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In this letter, the problem of joint spectrum sensing and data transmission in a cognitive relay network is studied. An optimal power allocation (OPA) strategy is proposed to maximize the secondary throughput under both sensing performance and total power constraints. The OPA problem is transformed into seeking an optimal cognitive relay amplifying gain. Analytical and simulation results show that there indeed exists an optimal amplifying gain to achieve maximum secondary throughput under certain conditions. Furthermore, compared with equal power allocation (EPA), the throughput gain by OPA increases with the total power budget.