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In this paper, the authors consider the robust transceiver design with Tomlinson-Harashima Precoding (THP) for multihop Amplify-and-Forward (AF) Multiple-Input Multiple-Output (MIMO) relaying systems. THP is adopted at the source to mitigate the spatial inter-symbol interference and then a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. Based on the elegant characteristics of multiplicative convexity and matrix-monotone functions, the optimal structure of the nonlinear transceiver is first derived. Based on the derived structure, the optimization problem is greatly simplified and can be efficiently solved.
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