Secrecy Sum-Rates for Multi-User MIMO Regularized Channel Inversion Precoding

In this paper, we propose a linear precoder for the downlink of a multi-user MIMO system with multiple users that potentially act as eavesdroppers. The proposed precoder is based on regularized channel inversion (RCI) with a regularization parameter alpha and power allocation vector chosen in such a way that the achievable secrecy sum-rate is maximized. We consider the worst-case scenario for the multi-user MIMO system, where the transmitter assumes users cooperate to eavesdrop on other users. We derive the achievable secrecy sum-rate and obtain the closed-form expression for the optimal regularization parameter alpha(LS) of the precoder using large-system analysis. We show that the RCI precoder with alpha(LS) outperforms several other linear precoding schemes, and it achieves a secrecy sum-rate that has same scaling factor as the sum-rate achieved by the optimum RCI precoder without secrecy requirements. We propose a power allocation algorithm to maximize the secrecy sum-rate for fixed alpha. We then extend our algorithm to maximize the secrecy sum-rate by jointly optimizing alpha and the power allocation vector. The jointly optimized precoder outperforms RCI with alpha(LS) and equal power allocation by up to 20 percent at practical values of the signal-to-noise ratio and for 4 users and 4 transmit antennas.