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In cognitive radio (CR) networks, the channel sensing performance has significant impact on the throughput of the system. In this study, the authors formulate the spectrum sensing to maximise the total throughput of the system under some constraints on the interference to the primary users (Pus). The total throughput defined in this study accounts not only for the throughput achieved by the CR user but also by the PU over each subband. In the numerical results, the authors compare their proposed idea with the previous work which finds the threshold of the detector to maximise CR throughput.