Contact time in random walk and random waypoint: Dichotomy in tail distribution

Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint.     

Spatial node distribution of the random waypoint mobility model with applications

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.     

The random waypoint mobility model with uniform node spatial distribution

In this paper, we tackle the problem of designing a random mobility model generating a target node spatial distribution. More specifically, we solve a long standing open problem by presenting two versions of the well-known random waypoint (RWP) mobility model in bounded regions generating a uniform steady-state node spatial distribution. In the first version, named temporal-RWP, we exploit the temporal dimension of node mobility and achieve uniformity by continuously changing the speed of a mobile node as a function of its location and of the density function of trajectories in the movement region R. In the second version, named spatial-RWP, we instead exploit the spatial dimension and achieve uniformity by selecting waypoints according to a suitably defined mix of probability density functions. Both proposed models can be easily incorporated in wireless network simulators, and are thus of practical use. The RWP models presented in this paper allow for the first time completely removing the well-known border effect causing possible inaccuracies in mobile network simulation, thus completing the picture of a “perfect” simulation methodology drawn in existing literature.     

The node distribution of the random waypoint mobility model for wireless ad hoc networks

The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closed-form expression of this distribution and an in-depth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulation-based performance results to corresponding analytical results. To overcome these problems, we present a detailed analytical study of the spatial node distribution generated by random waypoint mobility. More specifically, we consider a generalization of the model in which the pause time of the mobile nodes is chosen arbitrarily in each waypoint and a fraction of nodes may remain static for the entire simulation time. We show that the structure of the resulting distribution is the weighted sum of three independent components: the static, pause, and mobility component. This division enables us to understand how the model's parameters influence the distribution. We derive an exact equation of the asymptotically stationary distribution for movement on a line segment and an accurate approximation for a square area. The good quality of this approximation is validated through simulations using various settings of the mobility parameters. In summary, this article gives a fundamental understanding of the behavior of the random waypoint model.     

Stationary distributions for the random waypoint mobility model

In simulations of mobile ad hoc networks, the probability distribution governing the movement of the nodes typically varies over time and converges to a "steady-state" distribution, known in the probability literature as the stationary distribution. Some published simulation results ignore this initialization discrepancy. For those results that attempt to account for this discrepancy, the practice is to discard an initial sequence of observations from a simulation in the hope that the remaining values will closely represent the stationary distribution. This approach is inefficient and not always reliable. However, if the initial locations and speeds of the nodes are chosen from the stationary distribution, convergence is immediate and no data need be discarded. We derive the stationary distributions for location, speed, and pause time for the random waypoint mobility model. We then show how to implement the random waypoint mobility model in order to construct more efficient and reliable simulations for mobile ad hoc networks. Simulation results, which verify the correctness of our method, are included. In addition, implementation of our method for the NS-2 simulator is available.     

Network connectivity of one-dimensional MANETs with random waypoint movement

An analysis of network connectivity of one-dimensional mobile ad hoc networks with a particular mobility scheme is presented, focusing on the random waypoint mobility scheme. The numerical results are verified using simulation to show their accuracy under practical network conditions. Observations on RWP properties further lead to approximations and an eventual simple network connectivity formula.     

On Walsh differentiable dyadically stationary random processes

Some basic properties of dyadically stationary (DS) processes are introduced, including continuity and spectral representation. A sampling theorem based on the Walsh functions is investigated for random signals that are not necessarily sequency-limited. By using the concept of a dyadic derivative, the resulting aliasing error is calculated together with the speed of convergence. An example gives a glimpse into the possibilities of applying the sampling theorem as well as the dyadic derivative.     

Epoch, length of the random waypoint model in mobile ad hoc networks

In this paper, we derive the probability distribution of the epoch length for the random waypoint model in mobile ad hoc networks. An epoch here is referred to as the movement between two target locations in the mobility model. Such a study is important as the epoch length distribution may be required for the derivation of the link-duration distribution or node spatial distribution for mobile ad hoc networks. The analytical result is then verified via simulation.     

On the continuity of the stationary state distribution of DPCM

Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e. delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediction coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e. it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e. either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions     

Memory-universal prediction of stationary random processes

We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process (Xi)_i=-∞^∞. The best mean-square predictor of X₀ is its conditional mean given the entire infinite past (X_i)_i=-∞^-1. Given a sequence of observations X₁, X₂, X_N, we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension, for example, neural networks and Legendre polynomials. The proposed estimators select both the model memory and the model dimension, in a data-driven fashion, by minimizing certain complexity regularized least squares criteria. When the underlying predictor function has a finite memory, we establish that the proposed estimators are memory-universal: the proposed estimators, which do not know the true memory, deliver the same statistical performance (rates of integrated mean-squared error) as that delivered by estimators that know the true memory. Furthermore, when the underlying predictor function does not have a finite memory, we establish that the estimator based on Legendre polynomials is consistent     

两静止观测站的纯角度定位与跟踪

许多论文都讨论了当观测站处于运动状态时如何对运动的目标进行定位和跟踪.但是,当观测站处于静止状态的时候,这些方法就不能使用了.文章的目的是通过两个静止红外观测站对存在机动运动的目标进行定位.给出了一种同步两站数据时间的方法,然后用同步后的数据对机动目标进行定位.试验结果证明了该方法的有效性.     

Series expansion of wide-sense stationary random processes

This paper presents a general approach to the derivation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and convergence is in the mean-square sense. The method of derivation is based on the integral representation of such processes. It covers both the periodic and the aperiodic cases. A constructive procedure is presented to obtain an explicit expansion for a given spectral distribution.     

On the filtering problem for stationary random /spl Zopf//sup 2/-fields

It is shown that whenever a stationary random field (Z/sub n,m/)/sub n,m/spl isin/z/ is given by a Borel function f:/spl Ropf//sup z/ /spl times/ /spl Ropf//sup z/ /spl rarr/ /spl Ropf/ of two stationary processes (X/sub n/)/sub n/spl isin/z/ and (Y/sub m/)/sub m/spl isin/z/ i.e., then (Z/sub n, m/) = (f((X/sub n+k/)/sub k/spl epsi/z/, (Y/sub m + /spl lscr// )/sub /spl lscr/ /spl epsi/z/)) under a mild first coordinate univalence assumption on f, the process (X/sub n/)/sub n/spl isin/z/ is measurable with respect to (Z/sub n,m/)/sub n,m/spl epsi/z/ whenever the process (Y/sub m/)/sub m/spl isin/z/ is ergodic. The notion of universal filtering property of an ergodic stationary process is introduced, and then using ergodic theory methods it is shown that an ergodic stationary process has this property if and only if the centralizer of the dynamical system canonically associated with the process does not contain a nontrivial compact subgroup.     

On the retention time distribution of dynamic random access memory(DRAM)

The retention time distribution of high-density dynamic random access memory (DRAM) has been investigated. The key issue for controlling the retention time distribution has been clarified and its model has been proposed for the first time. Trench capacitor cell with 0.6-μm ground rule was evaluated. It was found that the retention time distribution consists of “tail distribution” and “main distribution.” “tail distribution,” by which DRAM refresh characteristics are restricted, depends on the boron concentration of the memory cell region. As boron concentration of the memory cell region increases, “tail distribution” is enhanced. This enhancement is due to the increase of the junction leakage current from the storage node. For the purpose of accounting for the nature of “Tail Distribution,” the concept of thermionic field emission (TFE) current has been introduced. The high electric field at pn junction of the storage node enhances thermionic field emission from a deep level. The activation energy of the deep level is normally distributed among the memory cells, which leads to the normal distribution of log(retention time). Two methods for reducing “tail distribution” are proposed. One is to reduce the electric field of the depletion layer of the storage node. The other is to reduce the concentration of the deep level for TFE current     

Unified study on the decomposition for deterministic signals and stationary random signals

The unified decomposition theories and methods for deterministic signals and stationary random signals were deeply studied.According to the stability theory of linear systems,the unified results of signal decomposition under both regular stable and boundary stable conditions were given respectively.The unified results of signal decomposition under both orthogonal projection and self projection conditions were also provided based on the linear space projection theory.The former is clear and definite in its physical meaning,and the latter is clear in its mathematical and geometrical meanings.They are both complement with each other.     

Spectral analysis of stationary components of periodically correlated random processes

The properties of stationary components of periodically correlated random processes separated by using zonal filtering have been considered. The properties of estimates of their correlation and spectral characteristics were investigated. The latter were built by using the Blackman-Tukey method.     

Alpha稳定分布随机变量仿真及模型参数估计

在现实的通信系统中,许多自然的以及人为的噪声是非高斯脉冲的.针对噪声的非高斯性引起的高斯假设下设计的最优接收机性能的显著退化.设计了对称α稳定分布(SαS)模型,该模型能够比较准确地描述许多类型的脉冲噪声.并进行了模型仿真和模型参数估计.结果表明,α稳定分布更能描述信道中的噪音     

高速连接器全球专利布局特点

我国是全球连接器的主要市场,但本土企业主要集中在中低端领域发展。随着连接器的快速发展,中国成为全球连接器增长最快和容量最大的市场。对全球高速连接器专利布局进行多角度分析,提出推动我国高速连接器企业知识产权能力建设的几点建议。     

Computing the distribution of sums of random sine waves and ofRayleigh-distributed random variables by saddle-point integration

The method of saddle-point integration is applied to calculating the cumulative distribution of sums of independent random variables that either have a Rayleigh distribution or are sine waves with independently random phases in the presence of Gaussian random noise