Price-based power control algorithm in cognitive radio networks based on monotone optimization

This paper considers a price-based power control problem in the cognitive radio networks(CRNs).The primary user(PU) can admit secondary users(SUs) to access if their interference powers are all under the interference power constraint. In order to access the spectrum, the SUs need to pay for their interference power.The PU first decides the price for each SU to maximize its revenue. Then, each SU controls its transmit power to maximize its revenue based on a non-cooperative game. The interaction between the PU and the SUs is modeled as a Stackelberg game. Using the backward induction, a revenue function of the PU is expressed as a non-convex function of the transmit power of the SUs. To find the optimal price for the PU, we rewrite the revenue maximization problem of the PU as a monotone optimization by variable substitution. Based on the monotone optimization, a novel price-based power control algorithm is proposed. Simulation results show the convergence and the effectiveness of the proposed algorithm compared to the non-uniform pricing algorithm.