2,048 research outputs found
A note on uniform power connectivity in the SINR model
In this paper we study the connectivity problem for wireless networks under
the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio
transmitters distributed in some area, we seek to build a directed strongly
connected communication graph, and compute an edge coloring of this graph such
that the transmitter-receiver pairs in each color class can communicate
simultaneously. Depending on the interference model, more or less colors,
corresponding to the number of frequencies or time slots, are necessary. We
consider the SINR model that compares the received power of a signal at a
receiver to the sum of the strength of other signals plus ambient noise . The
strength of a signal is assumed to fade polynomially with the distance from the
sender, depending on the so-called path-loss exponent .
We show that, when all transmitters use the same power, the number of colors
needed is constant in one-dimensional grids if as well as in
two-dimensional grids if . For smaller path-loss exponents and
two-dimensional grids we prove upper and lower bounds in the order of
and for and
for respectively. If nodes are distributed
uniformly at random on the interval , a \emph{regular} coloring of
colors guarantees connectivity, while colors are required for any coloring.Comment: 13 page
Beyond Geometry : Towards Fully Realistic Wireless Models
Signal-strength models of wireless communications capture the gradual fading
of signals and the additivity of interference. As such, they are closer to
reality than other models. However, nearly all theoretic work in the SINR model
depends on the assumption of smooth geometric decay, one that is true in free
space but is far off in actual environments. The challenge is to model
realistic environments, including walls, obstacles, reflections and anisotropic
antennas, without making the models algorithmically impractical or analytically
intractable.
We present a simple solution that allows the modeling of arbitrary static
situations by moving from geometry to arbitrary decay spaces. The complexity of
a setting is captured by a metricity parameter Z that indicates how far the
decay space is from satisfying the triangular inequality. All results that hold
in the SINR model in general metrics carry over to decay spaces, with the
resulting time complexity and approximation depending on Z in the same way that
the original results depends on the path loss term alpha. For distributed
algorithms, that to date have appeared to necessarily depend on the planarity,
we indicate how they can be adapted to arbitrary decay spaces.
Finally, we explore the dependence on Z in the approximability of core
problems. In particular, we observe that the capacity maximization problem has
exponential upper and lower bounds in terms of Z in general decay spaces. In
Euclidean metrics and related growth-bounded decay spaces, the performance
depends on the exact metricity definition, with a polynomial upper bound in
terms of Z, but an exponential lower bound in terms of a variant parameter phi.
On the plane, the upper bound result actually yields the first approximation of
a capacity-type SINR problem that is subexponential in alpha
A Unifying Framework for Local Throughput in Wireless Networks
With the increased competition for the electromagnetic spectrum, it is
important to characterize the impact of interference in the performance of a
wireless network, which is traditionally measured by its throughput. This paper
presents a unifying framework for characterizing the local throughput in
wireless networks. We first analyze the throughput of a probe link from a
connectivity perspective, in which a packet is successfully received if it does
not collide with other packets from nodes within its reach (called the audible
interferers). We then characterize the throughput from a
signal-to-interference-plus-noise ratio (SINR) perspective, in which a packet
is successfully received if the SINR exceeds some threshold, considering the
interference from all emitting nodes in the network. Our main contribution is
to generalize and unify various results scattered throughout the literature. In
particular, the proposed framework encompasses arbitrary wireless propagation
effects (e.g, Nakagami-m fading, Rician fading, or log-normal shadowing), as
well as arbitrary traffic patterns (e.g., slotted-synchronous,
slotted-asynchronous, or exponential-interarrivals traffic), allowing us to
draw more general conclusions about network performance than previously
available in the literature.Comment: Submitted for journal publicatio
The Topology of Wireless Communication
In this paper we study the topological properties of wireless communication
maps and their usability in algorithmic design. We consider the SINR model,
which compares the received power of a signal at a receiver against the sum of
strengths of other interfering signals plus background noise. To describe the
behavior of a multi-station network, we use the convenient representation of a
\emph{reception map}. In the SINR model, the resulting \emph{SINR diagram}
partitions the plane into reception zones, one per station, and the
complementary region of the plane where no station can be heard. We consider
the general case where transmission energies are arbitrary (or non-uniform).
Under that setting, the reception zones are not necessarily convex or even
connected. This poses the algorithmic challenge of designing efficient point
location techniques as well as the theoretical challenge of understanding the
geometry of SINR diagrams. We achieve several results in both directions. We
establish a form of weaker convexity in the case where stations are aligned on
a line. In addition, one of our key results concerns the behavior of a
-dimensional map. Specifically, although the -dimensional map might
be highly fractured, drawing the map in one dimension higher "heals" the zones,
which become connected. In addition, as a step toward establishing a weaker
form of convexity for the -dimensional map, we study the interference
function and show that it satisfies the maximum principle. Finally, we turn to
consider algorithmic applications, and propose a new variant of approximate
point location.Comment: 64 pages, appeared in STOC'1
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
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