Pricing for Uplink Power Control in Cognitive Radio Networks

We study the pricing issue in a competitive cognitive radio network in which the secondary users strategically adjust their uplink transmission power levels to maximize their own utilities, and the primary service provider (e.g., base station) charges the secondary users on their transmitted power levels to enhance its own revenue. We model the competitive behavior of the secondary users as a non-cooperative game and address the existence and uniqueness of Nash equilibrium (NE). Based on the unique equilibrium, we formulate the pricing problem for the primary service provider as a non-convex optimization problem. We propose a sub-optimal pricing scheme in terms of revenue maximization of the primary service provider, and we claim that this scheme is not only fair in terms of power allocation among secondary users but that it is also efficient. We perform extensive numerical studies to verify the sub-optimality, fairness, and efficiency of the proposed pricing scheme and investigate the impacts of system parameters on the performance of the proposed pricing scheme.