Nearest neighbor nodes and connectivity of wireless sensor networks with Poisson point process

The connectivity is vital to wireless sensor networks (WSNs), but power is constrained by the limited battery power in sensor nodes. So the trade-off between connectivity and power control becomes a critical problem in WSNs. In this paper we investigate nearest neighbor nodes of the two-dimensional WSNs with Poisson point process, which enables each node to find the 1^st(respectively, 2^nd and k^th) nearest neighbor node and adjust transmitting range according to local requirement, thereby it would contribute to the survival of overall network. And then we derive the probability expression of 1-connected (respectively, 2-connected and k-connected) network. Finally, we present the simulation results and discuss practical value for researchers in this domain.