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This letter addresses the beamforming issues for two way relay systems assuming that two source nodes S1 and S2 are equipped with single antenna each and relay node R with multiple antennas. We derive the optimal linear beamforming matrix at R in closed form based on convex optimization techniques, aiming to minimize the weighted mean squared error (MSE). To reduce complexity for implementation, two alternative relay schemes are also presented. In addition, all the proposed schemes' performance are analyzed and compared in terms of mean squared error (MSE) and computation complexity.