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In a cognitive radio (CR) network, cooperative spectrum sensing plays an important role in ensuring the quality of service (QoS) of primary users (PUs) and improving spectral utilization efficiency. Intuitively, the more secondary users (SUs) are involved in sensing, the more sensing accuracy the CR can achieve, whereas the more sensing overhead the SUs consume, the less throughput the CR network can achieve. In this paper, we investigate overhead-throughput tradeoff over fading channels in a cooperative CR network that consists of a number of the SUs employing energy detectors and a single decision fusion center. We propose a design strategy to maximize the throughput of the SU network by choosing appropriate sensing length and the number of the SUs reporting to a decision fusion center. Moreover, we extend our analysis to a two-stage cooperative sensing mechanism where the second-stage fine sensing is triggered whenever any SU reports the presence of a PU after the first-stage detection. Our numerical results show that compared with the single stage sensing, the two-stage sensing scheme achieves higher throughput via the reduction of the probability of false alarm.