Internets in the sky: capacity of 3D wireless networks
Preeti Gupta, P. Ranjith Kumar · 2000
Consider n nodes located in a sphere of volume V m/sup 3/, each capable of transmitting at a data rate of W bits/sec. Under a protocol based model for successful receptions, the entire network can carry only /spl Theta/(WV1/3n2/3) bit-meters/sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible performance even assuming the node locations, traffic patterns, and the range/power/timing of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power/range, then each node only obtains a throughput of /spl Theta/(w/(nlog/sup 2/n)1/3) bits/sec, if the network is optimally operated. Similar results hold under an alternate physical model where a minimum signal-to-interference ratio is specified for successful receptions. The proofs of these results require determination of the VC-dimensions of certain geometric sets, which may be of independent interest.