The joint estimation of differential delay, Doppler, and phase (Corresp.)

In radio and sonar applications it sometimes happens that narrow-band signals, originated from a remote source and observed at a pair of receivers, differ by unknown differential phase and Doppler shift in addition to the differential delay corresponding to the range difference. The correspondence presents the joint maximum likelihood (ML) estimate of the differential delay, Doppler, and phase and examines their accuracy by deriving the Cramér-Rao bound. It is shown that the joint ML estimators are the values of the delay and Doppler that maximize the magnitude of a generalized ambiguity function analogous to the one used in radar. It is also shown that for long observation time and high enough signal-to-noise ratio there is no degradation in the accuracy of the time-delay estimator due to the additional phase and Doppler uncertainty and that the differential Doppler is uncorrelated with the differential delay and phase estimators.     

Analysis of the variance threshold of Kay's weighted linearpredictor frequency estimator

A theoretical approximation for the variance of Kay's weighted linear predictor frequency estimator is derived. From this expression, an inequality describing the variance threshold of the estimator is found. The window weights are then optimized to improve the variance. Numerical simulations demonstrate that the variance approximations are valid for medium to high signal-to-noise ratios or for large numbers of samples     

Subspace-based noise variance and SNR estimation for MIMO OFDM systems

This paper proposes a subspace-based noise variance and Signal-to-Noise Ratio （SNR） estimation algorithm for Multi-Input Multi-Output （MIMO） wireless Orthogonal Frequency Division Multiplexing （OFDM） systems. The special training sequences with the property of orthogonality and phase shift orthogonality are used in pilot tones to obtain the estimated channel correlation matrix. Partitioning the observation space into a delay subspace and a noise subspace, we achieve the measurement of noise variance and SNR. Simulation results show that the proposed estimator can obtain accurate and real-time measurements of the noise variance and SNR for various multipath fading channels, demonstrating its strong robustness against different channels.     

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.     

Improved Single‐Tone Frequency Estimation by Averaging and Weighted Linear Prediction

This paper addresses estimating the frequency of a cisoid in the presence of white Gaussian noise, which has numerous applications in communications, radar, sonar, and instrumentation and measurement. Due to the nonlinear nature of the frequency estimation problem, there is threshold effect, that is, large error estimates or outliers will occur at sufficiently low signal‐to‐noise ratio (SNR) conditions. Utilizing the ideas of averaging to increase SNR and weighted linear prediction, an optimal frequency estimator with smaller threshold SNR is developed. Computer simulations are included to compare its mean square error performance with that of the maximum likelihood (ML) estimator, improved weighted phase averager, generalized weighted linear predictor, and single weighted sample correlator as well as Cramér‐Rao lower bound. In particular, with smaller computational requirement, the proposed estimator can achieve the same threshold and estimation performance of the ML method.     

Passive time delay estimation in non-Gaussian noise

This article deals with the structure of the maximum-likelihood (ML) estimator for time delay with arbitrary signal and noise statistics. At high signal-to-noise ratios (SNRs), the ML estimation performs a nonlinear operation on the delayed difference of the two received waveshapes. The required nonlinearity depends only on the noise statistics. At low SNR, a closed-form simple expression for the ML, which depends only on the noise statistics and on the second-order statistics of the signal, is provided. With statistically independent noise processes, the estimator correlates two vectors generated by separate nonlinear operations on the two received waveshapes     

On Clock Synchronization Algorithms for Wireless Sensor Networks Under Unknown Delay

In this paper, three clock-synchronization algorithms for wireless sensor networks (WSNs) under unknown delay are derived. They include the maximum-likelihood estimator (MLE), a generalization of the estimator of Noh , and a novel low-complexity estimator. Their corresponding performance bounds are derived and compared, and complexities are also analyzed. It is found that the MLE achieves the best performance with the price of high complexity. For the generalized version of the estimator of Noh , although it has low complexity, its performance is degraded with respect to the MLE. On the other hand, the newly proposed estimator achieves the same performance as the MLE, and the complexity is at the same level as that of the generalized version of the estimator of Noh      

Approximate maximum likelihood estimators for array processing inmultiplicative noise environments

We consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise. This scenario is encountered, for example, in communications, owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to-noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML₁) estimator is derived. The performance of the AML₁ estimator in the presence of additive noise is studied, and a theoretical expression for its asymptotic variance is derived. Its performance is shown to be close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered, and the corresponding AML₂ solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to both the multiplicative and additive noise powers, leaving out a two-dimensional (2-D) minimization problem instead of a four-dimensional (4-D) problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis     

Multichannel Time-Delay and Signal Model Estimation with Missing Observations

In this paper, we propose a maximum likelihood (ML) estimator in the frequency domain for estimating multichannel time delay and parameters with missing observations. The missing observations are described by a random Bernoulli pattern. In this context, the ML estimator for missing observations is highly sensitive to the initial conditions and complexity of a given problem. In conventional calculations, the complexity of problems will often make it difficult to obtain the optimal results. Thus, we adopted an iterative method using a genetic algorithm (GA) to develop an ML estimator for a model signal, the time delay, and the missing probability in the frequency domain. Several simulation examples were analyzed to evaluate the performance of the proposed method. The simulation results show that the performance is significantly improved if the effect of missing observations on the ML estimator is considered.     

Hilbert transformer and time delay: statistical comparison in thepresence of Gaussian noise

We have shown that in the presence of independent and identically distributed (i.i.d.) additive Gaussian noise, the performance of a time delay as a phase shifter, which produces a signal-dependent phase shift, is comparable with the performance of a Hilbert transformer which produces a signal-independent 90° phase shift, especially for high signal-to-noise ratios (SNRs) and the proper choice of the delay. Sinusoidal signals are considered. It is shown that the time-delay phase process in Gaussian noise can be approximated by the noise-free phase plus a non-Gaussian phase noise. As the SNR increases, the expected value of the time-delay phase estimator approaches the true value of the phase, and its variance substantially decreases and converges to the Cramer-Rao bound for all ranges of the effective parameters: the phase shift, the deterministic phase, and SNR. A symmetric transformation of the phase probability density function (PDF) that improves the performance of the time delay in Gaussian noise is also proposed     

Steady-state variance analysis of adaptive, digital, coherent MPSKreceiver

The phase estimation error variance of an adaptive, digital, coherent PSK receiver is analysed in the steady-state at high SNR. It is shown that, because of the risk function chosen in the gain adaptation algorithm of the phase estimator, the phase error variance is minimised     

Maximum Likelihood Carrier Phase Recovery for Linear Suppressed-Carrier Digital Data Modulations

The problem of ML estimation of the Phase of a general data-modulated carrier is considered. The shortcomings of current iterative approaches to the problem are pointed out, and the correct conceptual approach is proposed. The true ML estimator is then obtained and found to be nonimplementable. However, by specializing to limits of high and low SNR, the general ML estimator is shown to reduce to implementable DA and NDA ML estimators, respectively. The DA receiver's performance in terms of phase tracking and symbol error probability can be analyzed, and even the effects of past decision errors on current system performance can be assessed. For circular signal constellations, the DA receiver has a simple and totally linear structure which is easy to implement. The NDA ML estimator is shown to be equivalent to the common carrier loops. Our emphasis here on explicit computation of the ML phase estimate from the past received signal leads to detection strategies which do not require a carrier loop and a VCO for coherent detection.     

Speech Enhancement Using Phase‐Dependent A Priori SNR Estimator in Log‐Mel Spectral Domain

We propose a novel phase‐based method for single‐channel speech enhancement to extract and enhance the desired signals in noisy environments by utilizing the phase information. In the method, a phase‐dependent a priori signal‐to‐noise ratio (SNR) is estimated in the log‐mel spectral domain to utilize both the magnitude and phase information of input speech signals. The phase‐dependent estimator is incorporated into the conventional magnitude‐based decision‐directed approach that recursively computes the a priori SNR from noisy speech. Additionally, we reduce the performance degradation owing to the one‐frame delay of the estimated phase‐dependent a priori SNR by using a minimum mean square error (MMSE)‐based and maximum a posteriori (MAP)‐based estimator. In our speech enhancement experiments, the proposed phase‐dependent a priori SNR estimator is shown to improve the output SNR by 2.6 dB for both the MMSE‐based and MAP‐based estimator cases as compared to a conventional magnitude‐based estimator.     

Coherence and time delay estimation

This paper presents a tutorial review of work in coherence and time delay estimation. A review of coherence research and development is presented. A derivation of the ML estimator for time delay is presented together with an interpretation of that estimator as a special member of a class of generalized cross correlators. The performance of the estimator is given for both high and low signal-to-noise ratio cases. The proposed correlator is implemented and stimulated with synthetic data. The results are compared with performance predictions and found to be in good agreement.     

Maximum likelihood time delay estimation in non-Gaussian noise

In a non-Gaussian noise environment, it is theoretically possible to design a delay estimator that performs significantly better than the conventional linear correlator. We study the maximum likelihood estimator for passive time delay in non-Gaussian noise. We show that the form of the best estimator depends strongly on signal-to-noise ratio (SNR), and the estimator optimal at low SNR can fail catastrophically at high values of SNR. The paper uses simulations to examine this sensitivity problem and proposes an ad hoc instrumentation that is reasonably robust over a wide range of SNR values     

Derived PDF of maximum likelihood signal estimator which employs anestimated noise covariance

A probability density function (PDF) for the maximum likelihood (ML) signal vector estimator is derived when the estimator relies on a noise sample covariance matrix (SCM) for evaluation. By using a complex Wishart probabilistic model for the distribution of the SCM, it is shown that the PDF of the adaptive ML (AML) signal estimator (alias the SCM based minimum variance distortionless response (MVDR) beamformer output and, more generally, the SCM based linearly constrained minimum variance (LCMV) beamformer output) is, in general, the confluent hypergeometric function of a complex matrix argument known as Kummer's function. The AML signal estimator remains unbiased but only asymptotically efficient; moreover, the AML signal estimator converges in distribution to the ML signal estimator (known noise covariance). When the sample size of the estimated noise covariance matrix is fixed, it is demonstrated that there exists a dynamic tradeoff between signal-to-noise ratio (SNR) and noise adaptivity as the dimensionality of the array data (number of adaptive degrees of freedom) is varied, suggesting the existence of an optimal array data dimension that will yield the best performance     

Threshold region performance of maximum likelihood direction of arrival estimators

This paper presents a performance analysis of the maximum likelihood (ML) estimator for finding the directions of arrival (DOAs) with a sensor array. The asymptotic properties of this estimator are well known. In this paper, the performance under conditions of low signal-to-noise ratio (SNR) and a small number of array snapshots is investigated. It is well known that the ML estimator exhibits a threshold effect, i.e., a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard techniques such as the Crame/spl acute/r-Rao bound and asymptotic analysis. In this paper, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Both the deterministic ML and stochastic ML estimators are treated for the single-source and multisource estimation problems. These approximations alleviate the need for time-consuming computer simulations when evaluating the threshold region performance. For the special case of a single stochastic source signal and a single snapshot, it is shown that the ML estimator is not statistically efficient as SNR/spl rarr//spl infin/ due to the effect of outliers.     

UWB定位中的自适应时间延迟估计算法

研究了时延估计算法在超宽带(Ultra Wide Band)定位中的应用,其广义相关自适应时间延迟估计算法的收敛速度慢,在低信噪比条件下时间延迟估计精度较低。针对低信噪比条件下的收敛特性,提出一种最大似然加权的广义相关自适应时间延迟估计算法,并进一步提出了改进的基于最大似然(Maximum Likelihood)加权函数的广义互相关时延估计算法。改进的算法采用加窗法和自适应时变干扰删除滤波法,弥补了原算法计算量大及无法消除时变信号干扰的不足。仿真结果表明,改进的算法计算复杂度明显降低,能够有效地消除其他信号干扰,具有较高的时延估计精度和鲁棒性。     

Estimating the cumulative downtime distribution of a highlyreliable component

The distribution of the cumulative downtime for a highly reliable component over an interval of time is approximated using a compound Bernoulli process. Given a set of observed cumulative downtimes, the maximum likelihood (ML) and uniformly minimum variance unbiased (UMVU) estimator of the approximate cumulative downtime distribution are derived under the assumption of exponential repair times and are compared to the nonparametric estimator. The ML estimator is more efficient than the UMVU estimator which itself is more efficient than the nonparametric estimator     

Reduced complexity sphere decoding via a reordered lattice representation

In this letter, we propose a reordering of the channel representation for Sphere Decoding (SD) where the real and imaginary parts of each jointly detected symbol are decoded independently. Making use of the proposed structure along with a scalar quantization technique, we reduce the decoding complexity substantially. We show that this approach achieves 85% reduction in the overall complexity compared to the conventional SD for a 2 times 2 system, and 92% reduction for the 4 times 4 and 6 times 6 cases at low SNR values, and almost 50% at high SNR, thus relaxing the requirements for hardware implementation.