Distributed power control based on convex optimization in cognitive radio networks

We consider the power efficiency optimization problem in the cognitive radio (CR) networks under both the average packet delay constraints of each CR transmitter (CR-Tx) and the interference constraint at primary receiver (PU-Rx). We propose a cooperative approach to make each CR-Tx know the interference level at the PU-Rx when there is no central control node in the network and no assistant sensors are deployed to do the interference measuring jobs. The power control problem is proved to be a convex problem. Since the powers of CR-Tx nodes are coupled in constraints, we apply the Lagrange relaxation of the coupling constraints method and construct the subgradient iterative algorithm to solve the dual problem in a distributed way. To reduce the payload of the message exchange at each iterative process, an improved algorithm is proposed that could be implemented through Lagrange dual decomposition. Numerical results show that the two algorithms can converge very fast. When the delay constraints of CR users are not very small, it is better to apply the improved algorithm which has a good performance but with a much lower complexity.