Methods for Optimal Transmission over MIMO Wiretap Channels

Abstract

We discuss the architecture of wireless multiple-input multiple-output (MIMO) channels with additive white Gaussian noise. The transmission optimization problem over covariance matrix for achieving MIMO channel capacity is reviewed under the assumption that the channel state information (CSI) is available from both the transmitter and the receiver. We also discuss several transmission strategies such as beamforming and water-filling algorithm. The information-theoretic approach to physical-layer security for wireless communications system is discussed. Physical-layer security which is different from cryptographic approach security is achieved by exploiting the physical-layer properties of wireless channel. The principal results and concepts in this field such as equivocation rate and secrecy capacity are reviewed. The wiretap channel model is considered. We mainly discussed the Gaussian MIMO wiretap channel and the methods for obtaining its secrecy capacity. The optimization problem for the secrecy capacity of Gaussian MIMO wiretap channel under total transmit power constraint is discussed. CVX, which is a modeling toolbox for solving convex optimization problems, is reviewed. The precision variable of CVX is also considered. The performances of CVX and Monte Carlo optimization are compared. Differential Evolution algorithm is used to compute the secrecy capacity of Gaussian MIMO wiretap channel. The case of weak eavesdropper is considered and the closed form solution based on the necessary KKT conditions is validated. The algorithm for general cases based on the linear approximation and reformulation of the original optimization problem is also investigated and validated. It has been verified that the lower bound and the upper bound of secrecy capacity can be obtained by such algorithm.