Optimization for Outage Probability Constrained Robust Downlink Collaborative Beamforming

In this paper, we design an outage probability constrained robust collaborative beamforming approach for the distributed multi-relay network in the downlink, where the channel state information (CSI) available is imperfect. We aim to minimize the total transmit power of the relay nodes whilst keeping the outage probability at the destination node below the predefined threshold. Assuming that the CSI mismatches follow Gaussian distribution, the equivalent counterpart for the outage probability constraint on the required signal-to-noise-ratio (SNR) is given explicitly. We show that though the original optimization problem is non-convex thus very intractable, it could be optimally solved by using the well-known interior-point method together with an efficient one-dimension search. Simulation results reveal that our proposed approaches can guarantee the quality-of-service (QoS) in term of outage probability in statistical sense while the non-robust scheme fails to do so.