A Convex Scheme for the Secrecy Capacity of a MIMO Wiretap Channel with a Single Antenna Eavesdropper

Security has traditionally been dealt with at layers higher than the physical layer but in the wake of 5G, security at all layers is necessary to deal with the variations in complexity of connected devices. Low power devices may use physical layer security as a solution, while other devices may use physical layer security to complement security at higher layers. One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. Multiple Input Multiple Output (MIMO) and Massive MIMO systems look likely to play a part in 5G, but the secrecy capacity for such systems is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available. This paper presents an optimisation scheme that enables us to determine the secrecy capacity of a MIMO system with a single eavesdrop antenna. It is shown that, for certain parameters, the presented scheme is a concave problem which can therefore be solved efficiently using existing convex optimisation software.