— We consider a resource allocation problem for spectrum sharing in cognitive radio networks. Specifically, we investigate the joint subchannel, rate and power allocation for secondary users which share, in a non-disruptive manner, some frequency bands with primary users using OFDM technology. We consider the resource allocation problem for downlink and take into account the maximum total power constraints of the base station and the power constraints determined by distributed spectrum sensing and scanning. We formulate a resource allocation problem as an optimization problem which achieves max-min rate sharing among users. We propose both integer program based optimal and suboptimal fast and low complexity approaches for the spectrum sharing problem. Numerical results are then presented for the proposed heuristics and compared with the optimal solution.