On the Sensitivity of the MIMO Tomlinson–Harashima Precoder With Respect to Channel Uncertainties

The multiple-input multiple-output Tomlinson-Harashima (MIMO-TH) precoder is a well-known structure that mitigates interstream interference in flat fading MIMO systems. The MIMO-TH filters are designed by assuming perfect channel state information (CSI) at both the transmitter and the receiver. However, in practice, channel estimates are available instead of the true channels. In this work, we assess the MIMO-TH performance degradation in the cases where the channel estimates are used as if they were the true channels. More specifically, we develop second-order and high-SNR approximations to the excess mean-square error (EMSE) induced by channel uncertainties, uncovering the factors that determine the MIMO-TH performance degradation in practice. Numerical experiments are in agreement with our theoretical developments.