Sufficient conditions for regularity and strict identifiability in MIMO systems

We consider regularity and identifiability of convolutive multi-input multi-output (MIMO) systems with additive white Gaussian noise, modeling the source and finite impulse response (FIR) channel sequences as deterministic unknowns. In the blind context, the MIMO system is not locally identifiable; hence, its Fisher information matrix (FIM) is not regular. In fact, the dimension of the complex-valued blind FIM space is at least the number of sources squared. Because the FIM is singular, additional information about the system is required to resolve the degrees of uncertainty and thereby obtain a valid Cramer-Rao bound (CRB); therefore, it is of interest to know under what conditions the blind FIM ity reaches its lower bound. We develop sufficient conditions for the complex FIM to attain its minimum ity, refining previous necessary conditions, and extending single-input multi-output (SIMO) results. We show that the sufficient conditions for the complex FIM to have minimum ity are also equivalent to sufficient conditions for MIMO strict identifiability. These provide sufficient conditions on the richness of the sources, the required diversity, and the source lengths. Under these conditions, additional constraints, such as training, may be employed to yield an identifiable system with no ambiguities remaining.     

Surface-source modeling and estimation using biomagnetic measurements

We propose a number of electric source models that are spatially distributed on an unknown surface for biomagnetism. These can be useful to model, e.g., patches of electrical activity on the cortex. We use a realistic head (or another organ) model and discuss the special case of a spherical head model with radial sensors resulting in more efficient computations of the estimates for magnetoencephalography. We derive forward solutions, maximum likelihood (ML) estimates, and Cramér-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to decide on the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models and illustrate when it is possible to distinguish between surface and focal sources or line sources. Finally, we apply our methods to real biomagnetic data of phantom human torso and demonstrate the applicability of them.     

Bounds on maximum likelihood ratio-part I: application to antenna array detection-estimation with perfect wavefront coherence

The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the maximum LR. Since LR optimization is generally a nonconvex multiextremal problem, any practical solution could now be tested against these bounds, enabling a high probability of recognizing nonoptimal solutions. We demonstrate that in many applications, the lower bound is quite tight, with approximate maximum likelihood (ML) techniques often unable to approach this bound. The introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace-based direction-of-arrival (DOA) estimation techniques. We also demonstrate that by proper LR maximization, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates: a phenomenon that cannot be eliminated within the ML paradigm.     

一般SPT模型的抗差分和线性攻击安全性研究

为安全高效地在序列密码设计中应用SP网络,研究了一般SPT模型的抗差分攻击和线性攻击的能力,其中,S和T表示2个不同的可实现压缩的混淆层,P代表扩散层。给出了P为最佳扩散层时SPT模型的最大差分概率上界,给出了P为最佳扩散层且S和T均平衡时的最大线性逼近优势和最大线性包优势的上界,从而部分解决了该模型的抗差分和线性攻击安全性评估问题。     

Line-source modeling and estimation with magnetoencephalography

We propose a number of source models that are spatially distributed on a line for magnetoencephalography (MEG) using both a spherical head with radial sensors for more efficient computation and a realistic head model for more accurate results. We develop these models with increasing degrees of freedom, derive forward solutions, maximum-likelihood (ML) estimates, and Cramér-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to select the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models, to determine the regions where better estimates are possible and when it is possible to distinguish between line and focal sources. We demonstrate the usefulness of the proposed line-source models over the previously available focal source model in certain distributed source cases. Finally, we apply our methods to real MEG data, the N2O response after electric stimulation of the median nerve known to be an extended source.     

Some properties of sequential predictors for binary Markov sources

Universal predictions of the next outcome of a binary sequence drawn from a Markov source with unknown parameters is considered. For a given source, the predictability is defined as the least attainable expected fraction of prediction errors. A lower bound is derived on the maximum rate at which the predictability is asymptotically approached uniformly over all sources in the Markov class. This bound is achieved by a simple majority predictor. For Bernoulli sources, bounds on the large deviations performance are investigated. A lower bound is derived for the probability that the fraction of errors will exceed the predictability by a prescribed amount Δ>0. This bound is achieved by the same predictor if Δ is sufficiently small     

Intersymbol interference and probability of error in digital systems

Intersymbol interference and additive Gaussian noise are two important sources of distortion in digital systems, and a principal goal in the analysis of such systems is the determination of the resulting probability of error. Earlier related work has sought to estimate the error probability either by calculating an approximation based upon a truncated version of the random pulse train or by obtaining an upper bound which results from consideration of the worst case intersymbol interference. In this paper a new upper bound is derived for the probability of error which is computationally simpler than the truncated pulse-train approximation and which never exceeds the worst case bound. Moreover, the new bound is applicable in a number of cases where the worst case bound cannot be used. The bound is readily evaluated and depends upon three parameters: the usual signal-to-noise ratio; the ratio of intersymbol interference power to total distortion power; and the ratio of the maximum intersymbol interference amplitude to its rms value. To illustrate the utility of the bound, it is compared with the earlier methods in three cases which are representative of the most important situations occurring in practice.     

Imaging below the diffraction limit: a statistical analysis

The present paper is concerned with the statistical analysis of the resolution limit in a so-called "diffraction-limited" imaging system. The canonical case study is that of incoherent imaging of two closely-spaced sources of possibly unequal brightness. The objective is to study how far beyond the classical Rayleigh limit of resolution one can reach at a given signal to noise ratio. The analysis uses tools from statistical detection and estimation theory. Specifically, we will derive explicit relationships between the minimum detectable distance between two closely-spaced point sources imaged incoherently at a given SNR. For completeness, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the Cramér-Rao bound. To gain maximum intuition, the analysis is carried out in one dimension, but can be well extended to the two-dimensional case and to more practical models.     

The impact of network topology on delay bound in wireless Ad Hoc networks

We consider single channel wireless networks with interference constraint among the links that can be activated simultaneously. The traffic flows are assumed to be single hop. Delay performance of the well known throughput optimal maximum weight link scheduling algorithm has been studied recently. In this paper, we study the relation between network topology and delay of maximum weight link scheduling algorithm. First, we consider 1-hop interference model. Under this interference model, an upper bound for the average delay of packets is derived analytically in terms of edge chromatic number of the network graph. Then the results have been extended to the case of general interference model. Under this model of interference, an upper bound for delay as a function of chromatic number of conflict graph is derived. Since chromatic number and edge chromatic number are network topology parameters, the results show that how the upper bound of delay is affected by network topology. Simulation results confirm our analytical relations.     

Stochastic Crame/spl acute/r-Rao bound for noncircular signals with application to DOA estimation

After providing an extension of the Slepian-Bangs formula for general noncircular complex Gaussian distributions, this paper focuses on the stochastic Crame/spl acute/r-Rao bound (CRB) on direction-of-arrival (DOA) estimation accuracy for noncircular sources. We derive an explicit expression of the CRB for DOA parameters alone in the case of noncircular complex Gaussian sources by two different methods. One of them consists of computing the asymptotic covariance matrix of the maximum likelihood (ML) estimator, and the other is obtained directly from our extended Slepian-Bangs formula. Some properties of this CRB are proved, and finally, it is numerically compared with the CRBs under circular complex Gaussian and complex discrete distributions of sources.     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

Near-field multiple source localization by passive sensor array

The localization of multiple near-field sources in a spatially white Gaussian noise environment is studied. A modified two-dimensional (2-D) version of the multiple signal classification (MUSIC) algorithm is used to localize the signal sources; range and bearing. A global-optimum maximum likelihood searching approach to localize these sources is discussed. It is shown that in the single source situation, the covariances of both the 2-D MUSIC estimator and the maximum likelihood estimator (MLE) approach the Cramer-Rao lower bound as the number of snapshots increases to infinity. In the multiple source situation, it is observed that for a high signal-to-noise ratio (SNR) and a large number of snapshots, the root mean square errors (RMSEs) of both localization techniques are relatively small. However, for low SNR and/or small number of snapshots, the performance of the MLE is much superior that of the modified 2-D MUSIC     

On the a priori identifiability of the two-compartment distributed parameter model from residual tracer data acquired by dynamic contrast-enhanced imaging

Tracer kinetics models are commonly employed to estimate physiological parameters related to blood transport and capillary-tissue exchange. A priori identifiability addresses the question of whether the parameters in a model can be uniquely determined from a given experiment. It has been previously shown that the one- and two-compartment distributed parameter (DP) models are nonidentifiable from tracer outflow data obtained by arterial-venous sampling. In this correspondence, we show that both DP models are a priori identifiable from residual tracer data obtained by dynamic contrast-enhanced (DCE) imaging. We list the various parameters of the DP models that can be uniquely estimated from DCE imaging data, and discuss this seemingly different outcome for DCE imaging experiments, as compared with the arterial-venous sampling experiments.     

An efficient algorithm for the extraction of parameters with high confidence from nonlinear models

Analytical models with parameters numerically extracted from I-V data have been used in simulation of MOS circuits. The equations are quasi-physical and the extracted parameters do not normally relate to any single identifiable physical mechanism. We have developed an extraction system that can provide a measure of the level of confidence in the extracted parameters; hence, these parameters may be reliably used in circuit simulation as well as process control. The algorithm described is model independent and can be used for any nonlinear least-squares parameter extraction problem.     

多子阵互耦影响下的非圆信号自校正算法

针对多子阵互耦影响下的非圆信号波达方向(Direction-Of-Arrival,DOA)估计问题,给出了一种针对最大非圆率信号的互耦自校正算法.该算法利用均匀线阵互耦矩阵的带状、对称Toeplitz性和多子阵互耦矩阵的块状对角特性,能够与传统的互耦秩减估计器一样避免多维搜索和迭代运算.并且通过结合信号的非圆特性来扩展数据模型,使得其估计精度较传统的互耦秩减估计算法有明显提升,可分辨信源数也有所增加.对该算法的理论性能进行研究,分析了其对未知参数的可辨识性必要条件,并基于最大非圆率信号模型给出了相应的克拉美罗界(Cramér-Rao Bound,CRB).仿真结果表明,该算法较传统的互耦秩减估计算法在低信噪比、小快拍数下有更强的鲁棒性.     

Almost-sure identifiability of multidimensional harmonic retrieval

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size. Consider a mixture of 2-D exponentials, each parameterized by amplitude, phase, and decay rate plus frequency in each dimension. Suppose that I equispaced samples are taken along one dimension and, likewise, J along the other dimension. We prove that if the number of exponentials is less than or equal to roughly IJ/4, then, assuming sampling at the Nyquist rate or above, the parameterization is almost surely identifiable. This is significant because the best previously known achievable bound was roughly (I+J)/2. For example, consider I=J=32; our result yields 256 versus 32 identifiable exponentials. We also generalize the result to N dimensions, proving that the number of exponentials that can be resolved is proportional to total sample size     

PARAFAC-Based Blind Identification of Underdetermined Mixtures Using Gaussian Mixture Model

This paper presents a novel algorithm, named GMM-PARAFAC, for blind identification of underdetermined instantaneous linear mixtures. The GMM-PARAFAC algorithm uses Gaussian mixture model (GMM) to model non-Gaussianity of the independent sources. We show that the distribution of the observations can also be modeled by a GMM, and derive a maximum-likelihood function with regard to the mixing matrix by estimating the GMM parameters of the observations via the expectation-maximization algorithm. In order to reduce the computation complexity, the mixing matrix is estimated by maximizing a tight upper bound of the likelihood instead of the log-likelihood itself. The maximum of the tight upper bound is obtained by decomposition of a three-way tensor which is obtained by stacking the covariance matrices of the GMM of the observations. Simulation results validate the superiority of the GMM-PARAFAC algorithm.     

A connection control strategy for bursty sources in broadband packet networks

This paper proposes an admission strategy for connection-oriented services at the access node of a broadband integrated packet network based on asynchronous transfer mode. Based on an estimate of the probability of cell loss and in the absence of buffering, we determine the number of sources from different classes of bursty traffic which can be accepted. The parameters which are used to describe the traffic sources are average bit rate and peak bit rate. We will evaluate the cell loss estimate for homogeneous and heterogeneous cases. Furthermore, we will examine the variation of this estimate as the average to peak ratio changes. The estimate is an upper bound for the probability of cell loss. Based on this upper bound simple and robust allocation of resources to bursty sources can be developed. The proposed strategy can be implemented using simple computations or via a look-up table to determine admission or denial of an incoming call and therefore allocating the required capacity. The procedure results in efficient use of the bandwidth, ensuring the desired service quality for connection-oriented services and results in proactive control of network congestion.     

Estimating parameters of multiple wideband polynomial-phase sourcesin sensor arrays

We consider the problem of estimating the parameters of multiple wideband polynomial-phase signal (PPS) sources in sensor arrays. A new maximum likelihood (ML) direction-of-arrival (DOA) estimator is introduced, and the exact Cramer-Rao bound (CRB) is derived for the general case of multiple constant-amplitude polynomial-phase sources. Since the proposed exact ML estimator is computationally intensive, an approximate solution is proposed, originating from the analysis of the log-likelihood (LL) function in the single chirp signal case. As a result, a new form of spatio-temporal matched filter (referred to as the chirp beamformer) is derived, which is applicable to "well-separated" sources that have distinct time-frequency or/and spatial signatures. This beamforming approach requires solving a three-dimensional (3-D) optimization problem and, therefore, enjoys essentially simpler implementation than that entailed by the exact ML. Simulation results are presented, illustrating the performance of the estimators and validating our theoretical CRB analysis     

一种符号执行制导的循环内界分析方法

循环是计算机中重要的复杂程序结构.很多应用场景要求静态分析循环可能达到的最大迭代次数,即循环边界（Loop Bound）.对应技术在文献中被称为循环边界分析（Loop Bound Analysis）.现有的循环边界分析均使用保守方式进行外界分析,即产生略高于循环边界的近似值.基于这一现状,本文提出了一种自动地循环内界分析方法,产生略低于循环边界的近似值.当用户综合利用外界与内界分析,能将循环边界值约束到一个统计区间,从而能对分析结果获得更为完整的认识.本文基于循环条件制导的符号执行（Symbolic Execution）技术实现了循环内界分析,该技术的本质在于它能够利用符号执行符号化推导程序执行约束的特点,准确求解循环在程序所有合法输入条件下的边界值,并由生成的测试用例来保证该边界值一定可达（即保证是循环内界）.本文对符号执行制导技术进行了优化,并在多组已有研究采用的基准用例集上进行了实例评估,实验结果表明,本文的循环内界分析方法具备准确性和高效性,可以满足应用需求.