Game-theoretic quorum-based frequency hopping for anti-jamming rendezvous in DSA networks

Establishing communications in a dynamic spectrum access (DSA) network requires the communicating parties to 'rendezvous' before transmitting their data packets. Frequency hopping (FH) is an effective rendezvous method that does not rely on a predetermined control channel. Recently, 'quorum-based' FH approaches have been proposed for asynchronous rendezvous in DSA networks. These approaches are highly vulnerable to jamming, especially when the attacker is an insider node (i.e., a compromised node). In this paper, we investigate the problem of two secondary users (SUs), a transmitter and a receiver, try to rendezvous in the presence of a third SU acting as a jammer. The jammer is aware of the underlying (quorum-based) rendezvous design. First, we consider the case when all SUs are time-synchronized and are aware of the 'rendezvous channel.' We formulate the problem as a three-player game between the transmitter, receiver, and jammer. The transmitter and receiver try to maximize the number of successful rendezvous slots, while minimizing the number of jammed rendezvous slots. The jammer has the opposite objective. We show that this game does not have a pure Nash equilibrium (NE). Accordingly, we formulate a simplified two-player game between the receiver and jammer (assuming a uniform strategy by the transmitter), and derive multiple pure NE strategies. Next, we study the case when the rendezvous channel is unknown and obtain the Bayesian NE. Finally, the asynchronous case is addressed by exploiting the 'rotation closure property' of quorum systems. Our numerical experiments show that uncertainty about the transmitter's strategy improves the anti-jamming rendezvous performance. They also show that the rendezvous performance improves if the receiver and jammer are time-synchronized, and also improves if the receiver and jammer have a common guess about the transmitter's strategy.