Robust design of spatial Tomlinson-Harashima precoding in the presence of errors in the CSI

In this letter, we study spatial Tomlinson-Harashima. precoding (STHP) from an information theoretic point of view encompassing both the single and the multiuser scenarios. Since the performance of any communications precoding scheme relies on the quality of the channel state information (CSI) that is made available at the transmitter side, in this work we focus our attention on the analysis of the robustness of STHP in terms of rate loss when the CSI is imperfect. Precisely, we present a robust design of the set of moduli used in STHP and, consequently, of the corresponding power allocation, that maximizes the achievable rates for the worst-case errors in the CSI in the small errors regime.