On the connectivity of underlay ad-hoc D2D networks

This paper studies the connectivity of multihop device-to-device (D2D) networks underlaying a cellular network. Firstly, we derive a closed-form expression of the upper bound of the connection probability for D2D underlay networks. The bound is proved to be tight for sufficiently large D2D user density. We then analyze the phenomenon of phase transition where the connection probability drops sharply from close to 1 to close to 0. The critical point and sharpness of the phase transition is closely related to the cellular user location, the D2D transmit power, the D2D user density, and the size of the cell. Finally, our analytical results are validated by extensive simulations.