Analysis of Tomlinson–Harashima Precoding in Multiuser MIMO Systems With Imperfect Channel State Information

Tomlinson–Harashima precoding (THP) is a successive pre-equalization technique that arranges all the receivers into a group of layers and then suppresses the interlayer interference in sequence at the transmitter. There are two basic THP structures according to the positions of the diagonal weighted filter—decentralized at the receivers or centralized at the transmitter—which are denoted dTHP or cTHP, respectively. In this paper, the investigation of THP in downlink multiuser multiple-input–multiple-output (MIMO) systems with imperfect channel state information (CSI) is performed. The interference power caused by imperfect CSI is first derived, and then, the comparison between the two basic THP structures and the linear zero-forcing (ZF) precoding is carried out in terms of the interference power and the system capacity. Furthermore, the cases with different CSI errors among users are considered, through which the independence of the interference power among layers or subchannels is presented, including the cases with single-antenna and multiantenna receivers. Analytical and simulation results indicate that with imperfect CSI, THP leads to less interference power than linear-ZF, and dTHP leads to larger system capacity than cTHP and linear-ZF.