Outage protection for cellular-mode users in device-to-device communications through stochastic optimization

In device-to-device (D2D) communications, the stochastic nature of the wireless channel causes the coexistence problem between cellular-mode and D2D-mode users a nontrivial task, especially when protection of cellular-mode users is strictly required. While related work has investigated the interference management problem in different scenarios, most approaches have considered only the long-term channel gain without explicitly addressing the randomness of the channel. In this paper, we aim to investigate the problem of D2D-mode users sharing the same radio resource blocks with the cellular-mode user under Rayleigh channel fading through stochastic optimization. Our objective is to determine the transmission powers of all D2D-mode users for optimizing their sum data rates while ensuring the outage probability of data sent by the cellular-mode user to stay below the desired protection threshold. We first introduce a new technique to transform both the objective and constraint functions involving random variables into equivalent yet deterministic forms. Since the formulated problem is non-linear and non-convex, we further tighten the upper bound of the transmission power constraint to reduce the complexity and uncertainty of searching for the optimal solution. To solve the formulated problem, we propose two different algorithms: the first algorithm reformulates and solves the problem as a linear programming (LP) problem while the second algorithm directly solves the non-linear problem based on the meta-heuristic of differential evolution (DE). Simulation results demonstrate that using the proposed algorithms the outage probability of the cellular-mode user can be maintained below the desired threshold despite the uncertainty of channel conditions, while the sum rate of D2D-mode users outperforms baseline methods under the same constraint.