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This paper considers a Multiple Input Multiple Output (MIMO) two-way relay channel, where two nodes want to exchange data with each other using multiple relays. An iterative algorithm is proposed to achieve the optimal achievable rate region, when each relay employs an Amplify and Forward (AF) strategy. The iterative algorithm solves a power minimization problem at every step, subject to minimum signal-to-interference-and-noise ratio constraints, which is non-convex, however, for which the Karush Kuhn Tuker conditions are sufficient for optimality. The optimal AF strategy assumes global Channel State Information (CSI) at each relay.
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