Distribution of Path Durations in Mobile Ad Hoc Networks and Path Selection

We investigate the issue of path selection in multihop wireless networks with the goal of identifying a scheme that can select a path with the largest expected duration. To this end, we first study the distribution of path duration. We show that, under a set of mild conditions, when the hop count along a path is large, the distribution of path duration can be well approximated by an exponential distribution even when the distributions of link durations are dependent and heterogeneous. Second, we investigate the statistical relation between a path duration and the durations of the links along the path. We prove that the parameter of the exponential distribution, which determines the expected duration of the path, is related to the link durations only through their means and is given by the sum of the inverses of the expected link durations. Based on our analytical results, we propose a scheme that can be implemented with existing routing protocols and select the paths with the largest expected durations. We evaluate the performance of the proposed scheme using ns-2 simulation.     

Opportunistic Decode-and-Forward Relaying with Interferences at Relays

In this paper, a decode-and-forward cooperative interference-limited multiple relay network is considered. An efficient relay selection strategy and its performance analysis are proposed, where only the relay nodes are affected by multiple interferences. In the proposed relay selection scheme, the selected relay is not always used, depending on the power of interferences and the channel state information of all links, while the direct path between source and destination is always used. For analytical tractability the distribution of interference-limited channel is approximated as an exponential distribution with high accuracy. Analysis of cooperative networks with interference-limited relays can be performed using the approximate exponential distribution by the same methods which have been used without interferences. We derive the bit error probability and outage probability of the proposed opportunistic max-min relay selection (OMRS) scheme in independent non-identically distributed Rayleigh fading channels. Numerical results present the superiority of OMRS over the conventional relay selection scheme which always uses the selected relay path. The exactness of the approximate analysis for interference-limited relays is also shown in numerical results.     

Statistical properties of the delay spread in a two path mobile radio with Nakagami fading channel

In this paper we study the statistical properties of the rms delay spread in a two path mobile radio environment, where each path is subject to Nakagami fading. We assume a typical urban power delay profile (exponential decay) for each path. Closed form equations for the mean of the rms delay spread are derived for different values of the m parameter of the Nakagami distribution. Monte Carlo simulations are also generated and compared with the analytical results.     

A new spatial path persistency model for TOA-based indoor geolocation

Analysis of the persistency and birth/death of multipath components of the channel impulse response is essential for performance evaluation of indoor geolocation algorithms using indirect paths for ranging. The use of indirect paths via multipath diversity is particularly important for situations where the direct path gets blocked. In this letter, we propose a statistical model for the spatial behavior of the persistency of multipath components as a mobile moves inside a building. Based on empirical data from a measurement calibrated ray tracing algorithm we show that the persistency in a typical building is modeled by log-logistic distribution rather than commonly assumed exponential distribution and path birth can be modeled as a Poisson distribution.     

A two-year measurement of rainfall attenuation of CW microwaves inSingapore

The authors present two-year statistics on the rainfall attenuation of 21.225 GHz vertically polarized CW microwave signals in Singapore. The CCIR recommendation is found to underestimate the microwave specific attenuation (dB/km) per path average rain rate (mm/h) as well as the accumulated time of attenuation exceeding preset levels. A negative exponential raindrop size distribution based on spherical droplets is constructed from the measured data     

Modeling path duration distributions in MANETs and their impact on reactive routing protocols

We develop a detailed approach to study how mobility impacts the performance of reactive mobile ad hoc network routing protocols. In particular, we examine how the statistics of path durations including probability density functions vary with the parameters such as the mobility model, relative speed, number of hops, and radio range. We find that at low speeds, certain mobility models may induce multimodal distributions that reflect the characteristics of the spatial map, mobility constraints and the communicating traffic pattern. However, this paper suggests that at moderate and high velocities the exponential distribution with appropriate parameterizations is a good approximation of the path duration distribution for a range of mobility models. Analytically, we show that the reciprocal of the average path duration has a strong linear relationship with the throughput and overhead of dynamic source routing (DSR), which is also confirmed by simulation results. In addition, we show how the mathematical expression obtained for the path duration distribution can also be used to prove that the nonpropagating cache hit ratio in DSR is independent of velocity for the freeway mobility model. These two case studies illustrate how various aspects of protocol performance can be analyzed with respect to a number of significant parameters including the statistics of link and path durations.     

Reconciliation of a hot-electron distribution function with thelucky electron-exponential model in silicon

The lucky-electron-exponential model (LE-EM) has been used with some success to model hot-electron-induced degradation. Examination of the LE-EM shows its exponential form is an approximation to the high-energy tails of Monte-Carlo-generated hot-electron distribution functions (HEDFs). It is also suggested that the proper LE-EM mean-free path λ for use in calculating MOSFET gate leakage current is approximately 50 Å, while the commonly used value of 78 Å is appropriate for modeling phenomena related to impact ionization     

Distribution of time to failure of consecutive k-out-of n:F systems

It is shown that by modifying the path-evaluation technique due to R.C. Bollinger and A.A. Salvia (1985) it is possible to compute the cumulative distribution function (CDF) of the lifetime of any consecutive k-out-of-n:F system recursively, obtaining it as a mixture of the distributions of the failure times of the various paths. The distribution of the failure time given a path is a convolution of exponential distributions with the distributions of failure times of systems made up of disjoint modules in series, where each module is either a subsystem for which the recursive computation has already been done or an s-coherent system with nonoverlapping min-cut sets whose failure time CDF can be easily found     

Probabilistic properties of the exponential distribution

The exponential distribution is popular for modeling the lifetimes of components and systems. Probabilistic properties of the exponential distribution are scattered throughout textbooks and journal articles. This paper contains proofs of twelve properties of the exponential distribution that are useful for characterizing the distribution and statistical inference.     

Time-frequency representation of the electrogastrogram-applicationof the exponential distribution

The authors examined the applicability of the exponential distribution for the time-frequency representation of the electrogastrogram (EGG). The EGG is a noninvasive measurement of the electrical activity of the stomach by placing electrodes on the abdominal skin. Quantitative analysis of the EGG has relied on spectral methods. The normal frequency of the EGG in humans is 3 cycles/min. Electrical dysrhythmia observed in the EGG is associated with motor disorders of the stomach. The exponential distribution was applied here for the estimation of EGG frequency and for the detection of dysrhythmia in the EGG. A series of computer simulations was conducted, demonstrating the reliability of the exponential distribution in the analysis of nonstationary electrical signals of the stomach. Applications of the exponential distribution in the spectral analysis of typical EGGs are presented. The results show that there is a great potential for the use of the exponential distribution in EGG analysis     

基于复杂网络理论的校友网络研究

在某高校校友会网站的开发建设中,引入复杂网络机制,借鉴城市公共交通网络的space P和space L方法,构建了校友网络,分析了其平均路径长度、聚类系数和度分布等基本网络统计特性,并借用数学期望的思想,对构建的校友网络方法进行了验证。由分析结果可知,校友网络是一个具有指数型度分布的小世界网络;校友网络是由一些关键节点（主席、副主席和班长和团支书等）连接起来的,应该切实保障这类节点的桥梁作用;space P方法构造的校友网络比space L方法构造的校友网络更加合理,更能反映真实的校友关系。     

Detection and Tracking of MIMO Propagation Path Parameters Using State-Space Approach

This paper describes a novel approach for detection, estimation and tracking of multiple-input multiple-output (MIMO) radio propagation parameters from multidimensional channel sounding measurements. A realistic state-space model is developed for the purpose, and the extended Kalman filter (EKF) is applied in a particular computationally efficient form to track the geometrical double-directional propagation path parameters. The observation model utilizes the dense multipath component (DMC), describing the distributed scattering in the channel, as part of the underlying noise process. The DMC model assumes an exponential profile in delay, and allows for an arbitrary angular distribution. In addition, a novel dynamic state dimension estimator using statistical goodness-of-fit tests is introduced. The employed methods are supported by illustrative estimation examples from MIMO channel sounding measurements.      

雨衰减预测中的降雨率调整因子概念

利用ITUR数据库地面视距链路和地空链路雨衰减数据,分析了传统雨衰减预报中所使用的基于柱状雨胞模型的雨衰减物理模型导出的路径调整因子与实测数据之间的矛盾.在此基础上,基于指数雨胞建立的雨衰减物理模型,通过理论分析导出了降雨率调整因子的概念.利用降雨率调整因子,可以解释实测数据的主要特征,表明：基于指数雨胞的雨衰减物理模型是合理的,利用降雨率调整因子的概念,可为发展新的地面视距链路和地空链路雨衰减预报模式和方法提供理论依据.     

Survival function of a component under random strength attenuation

In this paper the survival of a component, prone to attacks by a succession of random stresses, is examined under the assumption that the strength of the component is attenuated and these attenuated factors are random variables. Expressions have been obtained for these attenuation factors: (i) when the stress strength follows exponential distribution and the random attenuation factors follow rectangular distribution; (ii) when the stress strength follows exponential distribution with the attenuation factors following beta distribution; (iii) when the stress following exponential distribution, strength following gamma distribution and the random attenuation factors following beta distribution.     

Path map symbol release rules and the exponential metric tree[source coding]

To design a tree coder for source coding with a fidelity criterion, one must choose a suitable code generator, an efficient tree search algorithm, an appropriate distortion measure, and a path map symbol release rule. The performance of several path map symbol release rules when used with exhaustive searching of the exponential metric tree is investigated. The average single-letter distortion of fixed-length symbol release rules and two variable-length symbol release rules are derived for shallow search depths and compared to simulation results. The incremental or single-symbol release rule is shown to yield the best performance     

Tolerance Regions for a Joint Exponential Distribution

The evaluation of the reliability of a system of components, when the components are assumed to follow a joint exponential distribution, is considered. The approach used is to develop tolerance regions for the joint exponential distribution or to estimate the probability content of the appropriate specification region.     

Path-tracking velocity control for robot manipulators with actuator constraints

An algorithm for high-performance path tracking for robot manipulators in the presence of model uncertainties and actuator constraints is presented. The path to be tracked is assumed given, and the nominal trajectories are computed using, for example, well-known algorithms for time-optimal path tracking. For online path tracking, the nominal, feedforward trajectories are combined with feedback in a control architecture with a secondary controller, such that robustness to uncertainties in model or environment is achieved. The control law is based on existing path-velocity control (PVC), or so called online time scaling, but in addition to speed adaptation along the tangent of the path, the algorithm also comprises an explicit formulation and approach, with several attractive properties, for handling the deviations along the transversal directions of the path. For achieving fast convergence along the normal and binormal directions of the path in 3D motion, the strategy proposed has inherent exponential convergence properties. The result is a complete architecture for path-tracking velocity control (PTVC). The method is evaluated in extensive simulations with manipulators of different complexity, and PTVC exhibits superior performance compared to PVC.     

指数分布环境因子的Bayes算法

对不同环境下指数分布环境因子的计算方法进行了讨论，并给出了检验指数分布有效性的统计方法。基于信仰推断的理论，得出环境因子的先验分布，进而对环境因子进行Dayes估计。最后运用仿真实例验证了该方法的有效性。     

串联系统的备件配置方法

针对非指数分布串联系统的备件配置问题,首先根据指数分布的良好特性,建立指数分布串联系统的备件需求预测和配置模型;然后根据期望累积失效相等的原则,将非指数分布等效成指数分布。在此基础上,利用指数分布串联系统的备件模型近似地计算非指数分布串联系统的备件需求量。并以几种典型非指数分布的串联系统为例,如Weibull分布、正态分布和Gamma分布,分别给出了给定时间内的备件配置结果。通过Monte-Carlo模拟仿真,结果表明比实际略偏保守,且与经典方法相比,具有计算过程简单,预测时间更长与可操作性更强的优点,满足实际的保障要求,能够为工程应用带来方便。     

Measurement of rain-induced zenith-path attenuation using 19.9 GHz radiometer at Amritsar (India)

The paper presents the results of 19.9 GHz radiometric propagation studies conducted over a period of one year at Amritsar, for determining rain-induced zenith path attenuation. The zenith path attenuation has been determined by the measurements of sky noise temperature received by the radiometer. The results obtained from the experiment are presented in the form of annual cumulative distributions of rain rate, sky noise temperature, and zenith path attenuation together with worst-month statistics. The rainfall rate cumulative distribution as predicted by ITU-R for our geographical location is lower than the actually measured rainfall rate cumulative distribution. The cumulative distribution of zenith path attenuation predicted by using ITU-R model overestimates the measured cumulative distribution of zenith path attenuation.