True Cramer-Rao bound for timing recovery from a bandlimited linearly Modulated waveform with unknown carrier phase and frequency

This paper derives the Cramer-Rao bound (CRB) related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency. We consider the following two scenarios: joint estimation of the time delay, the carrier phase, and the carrier frequency; and joint estimation of the time delay and the carrier frequency irrespective of the carrier phase. The transmit pulse is a bandlimited square-root Nyquist pulse. For each scenario, the transmitted symbols constitute either an a priori known training sequence or an unknown random data sequence. In spite of the presence of random data symbols and/or a random carrier phase, we obtain a relatively simple expression of the CRB, from which the effect of the constellation and the transmit pulse are easily derived. We show that the penalty resulting from estimating the time delay irrespective of the carrier phase decreases with increasing observation interval. However, the penalty, caused by not knowing the data symbols a priori, cannot be reduced by increasing the observation interval. Comparison of the true CRB to existing symbol synchronizer performance reveals that decision-directed timing recovery is close to optimum for moderate-to-large signal-to-noise ratios.     

基于约束最小二乘的纯方位多站被动跟踪算法

纯方位单站目标被动跟踪需要观测站作机动才能满足可观测条件,导致跟踪算法收敛时间较长。基于纯方位多站被动跟踪算法可以解决算法收敛时间较长的问题,文中提出了一种约束最小二乘算法用于纯方位多站被动跟踪,它首先为最小二乘算法引入约束条件,利用矩阵最小特征值所对应的特征向量,解决了EKF 算法需要初值的问题,避免了滤波的发散,同时也极大地减小了最小二乘估计的偏置。仿真表明,这种算法能够渐进地逼近估计误差的下限,并且其精度有所增加,是一种渐进、稳定以及近似无偏的估计算法。     

频率失配条件的自适应相位差无偏估计方法及性能分析

针对频率失配条件下受噪声影响导致相位差估计精度不高的问题,提出一种频率失配的自适应相位差无偏估计方法,提升相位差估计的精确性和抗噪性.为此,首先通过对两路正弦信号的展开式参数进行自适应估计,利用展开式参数估计值实时计算两路正弦信号的相位差;其次,利用泰勒级数展开式对相位差估计方法进行了估计偏差分析,证明了频率失配条件下所提相位差估计方法的无偏性,并给出了相位差估计方法的稳态性能;最后,给出了不同方法的相位差估计结果,并讨论了各参数对相位差估计的影响,计算结果表明所提方法的有效性与正确性.     

Carrier phase and frequency estimation for pilot-symbol assisted transmission: bounds and algorithms

In this paper we consider the Cramer-Rao lower bound (CRB) for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols (DSs) as well as known pilot symbols (PSs). We point out that the CRB depends on the location of the PSs in the burst, the number of PSs, the number of DSs, the signal-to-noise ratio (SNR), and the data modulation scheme. Distributing the PSs symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation, making the CRB for phase estimation independent of the specific location of the PSs. At low and moderate SNR, the CRBs for both phase and frequency estimation decrease as the fraction of the PSs in the burst increases. In addition, the CRB for frequency estimation decreases as the PSs are separated with more DSs. Numerical evaluation of the CRB indicates that the carrier phase and frequency of a "hybrid" burst (i.e., containing PSs and DSs) can be estimated more accurately when exploiting both the presence of the DSs and the a priori knowledge about the PSs, instead of using only the knowledge about the PSs (and ignoring the DSs), or considering all the received symbols (PSs and DSs) as unknown (and ignoring the knowledge about the PSs). Comparison of the CRB with the performance of existing carrier synchronizers shows that the iterative soft-decision-directed (sDD) estimator with data-aided (DA) initialization performs very closely to the CRB and provides a large improvement over the classical non-data-aided (NDA) estimator at lower SNR.     

Digital frequency estimation in burst mode QPSK transmission

In burst digital transmission using PSK (phase shift keying) modulation with coherent detection, the recovery of the carrier reference phase and the symbol clock is a key aspect. If all users have a common clock synchronization, symbol timing needs not to be recovered in each burst. A digital processor for carrier recovery without preambles, in the presence of frequency offset, is considered. As an example, a 2 Mb/s QPSK transmission system is considered in which E _b/N_o=10 dB, and the burst and estimation interval length L=15. Using the algorithm described and averaging eight successive estimated frequency offsets, in order to eliminate anomalous errors, the BER (bit error rate) degradation is equal to 0.14 dB when Δf=20 kHz     

频率无偏估计的有限冲激响应自适应陷波器方法研究

针对现有自适应陷波器频率估计方法结构复杂、抗噪性弱、结果有偏的问题,提出频率无偏估计的有限冲激响应自适应陷波器方法.该方法首先以结构较为简单的FIR自适应陷波器为基础,在分析其误差函数性能的基础上,提出频率估计的迭代递推计算式,提升频率估计的收敛性能;其次,对该频率估计迭代递推计算式进行偏差分析,在分析出偏差产生的原因...     

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.     

高速突发解调器的快速同步技术研究

突发通信中需重点考虑同步时间,提出了一种突发解调器方案,具有同步时间快、传输速率高的优点。重点介绍了符号定时和载波相位恢复,分析了定时估计算法和内插定时恢复中的关键点;分析了载波相位估计算法并结合工程实现提出了简化算法,分析了剩余载波频偏和相位估计时间的关系。Matlab定点仿真结果表明了该方案的可行性和有效性,最后根据提出的方案实现了90Mbps QPSK突发调制解调器。     

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     

Symbol Timing Recovery Algorithms and Their Evaluation for Burst Communication

This paper reviews and presents the simulationresults on the performance of four alternative symboltiming offset estimation algorithms for burst modecommunication. Two basically different approaches are taken to the problem. The first approach isbased on the concept of maximum likelihood estimation,of which two basic varieties are derived and evaluated.These are referred to as the data-driven and the non-data-driven versions. In thedata-driven mode, either the decision symbols from theoutput of the demodulator or a number of known referencesymbols may be used to drive the algorithm. The maximum likelihood algorithms generate an error signalthat can be used in a closed-loop control system toadjust the phase of the sampling clock to the optimumsymbol sampling instant. The second approach uses the basic signal processing technique of tonefiltering using effectively the discrete Fouriertransform. The tone filtering approach results in thedirect estimation of the optimum symbol sampling phase and hence is more of an open-loop approach. Thesimulation results indicate that excellent performanceis achieved with this kind of open-loop approach, evenat low signal to noise ratios and in the presence of some frequency offset as long as the symboltiming offset does not exceed 90% from its optimumpoint. It is also shown that by choosing the propersampling rate, this algorithm results in a simple IIR filtering implementation with one pole that isvery efficient from a processing point ofview.     

The true Cramer-Rao bound for carrier frequency estimation from a PSK signal

This paper considers the Cramer-Rao bound (CRB) related to estimating the carrier frequency of a noisy phase-shift keying signal. The following scenarios are discussed: 1) carrier frequency estimation irrespective of the carrier phase, based on either known or random data and 2) joint carrier phase and frequency estimation, based on either known or random data. Ideal symbol timing is assumed. We compare the results obtained from a (commonly used) simplified observation model against those resulting from the correct model. Because of the presence of nuisance parameters (random data and/or random carrier phase), the analytical computation of the corresponding CRBs is often not feasible. Here we present results that are based upon a combined analytical/numerical approach. Our results show that the choice of the observation model has essentially no effect on the CRBs at moderate and high signal-to-noise ratios. We also show that of the two scenarios considered, joint frequency and phase estimation yields the smaller CRB; the penalty resulting from frequency estimation, irrespective of the carrier phase, decreases with increasing observation interval.     

Sequence Design for Data-Aided Estimation of Synchronization Parameters

In this letter, we propose a systematic technique for optimum data-sequence design for data-aided (DA) estimation of synchronization parameters. It is assumed that the system operates in burst mode, transmitting a linearly modulated information signal over an additive white Gaussian noise channel. The method is based on the minimization of the corresponding Crameacuter-Rao lower bound subject to a power constraint and is applied in four practical receiver synchronization contexts: estimation of the symbol timing with known carrier frequency offset and either known or unknown carrier phase, joint estimation of the symbol timing and carrier phase with known carrier frequency offset, and joint estimation of the carrier phase and carrier frequency offset with known symbol timing     

相位编码信号的自适应接收回波处理

首先建立了匹配滤波器输出随多普勒频移的变化规律模型。分析得出通过缩短匹配滤波器长度,可减小多普勒频移对压缩输出的影响,采用一组部分相关匹配滤波器对接收回波处理,估计出回波中的多普勒频率,避免了传统方法的计算量大、结构复杂难以实现等缺陷。方法结构简单,能以较高精度对回波中的多普勒频率作出估计,有利于相位编码信号在快速动目标观测方面的应用。     

基于小波-卡尔曼的语音增强方法研究

提出了一种基于小波变换和卡尔曼滤波相结合的语音增强方法,这样既保留了小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,可以有效地减小非平稳噪声;并引入基于声学模型的感知滤波器,以提高语音信号的可懂度。实验证明该方法对于低信噪比的有色噪声干扰条件下的语音信号的增强效果要优于一般的语音增强系统。     

Performance evaluation of a carrier recovery scheme for satellite TDMA symbol synchronous burst transmissions

This paper presents and evaluates the performance of an open-loop scheme for carrier-phase estimation with Doppler compensation which independently operates on each TDMA burst without requiring any training sequences. The approach is based on two known open-loop algorithms independently used for phase and frequency error estimation. The paper shows how to properly interface these two algorithms and how they can be extended also to include Doppler rate estimation. Copyright © 1999 John Wiley & Sons, Ltd.     

含状态等式约束的分布式估计融合

在假设各传感器间观测噪声不相关的基础上,将最优线性无偏估计意义下的分布式最优估计融合公式推广至含状态等式约束的分布式估计融合问题中,并在此约束条件下,先将该约束系统直接转换为投影系统,再利用投影系统中的Kalman滤波估计,分别讨论了两种信息融合方式:中心式与分布式融合。进一步地指出中心式估计融合优于分布式估计融合,并在分布式融合结构下,得到了约束的Kalman滤波估计优于投影的Kalman滤波估计的结论。通过数值模拟论证了两种融合方式下的性能差异。     

Method for design of allpass filters

A new method for allpass filter design is presented. The method leads to a solution for the phase that is equal to the desired phase for 2N+1 values of frequency (if N is the order of the allpass filter). These values can be chosen at will in the approximation interval. The resulting phase error therefore displays a ripple behaviour. The solutions obtained in this way could be used as an initial solution for an exchange algorithm in order to produce an equiripple solution     

自适应陷波滤波器频率估计新方法及性能分析

现有的自适应陷波滤波器（ANF）受误差函数所限,导致其自适应频率估计方法收敛速度较慢,对初始迭代频率值设定范围要求较高,特别针对频率接近于0或π的信号,还存在频率估计精度不高、算法稳定性差的问题,为此,提出一种ANF频率估计新方法.首先,分析现有ANF方法估计信号频率时存在精度低、速度慢、稳定性差的原因,提出一种新误差函数以提升ANF收敛速度;然后,根据ANF估计信号频率时偏差产生的机理,通过偏差补偿方式,降低噪声对ANF的影响,以获得近似无偏的频率估计结果,提高ANF频率估计精度,同时与离散卡尔曼滤波相结合,以改善算法的稳定性,并对该方法进行稳态条件下的性能分析;最后,给出了ANF频率估计结果,并讨论了ANF各参数对频率估计精度的影响,给出了具体计算结果.计算表明本文方法的有效性与正确性.     

双站基于角度和时差的近似无偏定位算法

联合角度（DOA）和时差（TDOA）信息对运动目标进行无源定位实质上是一种非线性估计问题。针对将非线性观测方程转化为伪线性方程会产生有偏估计的缺点,该文基于双站定位中获得的角度和时差信息,给出了一种对三维空间目标定位跟踪的近似无偏估计滤波算法,它只需要对一对矩阵束进行广义特征分解,即可获得目标坐标和速度的估计值。计算机仿真结果表明,相比有偏估计滤波算法,如伪线性卡尔曼滤波（PLKF）算法或者最小二乘（LS）算法,该算法具有更高的定位精度,并且当观测误差增大时,其优势更加明显。     

Characterization of threshold for single tone maximum likelihoodfrequency estimation

This paper presents a simple and direct approach to understanding the threshold effect associated with maximum likelihood estimation of the frequency of a single complex tone. Motivation for the approach, stemming from known results in the field of phase locked loops, is given. It is shown both theoretically and experimentally that the onset of threshold can be directly characterized by a single, easily computed parameter, namely the Cramer-Rao bound on the phase estimation error variance