Distributionally Robust Collaborative Beamforming in D2D Relay Networks With Interference Constraints

In this paper, we consider a device-to-device (D2D) network underlying a cellular system wherein the densely deployed D2D user devices can act as wireless relays for a distant transceiver pair. We aim to devise a beamforming strategy for the relays that maximizes the data rate of the distant transceiver while satisfying interference constraints at the cellular receivers. Towards that end, we first formulate a beamforming problem whose solution is robust against the channel uncertainties in the relay-destination hop. Motivated by practical observations, we assume that the random channels in this hop follow unimodal distributions and propose a novel unimodal distributionally robust model to capture the channel uncertainties. Then, we extend the formulation so that it can also guard against the channel uncertainty in the source-relay hop under the worst case robust model. The resulting robust beamforming problem is generally non-convex and intractable. Therefore, we design an iterative algorithm, which is based on solving semidefinite programs, to find an approximate solution to it. Simulation results show that under mild conditions, our robust model significantly improves the throughput of D2D relay transmissions when compared with the conventional robust models that merely rely on the channels' moment information. It also outperforms the Bernstein-type inequality-based convex approximation, which assumes that the channel follows a Gaussian distribution.