Equilibrium Strategies and Social Welfare in Cognitive Radio Networks with Imperfect Spectrum Sensing

Spectrum sensing is essential in opportunistic cognitive radio (CR) systems for detecting primary users’ (PUs’) activities and protecting the PUs against harmful interference. By extending the perfect spectrum sensing in the literature to more realistic situations, a new random sensing error framework of secondary users (SUs) is proposed to study the SUs’ behavior so as to make the best benefit for the CR system in this paper. A novel queueing-game theoretical model is formulated first and then various system stationary performance measures are procured. Furthermore, the SU’s equilibrium joining strategies are obtained, the throughput of SUs is derived, and the CR system’s social welfare’s monotonous in terms of the sensing error and the SU’s request frequency are characterized. Particularly, three interesting but counterintuitive results are observed as below: (i) the expected delay for joining SUs can be non-monotone in their effective arrival rate; (ii) multiple equilibrium joining strategies of SUs can always exist; and (iii) the spectrum sensing error does not necessarily worsen the CS system’s social welfare, i.e., some sensing error in the system may possibly lead to more efficient outcomes in terms of throughput and social welfare. The results and observations offered in this paper are expected to extend spectrum sensing research in a more efficient way to better provide CR system services to various users.