  In this paper, we propose novel non-linear precoders for the downlink of a
multi-user MIMO system with the existence of multiple eavesdroppers. The
proposed non-linear precoders are designed to improve the physical-layer
secrecy rate. Specifically, we combine the non-linear successive optimization
Tomlinson-Harashima precoding (SO-THP) with generalized matrix inversion (GMI)
technique to maximize the physical-layer secrecy rate. For the purpose of
comparison, we examine different traditional precoders with the proposed
algorithm in terms of secrecy rate as well as BER performance. We also
investigate simplified generalized matrix inversion (S-GMI) and
lattice-reduction (LR) techniques in order to efficiently compute the
parameters of the precoders. We further conduct computational complexity and
secrecy rate analysis of the proposed and existing algorithms. In addition, in
the scenario without knowledge of channel state information (CSI) to the
eavesdroppers, a strategy of injecting artificial noise (AN) prior to the
transmission is employed to enhance the physical-layer secrecy rate. Simulation
results show that the proposed non-linear precoders outperform existing
precoders in terms of BER and secrecy rate performance.
