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In this paper, we investigate the optimal power allocation strategy in the joint spectrum overlay and underlay cognitive radio network where a licensee and multiple unlicensed users coexist and operate in the same spectrum. We propose an optimal power allocation scheme which achieves the maximum system utility while satisfying the QoS requirement of SUs and interference constrains of the PU. Particularly, since the unlicensed users adopting the overlay strategy do not necessarily have perfect sensing knowledge regarding the licensee, we modify the optimal power allocation scheme with the imperfect sensing knowledge. Moreover, we propose a QoS sensitivity based admission control algorithm to deal with the case that the optimal power allocation scheme is infeasible. The simulation results show that the proposed algorithm achieves better performance.