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This letter proposes a resource allocation scheme to mitigate the effect of sensing errors in cognitive radio networks. When a spectrum sensor misses primary signals, the secondary transmission can be interfered with by the primary transmission, whereas the interference to the primary system can be limited to a tolerable level. To deal with this problem, we consider the utility for inaccurate sensing in the proposed resource allocation scheme. Simulation results show that a higher outage performance is achieved by the proposed scheme than the resource allocation scheme that does not consider the utility for inaccurate sensing.