  Device-to-device (D2D) communications have recently emerged as a novel
transmission paradigm in wireless cellular networks. D2D transmissions take
place concurrently with the usual cellular connections, and thus, controlling
the interference brought to the macro-cellular user equipment (UE) is of vital
importance. In this paper, we consider the uplink transmission of a tier of D2D
users that operates as an underlay for the traditional cellular network. Using
network model based on stochastic geometry, we derive the equilibrium
cumulative distribution function (CDF) of the D2D transmit power. Considering
interference-limited and relatively lossy environment cases, closed form
equations are derived for the power CDF. Finally, a tight closed-form
upper-bound for the derived power distribution is proposed, and the analytical
results are validated via simulation.
