Distributed geometric-programming-based power control in cellular cognitive radio networks

Power control is critical for wireless communications that allow spectrum sharing among secondary users and primary users. In this paper, we derive an optimal distributed power control strategy aiming at the total capacity maximization of secondary network with interference constraints to primary users. Due to the nonconvexity of system utility, geometric programming is introduced to transform nonconvex optimization problems into convex optimization problems. Furthermore, system utility is usually coupled which means each utility depends not only on its local variables but also on the variables of other utilities. We introduce auxiliary variables and extra equality constraints to transfer the coupling in utility to coupling in constraints. The solution of the proposed power control strategy is shown to be globally optimal and leads to excellent performance.