Connectivity of magnetic induction-based ad hoc networks

Magnetic induction (MI) has been proven to be an efficient wireless communication technique for overcoming the transmission challenges in some very harsh propagation environments, such as underground, underwater, etc. For a random distributed MI ad hoc network in a 3-D space composed of uniform medium, we propose a method for determining the required node density and transmitting power that creates an almost surely fully connected network. For which we involve an MI path-loss model and consider the effect of eddy currents, the effective coverage space and the expected node degree of an MI node are then calculated by a Lambert W-function-based integration. Finally, we propose optimized frequency selection methods for improving the connectivity of MI networks. In addition to an ideal frequency-switching optimization method, we provide for engineering applications a practical frequency-fixed optimization method, which is based on the gradient descent algorithm, where an improved initialization is used to reduce iterations.