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In this study, the authors consider a cognitive radio scenario and focus on the spectrum efficiency of sensing-transmission protocols for a secondary dual-hop relay system. A straightforward dedicated sensing protocol is first considered as a benchmark, where sensing is performed in dedicated sensing periods at both the source (S) and the relay (R) before their respective transmissions. This, however, leads to a substantial loss in spectrum efficiency for the secondary system. In view of the spectrum efficiency loss in the dedicated sensing protocol, the authors propose an alternative approach, namely simultaneous sensing protocol. In this protocol, sensing is only performed at S, during the period when R transmits to destination (D), by cancelling out the self-interference component that is known a priori. The authors derive the closed-form expression of the average probability of detection for the proposed simultaneous sensing protocol. Furthermore, by deriving the average collision time and average utilisation time for both the dedicated and simultaneous sensing protocols, the authors show that the simultaneous sensing protocol significantly improves the spectrum efficiency for the secondary system and also achieves a higher overall spectrum utilisation of the spectrum band, compared to the dedicated sensing protocol.