Outage Based Robust Relay Beamforming Problem in Multi-User Networks

In this paper, a robust relay beamforming problem has been dealt with by using the stochastic approach with imperfect knowledge of channel state information. Specifically, we have modeled the channel estimation error as a Gaussian random variable. Our objective is to minimize the total relay's transmit power subject to outage SINR constraint criterion at each receiver. We aim to establish approximate probabilistic SINR constrained formulations in the form of convex conic optimization problem. It is shown that the original robust problem is a nonconvex problem, but it can be relaxed to an SDP convex problem using the semi-definite relaxation technique. In this paper, we have compared our stochastic method with the worst-case robust method in terms of power consumption efficiency and complexity. Simulation results verify that our robust method outperforms the worst case approach.