optical receivers with delay demodulation. Based on a numerical solution of a Fokker-Planck equation, the authors show that the phase at the output of the IF filter is very closely a Gaussian random process. The variance of phase fluctuations over a time equal to the integration time of the filter is reduced by a factor of 0.363. They show that receivers with minimum IF bandwidth can therefore operate with about 1.36 times the laser linewidth predicted disregarding the filtering effect. They outline a route to analysing the performance of receivers with broader than optimum IF filters.<>     

Bounds on bearing and symbol estimation with side information

We develop Cramer-Rao bounds (CRBs) for bearing, symbol, and channel estimation of communications signals in flat-fading channels. We do this using the constrained CRB formulation of German and Hero (1990), and Stoica and Ng (see IEEE Signal Processing Lett., vol.5, p.177-79, 1998), with the unknown parameters treated as deterministic constants. The equality constraints may be combined arbitrarily, e.g., we may develop CRBs for bearing estimation of constant modulus (CM) signals where a subset of the symbols are known (semi-blind, CM case). The results establish the value of side information in a large variety of communications scenarios. We focus on the CM and semi-blind properties and develop closed-form CRBs for these cases. Examples are presented indicating the relative value of the training and CIM property. These show the significant amount of signal processing information provided under these two conditions. In addition, we consider the performance of the maximum-likelihood beamformer for the semi-blind case, assuming the bearings are known. This semi-blind beamformer achieves the appropriate (constrained) CRB with finite data at finite SNR. Analysis also reveals that in a semi-blind scenario with two closely spaced sources, ten or more training symbols are sufficient to achieve the asymptotic training regime. Together with previous results on angle estimation for known sources, these results indicate that relatively few training samples enable both angle estimation and closely spaced co-channel source separation that approaches the CRB with finite data and finite SNR     

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.     

Performance analysis of OFDMA uplink systems with symbol timing misalignment

This letter presents our investigation for the effect of symbol timing errors in orthogonal frequency-division multiple access (OFDMA) uplink systems. We express the symbol timing errors between users as the symbol timing misalignments with respect to the desired user. Then, we derive an explicit expression of the signal-to-noise ratio (SNR) as a function of the maximum value of the symbol timing misalignments. Analyses and simulation results show that, to achieve an SNR of 20 dB, the maximum value of the symbol timing misalignments must be less than the cyclic prefix duration plus 6.25% of the useful symbol duration. Based on the resulting SNR degradation, we evaluate the SNR gain with guard subcarriers in order to mitigate the effect of the symbol timing misalignments.