Random graph theory based connectivity analysis in wireless sensor networks with Rayleigh fading channels

Connectivity is an essential merit of wireless sensor networks. There has been great interest in exploring the minimum density of sensor nodes that is needed to achieve a connected wireless network. This becomes difficult when uncertain features increase, such as Rayleigh fading channels. In this paper, we describe a range-dependent model for sensor networks by using random graph theory, and study the connectivity problem with this model. We calculate the probability of an arbitrary node being isolated, and thus obtain the probability of the whole network being connected. By giving the required minimum density, our work can guide in designing of the wireless sensor networks with fading channels. Moreover, the numerical results shows that the fading effect would degrade the connectivity of the wireless sensor networks.