相关论文: Interference Functionals in Poisson Networks
This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$…
We investigate interference of optical fields by examining the probability distribution of photon detection. The usual description of interference patterns in terms of superposition of classical mean fields with definite phases is…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden…
Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently…
Stochastic geometry models of wireless networks based on Poisson point processes are increasingly being developed with a focus on studying various signal-to-interference-plus-noise ratio (SINR) values. We show that the SINR values…
This survey will appear as a chapter of the forthcoming book [19]. A U-statistic of order $k$ with kernel $f:\X^k \to \R^d$ over a Poisson process is defined in \cite{ReiSch11} as$$ \sum\_{x\_1, \dots , x\_k \in \eta^k\_{\neq}} f(x\_1,…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…
We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…
Next-to-leading order parton fragmentation functions into light mesons are presented. They have been extracted from real and simulated $e^+e^-$ data and used to predict inclusive single particle distributions at different machines.
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
The Tweedie Compound Poisson-Gamma model is routinely used for modeling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping…
A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…
We consider the statistical mechanics of interfering transmissions in a wireless communications protocol. In this case, a connection between two nodes requires all other nodes within communication distance of the given two nodes to remain…
The signal-to-noise-plus-interference ratio (SINR) outage probability is one of the key performance parameters of a wireless cellular network, and its analytical as well as numerical evaluation has occupied many researchers. Recently, the…
We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…
Approximate outage probability expressions are derived for systems employing maximum ratio combining, when both the desired signal and the interfering signals are subjected to $\eta-\mu$ fading, with the interferers having unequal power.…
We consider arbitrary dense wireless networks, in which $n$ nodes are placed in an arbitrary (deterministic) manner on a square region of unit area and communicate with each other over Gaussian fading channels. We provide inner and outer…