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In cognitive radio (CR) networks, the radio access from opportunistic users depends on their capabilities to detect spectrum holes. Typically, the detection problem has been considered separately from the optimization of the transmission strategy. However, in a CR context, the detection phase has an impact on network efficiency as well as on the undesired interference generated towards licensed users. In this work, we consider the joint optimization of detection thresholds and power allocation across multichannel links, in order to maximize the aggregated opportunistic throughput, under a constraint on the interference generated towards the primary users.