Back to Publications of Piyush Gupta
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.