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In this paper, we address the downlink cross-tier interference of cognitive femtocell networks, which is a unique bottleneck of femtocell network performance. In particular, a new joint access and power control scheme is proposed to mitigate the cross-tier interference, maximize system throughput and provide quality of service (QoS) guarantee for both macrocell users and femtocell users. Based on the cognitive radio technology, the access control scheme greatly improves the performance of cognitive users near to femtocells. The jointly designed distributed access and power control algorithm is solved by game theory. Simulation results demonstrate that the proposed joint cognitive access and power control scheme improved the network throughput and reduced the cross-tier interference under most of the practical scenarios.