​Device-to-Device (D2D) communications underlying the cellular infrastructure is a technology that has recently been proposed as a promising solution to enhance cellular network capabilities: It improves spectrum utilization, overall throughput and energy efficiency while enabling new peer-to- peer and location-based applications and services. However, interference is the major challenge since the same resources are shared by both systems. Therefore, interference management techniques are required to keep the interference under control. In this work, in order to mitigate interference, we consider centralized and distributed power control algorithms in a one- cell random network model. Differently from previous works, we are assuming that the channel state information (CSI) may be imperfect and include estimation errors. We evaluate how this uncertainty impacts performances. In the centralized approach, we derive the optimal powers that maximize the coverage probability and the rate of the cellular user while scheduling as many D2D links as possible. These powers are computed at the base station (BS) and then delivered to the users, and hence the name ”centralized”. For the distributed method, the on-off power control and the truncated channel inversion are proposed. Expressions of coverage probabilities are established in function of D2D links intensity, pathloss exponent and estimation error variance.