Linear precoding for spatially correlated multiple-input single-output wiretap channel

A precoding scheme for physical layer security of multiple-input single-output (MISO) wiretap channel with spatial correlation is designed. Quality-of-service (QoS) of the link is defined in terms of upper bounds on average symbol error rate function at Bob (legitimate user) and Eve (illegitimate user). Specifically, two problems are considered. First, a precoder matrix is designed to minimise the average transmitted power subject to QoS requirements at Bob and Eve. Next, we propose two algorithms to minimize QoS of illegitimate party for a given reliability level, depending on whether main user link has no correlation or is fully correlated. Our result for uncorrelated case demonstrate that by increasing the allocated power, main user can increase secrecy level up to an optimum point above which both legitimate and illegitimate receivers experience adequate QoS in their links. In fully correlated case, the problem is identified as an instance of concave minimisation over a polytope, and optimum power allocation is obtained via the widely known vertex enumeration algorithm. In both cases, our simulations validate the analysis significantly. The results confirm that linear precoding is able to trade average power against minimum achievable Eve performance.