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In cognitive radio (CR) systems, cognitive users can use the frequency bands when the primary users are not present. Hence, reliable detection of available spectrum is foundation of cognitive radio technology. To ensure unimpaired operation of primary users, cooperative spectrum sensing is needed. To reduce the network overhead of cooperative spectrum sensing, a novel cooperative spectrum sensing algorithm based on credibility is proposed. In particular, the close-form expressions for probability of detection and false-alarm are derived for the novel algorithm, and expression for the average overhead used for cooperation is given. The thresholds design method for the algorithm is also discussed. The conclusion is proved by computer simulations.