Bits-per-Joule capacity of energy-limited wireless networks

For a wireless 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 deploved into the network. For a fixed network size, a finite number of information bits is delivered for each source-destination pair, under a fixed end-to-end probability of error constraint. We prove that under the one-to-one traffic model in which every node wants to send traffic to a randomly chosen destination node, the bits-per-joule capacity of a stationary wireless network grows asymptotically as Omega((N/log N)((q-1)/2)), where N is the number of nodes randomly deployed onto the surface of a sphere and q is the path loss exponent. Further, the length of the block codes used grows only logarithmically in N, which indicates manageable decoder complexity as the network scales. The fact that the bits-per-Joule capacity grows with the number of nodes contrasts sharply with the scaling laws that have been derived for throughput capacity and implies that large-scale deployments for energy-limited sensor and ad hoe networks may be suitable for delay-tolerant data applications.