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Cognitive radio network (CRN) has been proposed in recent years to solve the spectrum scarcity problem by exploiting the existence of spectrum holes. One of the important issues in a cellular CRN is how to efficiently allocate primary user (PU) spectrums without causing harmful interference to PUs. In this paper, we present a cross-layer framework which jointly considers spectrum allocation and relay selection with the objective of maximizing the minimum traffic demand of secondary users (SUs) in a cellular CRN. Specifically, we consider (1) CRN tries to utilize PU spectrums even when the CRN cell is not outside the protection region of the PU cell, and (2) cooperative relay is used in cellular CRNs to improve the utilization of PU spectrums. We formulate this cross-layer design problem as a mixed integer linear programming (MILP), and use LINGO to obtain the optimal solution. Compared with a simple channel allocation scheme, the numerical results show a significant improvement by using our method.