A novel primary-secondary user power control game for cognitive radios

In cognitive radio networks, secondary users need to access the licensed spectrum while neither disturbing the transmissions of the primary users nor introducing much interference to other secondary users. Hence, proper power controlling is of paramount importance to ensure efficient system operation. The previous work on power control in cognitive networks mainly focuses on the interactions among a set of secondary users. The primary users' influence is rarely considered. In this paper, a new power control game model is formulated, by including the primary users into the player set of the game. The primary users are rewarded for sharing their licensed spectrum with secondary users by setting a reasonable interference cap for the secondary transmissions. However, we ensure a minimum required Quality of Service (QoS) for primary users by severely penalizing their utility if their required transmission quality is not met. Simultaneously, the secondary users achieve energy efficient transmissions while not introducing much interference to both the primary and other secondary users. We prove that the proposed cognitive power control game has a unique Nash equilibrium (NE). The numerical examples show that the proposed game theoretical power control algorithm can provide the secondary users with energy efficient transmissions and the primary users with reasonable monetary rewards, while not compromising their required QoS.