A Generalized Nash Equilibrium Approach for Robust Cognitive Radio Networks via Generalized Variational Inequalities

Resource sharing between primary users (PUs) and secondary users (SUs) in cognitive radio (CR) networks is built on strict interference limitations. However, such limitations may be easily violated by SUs using imperfect SU-to-PU channel state information (CSI). In this paper, we propose a robust decentralized CR network design by explicitly taking into account imperfect SU-to-PU CSI from a game theoretical perspective. We formulate the CR network design as a generalized Nash equilibrium problem (GNEP), where the SUs compete with each other over the resources made available by the PUs, who are protected by the robust aggregate interference constraints. We establish a framework-based generalized variational inequality (GVI) theory to analyze the formulated robust GNEP. It is shown that the solution to the robust GNEP can be obtained by solving a GVI, which can be addressed by a distributed pricing mechanism in the CR network, where the SUs play a priced NEP with given prices and the PUs are in charge of setting prices. Then, we propose distributed algorithms, along with their convergence properties, for the SUs to solve the priced NEP and for the PUs to update prices, respectively. We also provide an efficient method to compute the optimal transmit strategy of each SU via convex optimization.