On the diameter of sensor networks

In space exploration, cooperative modulation techniques have been proposed for prolonging the life-time of sensor nodes within a multihop network. The desire to efficiently reduce the overall energy-per-bit of a node motivated this study on the hop diameter (synonymous to the number of hops in a path) of sensor networks. In this study, we analysed and found that when the number of transmissions are bounded by constants ≤ 20, the likelihood of successful broadcast is small. Using simulations, we observed that the diameter decreases very fast as the transmission radius increases. Another observation is that the largest connected component emerges when the transmission radius reaches 0.3√A, where A is the area containing the nodes. This may be used to determine the ideal amplification, although further simulations on larger networks could be helpful. We also found a large gap between the number of nodes required to populate the area, when all the nodes must be connected, or when only 90% of the nodes are connected.