偏振模色散统计特性的研究

利用动态方程研究了偏振模色散矢量的统计特性 ,分别用统计系综和频率系综两种方法进行数值模拟。数值结果表明 ,统计系综和频率系综两种方法的结果一致。在大归一化距离条件下 ,均方根时延的平方随归一化距离线性变化 ;偏振模色散矢量的各个分量服从高斯分布 ,差分群时延服从麦克斯韦分布 ;偏振模色散矢量弥散于整个邦加球     

The Influence of Cycle Slipping on the Error Probability of a PAM Receiver

In this paper, we evaluate the error probability of a PAM receiver, which derives symbol timing from the received waveform by means of a synchronizer. We point out that the conventional way (using the distribution of the synchronizer's modulo-2π- reduced phase error) of evaluating this error probability does not take into account the effect of the synchronizer's cycle slips. We present a correct expression for the error probability, which uses the distribution of the so-called renewal phase. Also, we derive simple but accurate approximations for both the conventional and the correct error probability, which clearly show the influence of the characteristics of the PAM receiver. These approximate expressions indicate that, for a decreasing additive noise level at the receiver input, the conventional error probability becomes vanishingly small, whereas the correct error probability approaches a nonzero value, which is inversely proportional to the mean time between slips. Hence, cycle slipping imposes a (sometimes rather large) lower limit on the attainable error probability.     

钝角二面角全极化双基地RCS统计建模

钝角二面角结构在目标的隐身特性中发挥着重要作用,但其双基地特性尚不明确.采用电磁仿真与统计建模相结合的方法,从频域、空域、极化域和统计分布角度对其双基地散射特性进行分析.研究表明,在电尺寸较小时,双基地散射增强特性并不明显,单/双基地RCS概率密度分布差异大,共极化的双基地RCS概率密度分布呈现双峰特性,为此提出了双对...     

Displacement of rays in a turbulent medium

The Fokker-Planck equation associated with the fluctuation (ray) equation is derived. The resulting equation for an isotropic turbulence is in the form of a diffusion equation. It has been found that the diffusion coefficient is more naturally defined in terms of the logarithmic refractive index. In the limit of weak turbulence, the present definition reduces to the conventional one. For a general and arbitrary "initial" condition, certain moments of the diffusion equation have been obtained. These moments give 1) the probability of finding a ray with a given ray direction and given path length, and 2) the mean and mean-square position of the ray in a given direction and given path length.     

运动序列的短期统计特性

本文利用动态图象序列研究了运动序列的短期统计特性,对每个宏块经过压缩后所产生的比特数进行了分析,研究了量化比例因子和量化加权矩阵对短期统计特性的影响.统计结果表明,量化比例因子对每个宏块比特数的概率分布影响最为明显,量化加权矩阵对分布特性的轮廓影响很小,当量化比较精细时图象内容对分布特性的低比特部分影响比较明显,而粗量化时它的影响较弱.     

A new statistical model for site-specific indoor radio propagationprediction based on geometric optics and geometric probability

The ray-tracing (RT) algorithm has been used for accurately predicting the site-specific radio propagation characteristics, in spite of its computational intensity. Statistical models, on the other hand, offers computational simplicity but low accuracy. In this paper, a new model is proposed for predicting the indoor radio propagation to achieve computational simplicity over the RT method and better accuracy than the statistical models. The new model is based on the statistical derivation of the ray-tracing operation, whose results are a number of paths between the transmitter and receiver, each path comprises a number of rays. The pattern and length of the rays in these paths are related to statistical parameters of the site-specific features of indoor environment, such as the floor plan geometry. A key equation is derived to relate the average path power to the site-specific parameters, which are: 1) mean free distance; 2) transmission coefficient; and 3) reflection coefficient. The equation of the average path power is then used to predict the received power in a typical indoor environment. To evaluate the accuracy of the new model in predicting the received power in a typical indoor environment, a comparison with RT results and with measurement data shows an error bound of less than 5 dB     

A Study of the Influence of Shadowing on the Statistical Properties of the Capacity of Mobile Radio Channels

This paper studies the influence of shadowing on the statistical properties of the channel capacity. The problem is addressed by using a Suzuki process as an appropriate statistical channel model for land mobile terrestrial channels. Using this model, exact solutions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity are derived. The results are studied for different levels of shadowing, corresponding to different terrestrial environments. It is observed that the shadowing effect has a significant influence on the variance and the maximum value of the PDF and LCR of the channel capacity, but it has almost no impact on the mean capacity of the channel. The correctness of the theoretical results is confirmed by simulation using a stochastic channel simulator based on the sum-of-sinusoids principle.     

Tartaglia-Pascal’s triangle: a historical perspective with applications

The aim of this paper is to provide a historical perspective of Tartaglia-Pascal’s triangle with its relations to physics, finance, and statistical signal processing. We start by introducing Tartaglia’s triangle and its numerous properties. We then consider its relationship with a number of topics: the Newton binomial, probability theory (in particular with the Gaussian probability density function, pdf), the Fibonacci sequence, the heat equation, the Schrödinger equation, the Black–Scholes equation of mathematical finance and stochastic filtering theory. Thus, the main contribution of this paper is to present a systematic review of the triangle properties, its connection to statistical theory, and its numerous applications. The paper has mostly a scientific-educational character and is addressed to a wide circle of readers. Sections 7 and 8 are more technical; thus, they may be of interest to more expert readers.     

Investigation of the performance characteristics of a system for the incoherent search for noise-like signals

A system for the search for the noise-like signals with verification of the results is considered for the case of incoherent reception. Basic statistical characteristics of the system are determined. The problem of decreasing the mean acquisition time is studied. It is shown that the proposed algorithm provides selection of the points of possible detection and thus reduction of the mean acquisition time. The probability of error in the selection of the points of possible detection is estimated.     

WPAN应用电磁环境中干扰模型的分析及仿真

文中首先介绍了无线个域网所要面对的各种干扰及它们各自的特点，给出了干扰的拓扑结构和传播模型；针对干扰的特点，由阻塞率的模型，经过数学变换推导出以干扰总电平为变量的统计模型，以此为基础分析干扰的统计特性；利用统计模型分析跳频技术在WPAN应用环境下性能的同时，也利用有关软件对跳频技术在这些干扰环境中的性能作了仿真，从两者比较结果中可以看出，干扰的统计模型是比较准确的，它对今后的实际研究工作具有一定的指导意义。     

Statistical Properties of First-Order Bang-Bang PLL With Nonzero Loop Delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state flow diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.      

On the Theory of Randomly Misaligned Beam Waveguides

A straightforward method for the determination of the expected attenuation in misaligned beam waveguides is presented. It applies to confocal guides and assumes that the misalignment consists of random displacements of the lenses in directions perpendicular to the beam axis. Reiterative fields, as they are present in perfectly aligned beam waveguides, do not exist in misaligned guides. However, it can be shown that there are beams whose expected field distribution is repeated from lens to lens. These "statistical modes" are determined by the eigenfunctions of a homogeneous integral equation of the second kind. The corresponding eigenvalues determine the expected attenuation per iteration. The absolute squares of the eigenvalues yield an upper bound for the expected power loss per iteration. The integral equation is solved for small mean square displacements of the lenses by a perturbation method. For infiitely extended lenses, the equation can be solved in closed form. In both cases the expected attenuation of the lower-order statistical modes has been calculated; the results are shown as function of the mean square displacement of the lenses.     

On the optimality of solutions of the max-productbelief-propagation algorithm in arbitrary graphs

Graphical models, such as Bayesian networks and Markov random fields (MRFs), represent statistical dependencies of variables by a graph. The max-product “belief propagation” algorithm is a local-message-passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tree. Furthermore, when the graph is a tree, the assignment based on the fixed point yields the most probable values of the unobserved variables given the observed ones. Good empirical performance has been obtained by running the max-product algorithm (or the equivalent min-sum algorithm) on graphs with loops, for applications including the decoding of “turbo” codes. Except for two simple graphs (cycle codes and single-loop graphs) there has been little theoretical understanding of the max-product algorithm on graphs with loops. Here we prove a result on the fixed points of max-product on a graph with arbitrary topology and with arbitrary probability distributions (discrete- or continuous-valued nodes). We show that the assignment based on a fixed point is a “neighborhood maximum” of the posterior probability: the posterior probability of the max-product assignment is guaranteed to be greater than all other assignments in a particular large region around that assignment. The region includes all assignments that differ from the max-product assignment in any subset of nodes that form no more than a single loop in the graph. In some graphs, this neighborhood is exponentially large. We illustrate the analysis with examples     

Predicting the threshold of single-pulse electrical stimuli using a stochastic auditory nerve model: the effects of noise

An important factor that may play a role in speech recognition by individuals with cochlear implants is that electrically stimulated nerves respond with a much higher level of synchrony than is normally observed in acoustically stimulated nerves. Recent work has indicated that the addition of noise to an electrical stimulus may result in neural responses whose statistical characteristics are more similar to those observed in acoustically driven neurons. Psychophysical data have indicated that performance on some tasks might also be enhanced by the addition of noise. However, little theoretical work has been done toward predicting the effect of noise on psychoacoustic measurements. In this paper, theoretical predictions of these effects are developed through the use of a stochastic computational model. The effect of additive noise on the input and output characteristics and aggregate threshold behavior of modeled auditory nerves (ANs) is specifically studied. This paper derives the stochastic properties of the model input and output when using adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models for both one-down one-up (1D1U) and two-down one-up (2D1U) experimental paradigms. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations with the model. Theoretical threshold is predicted as a function of noise level based on these PMFs and the predictions match simulated performance. The results indicate that threshold may be adversely affected by the presence of high levels of noise.     

A taxonomy for software voting algorithms used in safety-critical systems

Voting algorithms are used to provide an error masking capability in a wide range of highly dependable commercial & research applications. These applications include N-Modular Redundant hardware systems and diversely designed software systems based on N-Version Programming. The most sophisticated & complex algorithms can even tolerate malicious (or Byzantine) subsystem errors. The algorithms can be implemented in hardware or software depending on the characteristics of the application, and the type of voter selected. Many voting algorithms have been defined in the literature, each with particular strengths and weaknesses. Having surveyed more than 70 references from the literature, a functional classification is used in this paper to provide taxonomy of those voting algorithms used in safety-critical applications. We classify voters into three categories: generic, hybrid, and purpose-built voters. Selected algorithms of each category are described, for illustrative purposes, and application areas proposed. Approaches to the comparison of algorithm behavior are also surveyed. These approaches compare the acceptability of voter behavior based on either statistical considerations (e.g., number of successes, number of benign or catastrophic results), or probabilistic computations (e.g., probability of choosing correct value in each voting cycle or average mean square error) during q voting cycles.     

Process variation-aware performance analysis of asynchronous circuits

Current technology trends have led to the growing impact of process variations on performance of asynchronous circuits. As it is imperative to model process parameter variations for sub-100nm technologies to produce a more real performance metric, it is equally important to consider the correlation of these variations to increase the accuracy of the performance computation. In this paper, we present an efficient method for performance evaluation of asynchronous circuits considering inter- and intra-die process variation. The proposed method includes both statistical static timing analysis (SSTA) and statistical Timed Petri-Net based simulation. Template-based asynchronous circuit has been modeled using Variant-Timed Petri-Net. Based on this model, the proposed SSTA calculates the probability density function of the delay of global critical cycle. The efficiency for the proposed SSTA is obtained from a technique that is derived from the principal component analysis (PCA) method. This technique simplifies the computation of mean, variance and covariance values of a set of correlated random variables. In order to consider spatial correlation in the Petri-Net based simulation, we also include a correlation coefficient to the proposed Variant-Timed Petri-Net which is obtained from partitioning the circuit. We also present a simulation tool of Variant-Timed Petri-Net and the results of the experiments are compared with Monte Carlo simulation-based method.     

内禀退相干对光场量子统计性质的影响

通过求解系统的Milburn方程,研究了两能级原子与双模SU(1,1)相干态光场相互作用系统的量子统计性质,分析了内禀退相干、双模光子数差和平均光子数对量子统计性质的影响.结果表明,内禀退相干增强了光场两模的聚束效应和模间相关程度,并使第一模始终处于亚泊松分布;存在内禀退相干时,场的二阶相干度仍具有明显的崩塌-回复现象,随着时间的演化,光场第一模处于亚泊松分布,光子呈现反聚束效应,光场两模间呈正相关,且为非经典相关,而在大部分时间区域,光场第二模处于泊松分布,光子呈现聚束效应.     

DWDM光纤通信系统中受激喇曼散射的统计特性

随着通信容量的增大,密集波分复用(DWDM)光纤通信系统中的受激喇曼散射(SRS)非线性效应成为影响系统质量的重要因素.采用时域分步法模型,对色散下的SRS统计特性进行了深入研究,得到了在整码元色散走离时,DWDM系统各信道传输功率的统计特性,推导了各信道传输功率的数学期望、标准差,证实了各信道传输功率符合高斯分布,计算了概率密度函数,并且与仿真数据取得了较好的一致.

Abstract：

With the enlargement of communication capacity, the performance of dense wavelength division multiplexed (DWDM) fiber communication systems might be degraded by nonlinear effect of stimulated Raman scattering (SRS) in the optical fiber. To resolve these problems, the time-domain split-step method is applied to investigate the statistical characteristics of SRS. The mean and the standard deviation of transmission powers of all channels are derived analytically in a closed-form formula for DWDM systems with SRS and integer bits dispersion walk-off. The probability density function (PDF) of output powers of all channels is confirmed to be Gaussian distribution. The numerical results show a good correspondence with analytical formulae.     

Statistical modeling of the received signal envelope in a mobileradio channel

Propagation loss measurements taken in the Ottawa region in the 900-MHz frequency band are reported and discussed. Significant statistical parameters for a mobile radio channel, such as the mean, the standard deviation of the signals, the level crossing rates and the fading distance, are presented. The signal is first transformed from a time scale to a distance scale; it is then separated into slow and rapid variation components, a low-pass filter with a cutoff point corresponding to 0.125 cycle per wavelength being used to estimate the slow variation component. The statistical analysis of the rapid variation is related to the Rice probability law and to a direct-component-to-multipath-component ratio. For the medium-density urban area under consideration, this ratio is shown to change from around 5 dB to around 9 dB as one moves from medium-density urban to the surrounding open areas     

Methods for estimation of statistical properties of envelopes of ultrasonic echoes from myocardium

Several investigators have characterized various forms of heart disease from the statistical properties of envelopes of ultrasonic echos from myocardium. In particular, the mean-to-standard deviation ratio (MSR), skewness, and kurtosis of the envelope probability density function have been used for the detection of myocardial ischemia, infarction, reperfusion, and hypertrophy. In this paper, the effects of phenomena other than tissue acoustic properties upon estimates of statistical parameters are investigated. These include system characteristics (center frequency, bandwidth, beam width, etc.), sample volume dimensions, and tissue velocity. In myocardium, relatively small amounts of tissue are available for interrogation. It is shown that, under these limited data acquisition conditions, substantial systematic biases in the estimates of statistical parameters may occur. Analytic forms for errors in the envelope variance estimate are derived. Estimation of the envelope mean, variance, MSR, skewness, and kurtosis is investigated experimentally, using a commercial medical ultrasound scanner and a tissue-mimicking phantom.