#
Design and Performance Analysis of Wireless Networks

### Abstract

In this thesis we are concerned with the problems of data transport in
wireless networks. We study some issues related to the design and
performance evaluation of multihop wireless networks, also known as
*ad hoc networks*.
The first issue that we address is the power requirement for assuring
connectivity of wireless networks. Employing some results from
continuum percolation theory, we obtain a precise characterization of
the critical transmission range of nodes in a wireless network such
that the network is connected with probability approaching one as
the number of nodes increases.

We next analyze the traffic-carrying capacity of multihop wireless
networks. We show that under some noninterference models motivated by
current technology, the average throughput obtained by nodes in a
two-dimensional wireless network decreases as the reciprocal of the
square root of the number of nodes in the network. We also show that
a similar cube root law holds for three-dimensional wireless networks.
In doing so, we determine the Vapnik-Chervonenkis dimensions of
certain geometric sets, which may be of independent interest.

We also study wireless networks in a more information-theoretic
framework, which allows for more sophisticated receiver operation.
We construct a network information-theoretic scheme for obtaining
an achievable inner bound on the capacity region of a
network of nodes.

The last issue that we study is routing in wireless networks. We
propose a new routing algorithm, STARA, which employs a more
appropriate metric, the average delay along a path, instead of the
number of hops used in most existing algorithms. We also study
the steady-state behavior of STARA by mapping the communication
network into an electrical network.

We conclude with the results of a throughput scaling experiment
conducted on a network of laptops with wireless modems.

Back to Publications of Piyush Gupta