  Heterogeneous cellular networks (HCNs) with millimeter wave (mm-wave)
communications are considered as a promising technology for the fifth
generation mobile networks. Mm-wave has the potential to provide multiple
gigabit data rate due to the broad spectrum. Unfortunately, additional free
space path loss is also caused by the high carrier frequency. On the other
hand, mm-wave signals are sensitive to obstacles and more vulnerable to
blocking effects. To address this issue, highly directional narrow beams are
utilized in mm-wave networks. Additionally, device-to-device (D2D) users make
full use of their proximity and share uplink spectrum resources in HCNs to
increase the spectrum efficiency and network capacity. Towards the caused
complex interferences, the combination of D2D-enabled HCNs with small cells
densely deployed and mm-wave communications poses a big challenge to the
resource allocation problems. In this paper, we formulate the optimization
problem of D2D communication spectrum resource allocation among multiple
micro-wave bands and multiple mm-wave bands in HCNs. Then, considering the
totally different propagation conditions on the two bands, a heuristic
algorithm is proposed to maximize the system transmission rate and approximate
the solutions with sufficient accuracies. Compared with other practical
schemes, we carry out extensive simulations with different system parameters,
and demonstrate the superior performance of the proposed scheme. In addition,
the optimality and complexity are simulated to further verify effectiveness and
efficiency.
