Secrecy Capacity of Two-Hop Relay Assisted Wiretap Channels

Incorporating the physical layer characteristics to secure communications has received considerable attention in recent years. Moreover, cooperation with some nodes of network can give benefits of multiple-antenna systems, increasing the secrecy capacity of such channels. In this paper, we consider cooperative wiretap channel with the help of an Amplify and Forward (AF) relay in the middle of transmission to transmit confidential messages from source to legitimate receiver in the presence of an eavesdropper. In this regard, the secrecy capacity of AF relaying is derived, assuming the relay is subject to a peak power constraint. To this end, an achievable secrecy rate for Gaussian input assumption is derived. Then, it is proved that any rate greater than this secrecy rate is not achievable. To do this, the capacity of a genie-aided channel as an upper bound for the secrecy capacity of the underlying channel is derived, showing this upper bound is equal to the computed achievable secrecy rate with Gaussian input assumption. Moreover, the power allocation policy at the relay is formulated as a fractional quadratic problem, and the optimal solution is analytically derived. Accordingly, the corresponding secrecy capacity is compared to the Decode and Forward (DF) strategy which is served as a benchmark in the current work.