Near-Optimal Precoding Design for MIMO Gaussian Wiretap Channel under Power Constraint

We consider the optimal precoding design under power constraint for the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, and an eavesdropper, each equipped with arbitrary number of antennas. The transmitter has access to full channel state information (CSI) of the legitimate link and eavesdropper link. Such an optimization problem is non-convex and an analytical optimal solution is difficult to obtain. In this paper, by resorting to the majorization theory, we develop a theoretical upper bound on the secrecy capacity which is proved useful in evaluating existing sub-optimal methods. Our analysis shows that, given that the number of antennas at the eavesdropper is no less than that of the transmitter, the generalized singular value decomposition (GSVD)-based method proposed in [1], albeit generally non-optimal, provides a near-optimal solution to the MIMO wiretap precoding design in the high signal-to-noise ratio (SNR) regime. Numerical results are provided to corroborate our theoretical results.