Optimal density and power allocation of D2D communication under heterogeneous networks on multi-bands with outage constraints

This paper analyzes the maximum achievable transmission capacity of the Device-to-Device (D2D) communication in heterogeneous networks with multi-bands. The heterogeneous networks contain one or several cellular systems, and D2D communication shares uplink resources with them. By utilizing stochastic geometry, the problem is formed as sum capacity optimization problem for D2D network with constraints that guarantee outage probabilities of both cellular and D2D transmissions. We find the optimal power allocation on each band has a remarkably simple nature: depending on the D2D pair density and outage constraint, it is equal to either the upper bound of transmit power or zero. Besides, we prove that the optimal D2D pair density only exist in a limited interval. Since the primal problem is non-convex, we propose a linear searching algorithm with computation complexity O(KN) compared to the complexity O(K^N+1) of exhaustive search (K is the number of pieces which the feasible region is divided according to some step size and N is the number of frequency bands). The simulation results prove the effectiveness of the proposed algorithm.