Detectability of Symbol Manipulation by an Amplify-and-Forward Relay

This paper studies the problem of detecting a potential malicious relay node by a source node that relies on the relay to forward information to other nodes. The channel model of two source nodes simultaneously sending symbols to a relay is considered. The relay is contracted to forward the symbols that it receives back to the sources in the amplify-and-forward manner. However there is a chance that the relay may send altered symbols back to the sources. Each source attempts to individually detect such malicious acts of the relay by comparing the empirical distribution of the symbols that it receives from the relay conditioned on its own transmitted symbols with known stochastic characteristics of the channel. It is shown that maliciousness of the relay can be asymptotically detected with sufficient channel observations if and only if the channel satisfies a non-manipulable condition, which can be easily checked. As a result, the non-manipulable condition provides us a clear-cut criterion to determine the detectability of the aforementioned class of symbol manipulation attacks potentially conducted by the relay.