The invention of cognitive radio concept is aimed to overcome the spectral scarcity issues of emerging radio systems by exploiting under-utilization of licensed spectrum. In cognitive radio networks, unlicensed users, which are referred to as cognitive radios (CRs), are allowed to dynamically access the frequency bands when licensed users (primary users) are inactive. Determining how to allocate unused frequency bands among CRs is one of the most important problems in cognitive radio networks. In this paper, a non-cooperative game theoretic framework to jointly allocate power and frequency bands among CRs in cognitive radio networks is proposed. The proposed game is proved to be an exact potential game, which will finally converge to Nash equilibrium by following the best response dynamics. Determining the best response strategy of each cognitive radio based on the observed opponent strategies is also provided in this paper. From the simulation, it can be seen that the resources have been shared fairly among all CRs.
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