Novel power control algorithm by decomposed Geometric Programming method for CDMA cognitive radio networks

Traditionally, the frequency spectrum is licensed to users in a rigid manner where the licensee has the exclusive right to access the allocated band. However, an unlicensed (cognitive) user may share a frequency band with a licensed (primary) owner as long as the interference is below a certain threshold. This makes power control a critical important issue in these networks. In this paper, we consider a decentralized power control algorithm that satisfies the most two significant metrics in cognitive radio network, capacity of cognitive network and total interference to primary users. The problem might be formulated as a power optimization problem, where rate allocation and power control are modeled through the objective function in which each user utility depends not only on its variables but also on the variables of other user utilities. Geometric Programming (GP) Problem is used to convert nonconvex optimization problem to convex optimization problem by introducing auxiliary variables and adding extra equality constraints, thus transferring the coupling in the objective to coupling in the constraints, which can be decoupled by primal-dual decomposition method, then can be efficiently solved even with a large number of users. The benefits of the method are illustrated through numerical results.