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