Power allocation in D2D enabled cellular network with probability constraints: A robust Stackelberg game approach

In this paper, we develop a Stackelberg game with a non-uniform pricing in a two-tier network environment, where multiple device-to-device (D2D) users reuse the uplink spectrum resources of the cellular user (CU). Assuming that the base station (BS) is protected by pricing the interference from D2D users, we propose a Stackelberg game framework where BS and D2D users are treated as the leader and followers respectively. Besides, the channel state information (CSI) uncertainty in the actual communication environment is considered to be suppressed the interference fluctuation effects. Specifically, the probability constraint is included to optimize the user utility. The complex probability constraint is transformed to the deterministic form of the convex second-order cone constraint by a novel method. Furthermore, a norm approximation method is proposed to reduce the computational complexity. Finally, the analytical solution of Nash equilibrium is acquired to generate the best response to the leader and all followers. Simulation results show that the proposed scheme is more effective comparing to the algorithms without the CSI probability constraint.