On Cooperative and Malicious Behaviors in Multirelay Fading Channels

Multirelay networks exploit spatial diversity by transmitting user's messages through multiple relay paths. Most works in the literature on cooperative or relay networks assume that all terminals are fully cooperative and neglect the effect of possibly existing malicious relay behaviors. In this work, we consider a multirelay network that consists of both cooperative and malicious relays, and aims to obtain an improved understanding on the optimal behaviors of these two groups of relays via information-theoretic mutual information games. By modeling the set of cooperative relays and the set of malicious relays as two players in a zero-sum game with the maximum achievable rate as the utility, the optimal transmission strategies of both types of relays are derived by identifying the Nash equilibrium of the proposed game. Our main contributions are twofold. First, a generalization to previous works is obtained by allowing malicious relays to either listen or attack in Phase 1 (source-relay transmission phase). This is in contrast to previous works that only allow the malicious relays to listen in Phase 1 and to attack in Phase 2 (relay-destination transmission phase). The latter is shown to be suboptimal in our problem. Second, the impact of CSI knowledge at the destination on the optimal attack strategy that can be adopted by the malicious relays is identified. In particular, for the more practical scenario where the interrelay CSI is unknown at the destination, the constant attack is shown to be optimal as opposed to the commonly considered Gaussian attack.