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This paper presents a joint resource allocation and interference avoidance algorithm for uplink transmissions in a multi-cell cognitive radio network (CRN), which overlays with a multi-cell primary network (PN). We consider a primary willingness based coexistent architecture. Primary base stations will broadcast pilot signals and interference margins to the CRN for interference channel evaluation and power control. The objective of the algorithm is to maximize the sum rate of cognitive radio cells without causing unacceptable interference to primary receivers, where Lagrangian duality based technique has been utilized to solve the maximization problem and jointly allocate the subchannels and power for each user. The fairness among users is considered within the joint resource allocation to guarantee that the instantaneous rate for each user is larger than a given minimum rate. Simulation results show the efficiency of our algorithm, which has good convergent performance. Moreover, compared to the conventional schemes, the proposed algorithm can satisfy the fairness well, and also obtain a large gain on cell-edge user throughput only with a small reduction in cell sum rate.