Distributed Spectrum Sensing in Cognitive Radio Networks with Fairness Consideration: Efficiency of Correlated Equilibrium

Cooperative spectrum sensing improves the reliability of detection. However, if the secondary users are selfish, they may not collaborate for sensing. In order to address this problem, Medium Access Control (MAC) protocols can be designed to enforce cooperation among secondary users for spectrum sensing. In this paper, we investigate this problem using game theoretical framework. We introduce the concept of correlated equilibrium for the cooperative spectrum sensing game among non-cooperative secondary users and formulate the optimization problem for the case where secondary users have heterogeneous traffic dynamics. We show that the correlated equilibrium improves the system utility, as compared to the mixed strategy Nash equilibrium. While maximizing system payoff is important, fairness is also equally important in systems with dissimilar users. In order to address fairness issue, we propose a new fair social welfare correlated equilibrium, which maximizes the system utility and ensures that the less well-off users do not starve. We employ a no-regret learning algorithm for distributed implementation of the correlated equilibrium. Finally, we propose a neighbourhood based learning algorithm and show that it achieves better performance than the no-regret algorithm.