Secrecy rate maximization for MIMO Gaussian wiretap channels with multiple eavesdroppers via alternating matrix POTDC

In this paper, we consider the problem of optimizing the transmit co-variance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convex difference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the co-variance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.