Secure amplify-and-forward relaying in linear chains with a single eavesdropper

The problem of secure unicast communication over multihop wireless relay networks with directed links in the presence of an eavesdropper is considered. In the existing literature this problem has been considered in one or both of the following two scenarios: (A) relay nodes employ relaying schemes, such as Decode-and-Forward (DF), (B) the source communicates with the destination over a two-hop relay network. We argue that computationally complex relaying schemes such as DF render end-to-end performance characterization intractable, without providing any performance guarantee in general channel and network scenarios. Therefore, we consider one of the simplest relaying scheme: Amplify-and-Forward (AF) that allows us to provide guarantees on the optimal performance over a wide range of channel conditions. A node performing AF-relaying scales and forwards the signal received at its input. Further, with AF-relaying the end-to-end performance characterization problem remains tractable for much larger class of networks than those that can be considered with other relaying schemes. The key contribution of this work is twofold. We first provide the optimal vector of scaling factors that maximizes the achievable AF secrecy rate, no matter which relay the eavesdropper listens to. Further, we prove that in high-SNR regime, the optimal AF secrecy rate thus achieved is within a constant gap from the cutset upper bound on the secrecy capacity.