The joint design of secure precoding and artificial noise (AN) transmission scheme is promising to improve secrecy performance. However, in downlink multi-user multiple-input multiple-output (MU-MIMO) systems with multiple eavesdroppers, joint design of secure precoding and AN structure involves several challenges: an objective function is non-convex and non-smooth, and a precoding matrix and AN matrix have different design principles. Classically, to jointly design precoding and AN covariance matrix, an alternating optimization approach is used which has limitations in terms of the secrecy rate performance since it does not offer joint and simultaneous optimization of the precoding and AN covariance matrices. In this paper, we propose a novel optimization framework that optimizes the precoder and the AN covariance matrix jointly and simultaneously to maximize the secrecy rate. First, we approximate the objective function to a tractable non-convex form. Next, we derive the first-order optimality condition by leveraging the nonlinear eigenvalue problem (NEP) form. Finally, we utilize an efficient technique with low computational complexity for identifying the major eigenvector of the NEP which corresponds to the best stationary point. Simulations illustrate that the proposed methods enhance the secrecy rate performance compared to the existing secure precoding methods.

Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.