Device-to-device (D2D) communications underlying the cellular infrastructure are a technology that have been proposed recently 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 paper, in order to mitigate interference, we consider centralized and distributed power control algorithms in a one-cell random network model. Existing results on D2D underlay networks assume perfect channel state information (CSI). This assumption is usually unrealistic in practice due to the dynamic nature of wireless channels. Thus, it is of great interest to study and evaluate achievable performances under channel uncertainty. Differently from previous works, we are assuming that the CSI may be imperfect and include estimation errors. 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 the function of D2D links intensity, pathloss exponent, and estimation error variance. Results show the important influence of CSI error on achievable performances and thus how crucial it is to consider it while designing networks and evaluating performances.