| We establish a theoretical basis for the analysis and design of energy-efficient wireless ad hoc networks. For a wireless ad hoc network in which every node is bounded in its energy supply, we define a new concept of network capacity called "bits-per-Joule capacity", which is the maximum total number of bits that the network can deliver per Joule of energy deployed into the network. We prove that, under the one-to-one traffic model, the bits-per-Joule capacity of a stationary wireless ad hoc network grows asymptotically as O(( N/log N)(q -1)/2), where N is the number of nodes deployed onto the surface of a sphere and q is the path loss exponent.; We examine the potential of commercial energy-limited wireless ad hoc networks to grow in the number of users. We introduce a dollars-per-Joule pricing system in which every node can charge any other node per Joule of energy that it spends on that node's traffic. We define the "core capacity region" of an energy-limited wireless ad hoc network to be the set of utility vectors that the network can achieve under a pricing system such that no subset of the nodes has an incentive to withdraw from the network. We show that the core capacity region is non-empty. We also show that in the core capacity region, an average utility growth of O(( N/log N)(q -1)/2) per user is feasible under the one-to-one traffic model. |
