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.
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