Low-complexity robust relay optimisation for multiple peer-to-peer beamforming: a safe tractable approximation approach

In this study, the authors present a novel outage-based approach for distributed multiuser relay beamforming problem which can provide robustness against channel uncertainty. They assume all the channels are subject to Gaussian perturbation. The relay beamforming design is based on stochastic performance optimisation and has been shown to provide an excellent robustness against channel uncertainty. The robust problem aims to minimise the total power transmission of the relays that are subject to the probability of each receiver's signal-to-interference noise ratio (SINR) do not fall below a given outage-probability specification. The underlying goal is to establish approximate probabilistic SINR constrained formulations in the form of convex conic optimisation problem. They show that the aforementioned problem is non-convex, in general. They develop two novel conservative approximation schemes for handling non-convex probabilistic constraint. Simulation results show the robustness of the proposed methods significantly improves the existing methods, both in terms of the solution quality and the computational complexity.