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Most nonlinear transceiver designs in Amplify-and-Forward (AF) Multiple-Input-Multiple-Output (MIMO) relay systems assume that instantaneous perfect Channel State Informations (CSIs) are available. Transceiver design with imperfect CSIs has rarely been addressed. In this paper, the authors consider an AF MIMO system in which a Tomlinson-Harashima Pre-coder (THP) is used at the source, a linear pre-coder at the relay, and a Minimum-Mean-Squared-Error (MMSE) receiver at the destination. With the imperfect CSIs, they propose a new robust transceiver design method. It is shown that the optimization problem for the design is difficult due to the fact that the objective function is a nonlinear functions of the source and relay pre-coders and yet the constraints are coupled.
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