Transmission Capacity of D2D Communication Under Heterogeneous Networks with Multi-Bands

This paper analyzes the optimal density and power allocation for D2D (Device-to-Device) communication in heterogeneous networks on multi-bands with target of maximizing D2D transmission capacity. The heterogeneous networks contain one or several cellular systems, and D2D communication shares uplink resources with them. By utilizing stochastic geometry, it is formed as a sum capacity optimization problem for D2D network with constraints that guarantee outage probabilities of both cellular and D2D transmissions. Since the original problem is non-convex, we divide the proof into two steps: first we prove the power allocation problem is convex when the D2D density is fixed, which can be solved by lagrangian method; then we prove that the optimal D2D density exists in a semi-closed interval. We propose a linear searching algorithm based on the former conclusions: with discretizing the interval of D2D density, a series of solutions can be obtained by solving the optimization problem of each D2D density; hence the global optimal capacity can be selected from them. The simulation results demonstrate the effectiveness of the proposed algorithm and it also shows that optimal parameters of D2D transmission is affected by outage constraints as well as the interference from cellular systems.