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In this paper, the authors consider the design of Minimum Mean Square Error (MMSE) transceivers for non-regenerative multiuser Multiple-Input Multiple-Output (MIMO) relay systems, where the main challenge resides in the joint optimal design of the pre-coder to be used at the base station and the relaying algorithms. They propose the use of non-linear pre-coding techniques, such as Tomlinson-Harashima Pre-coding (THP) and Vector Pre-coding (VP), at the downlink relayed transmission scenario with the aim of outperforming the more common linear strategies. In order to reduce the computational cost of the proposed schemes, they propose a novel suboptimal matrix design approach for VP transmission.
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