Optimal Price-Based Power Control Algorithm in Cognitive Radio Networks

Abstract

This paper investigates the price-based power control problem in the spectrum sharing cognitive radio networks. The primary user (PU) can admit secondary users (SUs) to access by pricing their interference power under the interference power constraint. We model the interaction between the PU and the SUs as a Stackelberg game. The revenue function of the PU is expressed as a nonconcave function of SU's transmit power by backward induction. Variable substitution is used to transform the nonconcave maximization problem into a concave maximization problem. Based on the equivalent concave maximization problem, a novel algorithm is proposed to find the optimal price for the PU to maximize its revenue. The optimal price of each SU is given as a closed-form expression with one parameter, which can be determined with the complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$O(K)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> is the number of the SUs. Furthermore, asymptotic analysis is exploited to derive the number of the admitted SUs at low and high interference-to-noise ratio. Simulation results show the effectiveness of the proposed algorithm in comparison with the nonuniform pricing algorithm.