5,748 research outputs found
Using Poisson processes to model lattice cellular networks
An almost ubiquitous assumption made in the stochastic-analytic study of the
quality of service in cellular networks is Poisson distribution of base
stations. It is usually justified by various irregularities in the real
placement of base stations, which ideally should form the hexagonal pattern. We
provide a different and rigorous argument justifying the Poisson assumption
under sufficiently strong log-normal shadowing observed in the network, in the
evaluation of a natural class of the typical-user service-characteristics
including its SINR. Namely, we present a Poisson-convergence result for a broad
range of stationary (including lattice) networks subject to log-normal
shadowing of increasing variance. We show also for the Poisson model that the
distribution of all these characteristics does not depend on the particular
form of the additional fading distribution. Our approach involves a mapping of
2D network model to 1D image of it "perceived" by the typical user. For this
image we prove our convergence result and the invariance of the Poisson limit
with respect to the distribution of the additional shadowing or fading.
Moreover, we present some new results for Poisson model allowing one to
calculate the distribution function of the SINR in its whole domain. We use
them to study and optimize the mean energy efficiency in cellular networks
Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks
Stochastic orders on point processes are partial orders which capture notions
like being larger or more variable. Laplace functional ordering of point
processes is a useful stochastic order for comparing spatial deployments of
wireless networks. It is shown that the ordering of point processes is
preserved under independent operations such as marking, thinning, clustering,
superposition, and random translation. Laplace functional ordering can be used
to establish comparisons of several performance metrics such as coverage
probability, achievable rate, and resource allocation even when closed form
expressions of such metrics are unavailable. Applications in several network
scenarios are also provided where tradeoffs between coverage and interference
as well as fairness and peakyness are studied. Monte-Carlo simulations are used
to supplement our analytical results.Comment: 30 pages, 5 figures, Submitted to Hindawi Wireless Communications and
Mobile Computin
HetHetNets: Heterogeneous Traffic Distribution in Heterogeneous Wireless Cellular Networks
A recent approach in modeling and analysis of the supply and demand in
heterogeneous wireless cellular networks has been the use of two independent
Poisson point processes (PPPs) for the locations of base stations (BSs) and
user equipments (UEs). This popular approach has two major shortcomings. First,
although the PPP model may be a fitting one for the BS locations, it is less
adequate for the UE locations mainly due to the fact that the model is not
adjustable (tunable) to represent the severity of the heterogeneity
(non-uniformity) in the UE locations. Besides, the independence assumption
between the two PPPs does not capture the often-observed correlation between
the UE and BS locations.
This paper presents a novel heterogeneous spatial traffic modeling which
allows statistical adjustment. Simple and non-parameterized, yet sufficiently
accurate, measures for capturing the traffic characteristics in space are
introduced. Only two statistical parameters related to the UE distribution,
namely, the coefficient of variation (the normalized second-moment), of an
appropriately defined inter-UE distance measure, and correlation coefficient
(the normalized cross-moment) between UE and BS locations, are adjusted to
control the degree of heterogeneity and the bias towards the BS locations,
respectively. This model is used in heterogeneous wireless cellular networks
(HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic
on the network performance. This network is called HetHetNet since it has two
types of heterogeneity: heterogeneity in the infrastructure (supply), and
heterogeneity in the spatial traffic distribution (demand).Comment: JSA
Connectivity in Sub-Poisson Networks
We consider a class of point processes (pp), which we call {\em sub-Poisson};
these are pp that can be directionally-convexly () dominated by some
Poisson pp. The order has already been shown useful in comparing various
point process characteristics, including Ripley's and correlation functions as
well as shot-noise fields generated by pp, indicating in particular that
smaller in the order processes exhibit more regularity (less clustering,
less voids) in the repartition of their points. Using these results, in this
paper we study the impact of the ordering of pp on the properties of two
continuum percolation models, which have been proposed in the literature to
address macroscopic connectivity properties of large wireless networks. As the
first main result of this paper, we extend the classical result on the
existence of phase transition in the percolation of the Gilbert's graph (called
also the Boolean model), generated by a homogeneous Poisson pp, to the class of
homogeneous sub-Poisson pp. We also extend a recent result of the same nature
for the SINR graph, to sub-Poisson pp. Finally, as examples we show that the
so-called perturbed lattices are sub-Poisson. More generally, perturbed
lattices provide some spectrum of models that ranges from periodic grids,
usually considered in cellular network context, to Poisson ad-hoc networks, and
to various more clustered pp including some doubly stochastic Poisson ones.Comment: 8 pages, 10 figures, to appear in Proc. of Allerton 2010. For an
extended version see http://hal.inria.fr/inria-00497707 version
Spatial networks with wireless applications
Many networks have nodes located in physical space, with links more common
between closely spaced pairs of nodes. For example, the nodes could be wireless
devices and links communication channels in a wireless mesh network. We
describe recent work involving such networks, considering effects due to the
geometry (convex,non-convex, and fractal), node distribution,
distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina
Wireless networks appear Poissonian due to strong shadowing
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 high variance, the statistics of the propagation loss of a single
user with respect to different network stations are invariant with respect to
their geographic positioning, whether regular or not, for a wide class of
empirically homogeneous networks. Even in perfectly hexagonal case they appear
as though they were realized in a Poisson network model, i.e., form an
inhomogeneous Poisson point process on the positive half-line with a power-law
density characterized by the path-loss exponent. At the same time, the
conditional distances to the corresponding base stations, given their observed
propagation losses, become independent and log-normally distributed, which can
be seen as a decoupling between the real and model geometry. The result applies
also to Suzuki (Rayleigh-log-normal) propagation model. We use
Kolmogorov-Smirnov test to empirically study the quality of the Poisson
approximation and use it to build a linear-regression method for the
statistical estimation of the value of the path-loss exponent
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