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In this paper, we investigate the robust relay beamforming design for a multi-input multi-output (MIMO) two-way relay networks (TWRN) by considering imperfect and reciprocal channel state informations (CSIs). In order to maximize the sum-rate (SR) subject to the individual relay power constraint, we first equivalently convert the objective problem into a sum of the inverse of the signal-to-residual-interference-plus-noise ratio (SI-SRINR) problem. The SI-SRINR problem can be reformulated as a biconvex semi-definite programming (SDP) which employs bounded channel uncertainties as the worst-case model. Then, we convert residual-interference-plus-noise (RIN) and relay power constraints into linear matrix inequalities (LMIs). By this way, the objective problem can be tackled by the proposed efficient iterative algorithm. The analysis demonstrates the procedures of the proposed SI-SRINR robust design.

Sum-rate maximization and robust beamforming design for MIMO two-way relay networks with reciprocal and imperfect CSI