Modeling the power allocation in dynamic spectrum access for cognitive radios as a generalized Nash equilibrium problem

The demand of radio resources like mobile phones and Internet services is dramatically increasing and inefficiency in the traditional allocation of electromagnetic spectrum is apparent. A novel paradigm for allocating resources is the Dynamic Spectrum Access, where primary and secondary users share the same frequency band. In this paper, in a Cognitive Radio context, we model the power allocation for secondary users coexisting in the same frequency band with primary ones as a Generalized Nash Equilibrium Problem. We develop a theoretic analysis showing existence and uniqueness of the Generalized Nash Equilibrium and convergence of the Best Response Algorithm to it. In practical implementations, the conditions we propose are natural (a lower and an upper bound for the Signal-to-Interference-plus-Noise-Ratio of the radio devices are involved) and easy to be locally verified by users, which just need the knowledge of the total interference they experience near their own receiver.