Design and Performance Analysis of Wireless Network

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 rst 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 traÆc-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 allow