Robust Power Control for Cognitive Radio Networks with Proportional Rate Fairness

This paper studies the power control problem in cognitive radio networks where a primary user and multiple secondary users (SUs) coexist. Imperfect channel state information is considered. The objective is to maximize the SUs' sum rate while guaranteeing the proportional rate fairness among SUs. The problem under consideration is non-convex. By doing a transformation, it is equivalently changed to a second-order cone programming problem, which can be efficiently solved by existing standard methods. Simulations have been done to verify the network performance under different channel uncertainty conditions.