Hierarchical Mean Field/Stackelberg Game Power Control for D2D Cooperative Relaying Networks

Device-to-device (D2D) communications is widely adopted as the underlay to cellular primary networks. By reusing the licensed spectrum and directly transmitting to other nearby devices, D2D users can significantly enhance system spectrum efficiency. However, D2D communications usually faces the restrictions of short transmission distance and limited energy supply. Mutual interference among different devices increases energy consumption and exacerbates communication quality-of-service degradation. In this paper, we consider a dense D2D network where the D2D devices communicate using cooperative relaying. We propose a hierarchical game framework consisting of a Stackelberg game to model intra-tier interactions within each D2D link and a mean field game to model inter-tier interactions among different D2D links. A finite difference method is used to derive an optimal power control scheme, and numerical results are presented to demonstrate the performance of the proposed hierarchical power control scheme. We also make comparisons to a proportional power control scheme, where the experimental result shows clear advantage of the proposed hierarchical scheme.