Effective Coverage for the Connectivity of Magnetic Induction-Based Ad Hoc Networks

Magnetic induction (MI) is a promising technique for communications in the very harsh propagation conditions like underground or underwater, etc. In this paper we investigate the connectivity issue of MI ad hoc networks deployed in a three-dimensional space. The transmitting distance of MI covers a quasi- ellipsoid space other than a standard sphere space in a traditional wireless propagation case. We derive a closed-form expression for the effective coverage space of an MI node to evaluate the expectation of node degree. Moreover, the probability of node isolation is derived, which provides an upper bound of network connectivity probability. With these results, pairs of the critical transmitting magnetic momentum and node density can be obtained to keep the network connected with a probability close to one. Our analytic method provide a guidelines for future studies on MI networking.