Robust beamforming with channel uncertainty for two-way relay networks

This paper presents the design of a robust beamforming scheme for a two-way relay network, composed of one multi-antenna relay and two single-antenna terminals, with the consideration of channel estimation errors. Given the assumption that the channel estimation error is within a certain range, we aim to minimize the transmit power at the multi-antenna relay and guarantee that the signal to interference and noise ratios (SINRs) at the two terminals are larger than a predefined value. Such a robust beamforming matrix design problem is formulated as a non-convex optimization problem, which is then converted into a semi-definite programming (SDP) problem by the S-procedure and rank one relaxation. The robust beamforming matrix is then derived from a principle eigenvector based rank-one reconstruction algorithm. We further propose a hybrid approach based on the best-effort principle to improve the outage probability performance, which is defined as the probability that one of two resulting terminal SINRs is less than the predefined value. Simulation results are presented to show that the robust design leads to better outage performance than the traditional non-robust approaches.