  Heterogeneous cellular networks (HCNs) with millimeter wave (mmWave)
communications included are emerging as a promising candidate for the fifth
generation mobile network. With highly directional antenna arrays, mmWave links
are able to provide several-Gbps transmission rate. However, mmWave links are
easily blocked without line of sight. On the other hand, 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 mmWave and the cellular carrier band is needed. In this paper, we
first formulate the problem of the resource allocation among mmWave and the
cellular band for multiple D2D pairs from the view point of game theory. Then,
with the characteristics of cellular and mmWave 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.
