Lattice reduction (LR) has been used widely in conventional multiple-input multiple-output (MIMO) systems to enhance the performance. However, LR is hard to be applied to the relay systems which are important but more complicated in the wireless communication theory. This paper introduces a new viewpoint for utilizing LR in multiuser MIMO relay systems. The vector precoding (VP) is designed along with zero force (ZF) criterion and minimum mean square error (MMSE) criterion and enhanced by LR

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... orithm. This implementable precoder design combines nonlinear processing at the base station (BS) and linear processing at the relay. This precoder is capable of avoiding multiuser interference (MUI) at the mobile stations (MSs) and achieving excellent performance. Moreover, it is shown that the amount of feedback information is much less than that of the singular value decomposition (SVD) design. Simulation results show that the proposed scheme using the complex version of the Lenstra--Lenstra--Lovász (LLL) algorithm significantly improves system performance.