Most of the non-linear transceivers, which are based on Tomlinson-Harashima (TH) precoding and have been proposed in the literature for two-way relay systems, assume perfect channel state information (CSI). In this paper, a novel and robust TH precoding scheme has been investigated for two-way relay systems, with multiple antennas at the transceiver and relay nodes. We assume imperfect CSI and the channel uncertainty is bounded by a spherical region. The minimum mean square error at the destinations is used as the design criterion and we develop an iterative method to solve this nonconvex problem to obtain TH precoding matrices at the transmitter, linear precoding matrix at the relay and linear equalizer at the destination nodes, where each subproblem is convex. Simulations are provided to evaluate the performance and to validate the efficiency of the proposed scheme.
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