Optimal power allocation schemes for single-relay af wire-tap channels

This paper considers the wire-tap channel in which a source node communicates to a destination node with the help of a single amplify-and-forward (AF) relay and in the presence of an eavesdropper. The secrecy capacity and respective optimal power allocation scheme at the source and relay are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered. These include combinations of dual-hop, orthogonal AF and direct transmission schemes. To deal with the non-concave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes´ rule of signs. It is then shown that the power allocation strategies that maximize the secrecy rates can be obtained in closed form. Simulation results are finally provided to verify the optimality of the proposed schemes.