Resource Allocation for Device-to-Device Communications Underlaying Heterogeneous Cellular Networks Using Coalitional Games

Heterogeneous cellular networks (HCNs) with millimeter wave (mm-wave) communications included are emerging as a promising candidate for the fifth generation mobile network. With highly directional antenna arrays, mm-wave links are able to provide several Gbps transmission rate. However, mm-wave links are easily blocked without line of sight. On the other hand, device to device (D2D) communications have been proposed to support many content-based applications and need to share resources with users in HCNs to improve spectral reuse and enhance system capacity. Consequently, an efficient resource allocation scheme for D2D pairs among both mm-wave and the cellular carrier band is needed. In this paper, we first formulate the problem of the resource allocation among mm-wave and the cellular band for multiple D2D pairs from the view point of game theory. Then, with the characteristics of cellular and mm-wave communications considered, we propose a coalition formation game to maximize the system sum rate in statistical average sense. We also theoretically prove that our proposed game converges to a Nash-stable equilibrium and further reaches the near-optimal solution with fast convergence rate. Through extensive simulations under various system parameters, we demonstrate the superior performance of our scheme in terms of the system sum rate compared with several other practical schemes.