Robust Relay Beamforming for Two-Way Relay Networks

We study the design of robust relay beamforming for two-way relay networks by considering channel feedback errors. Our objective is to maximize the minimum worst-case signal-to-noise ratios (SNRs) of two sources subject to a total relay power budget. We first decompose this non-convex problem into a series of relay power minimization problems under minimum SNR constraints by using bisection search. Then the relay power minimization problem is recast to a semidefinite programming relaxation (SDR) problem. A suboptimal but efficient solution is finally obtained for the original design. A necessary condition for the power minimization problem to be feasible is also given. For the special case with perfect channel state information, an alternative algorithm is introduced to find the optimal beamformer, which has lower complexity than the existing method.