Secrecy graphs model the connectivity of wireless networks under secrecy
constraints. Directed edges in the graph are present whenever a node can talk
to another node securely in the presence of eavesdroppers. In the case of
infinite networks, a critical parameter is the maximum density of eavesdroppers
that can be accommodated while still guaranteeing an infinite component in the
network, i.e., the percolation threshold. We focus on the case where the
location of the nodes and the eavesdroppers are given by Poisson point
processes.
Mat\'ern hard core processes of types I and II are the point processes of
choice to model concurrent transmitters in CSMA networks. We determine the mean
interference observed at a node of the process and compare it with the mean
interference in a Poisson point process of the same density. It turns out that
despite the similarity of the two models, they behave rather differently. For
type I, the excess interference (relative to the Poisson case) increases
exponentially in the hard-core distance, while for type II, the gap never
exceeds 1 dB.
Lattices are important as models for the node locations in wireless networks
for two main reasons: (1) When network designers have control over the
placement of the nodes, they often prefer a regular arrangement in a lattice
for coverage and interference reasons. (2) If nodes are randomly distributed or
mobile, good channel access schemes ensure that concurrent transmitters are
regularly spaced, hence the locations of the transmitting nodes are well
approximated by a lattice.
Outage probabilities in wireless networks depend on various factors: the node
distribution, the MAC scheme, and the models for path loss, fading and
transmission success. In prior work on outage characterization for networks
with randomly placed nodes, most of the emphasis was put on networks whose
nodes are Poisson distributed and where ALOHA is used as the MAC protocol. In
this paper we provide a general framework for the analysis of outage
probabilities in the high-reliability regime.
We consider a two-hop cellular system in which the mobile nodes help the base
station by relaying information to the dead spots. While two-hop cellular
schemes have been analyzed previously, the distribution of the node locations
has not been explicitly taken into account. In this paper, we model the node
locations of the base stations and the mobile stations as a point process on
the plane and then analyze the performance of two different two-hop schemes in
the downlink.
We develop a new metric for quantifying end-to-end throughput in multihop
wireless networks, which we term random access transport capacity, since the
interference model presumes uncoordinated transmissions. The metric quantifies
the average maximum rate of successful end-to-end transmissions, multiplied by
the communication distance, and normalized by the network area.
We develop a new metric for quantifying end-to-end throughput in multihop
wireless networks, which we term random access transport capacity, since the
interference model presumes uncoordinated transmissions. The metric quantifies
the average maximum rate of successful end-to-end transmissions, multiplied by
the communication distance, and normalized by the network area.