Some Capacity Results for Ad Hoc Networks

We present results on the capacity of ad hoc networks in two different settings. In the first, all nodes wish to communicate with a single common node, possibly using multiple hops, power control and time division. Bounds on the performance of the network are derived in the form of a capacity region, and it is shown that power control only marginally improves the performance. In the second setting, we develop a similar framework for the case when nodes wish to communicate with arbitrary collections of other nodes.