Abstract: Spectrum sensing is a fundamental task for cognitive radio. In cognitive radio networks, multiple secondary users work cooperatively to perform reliable detection of the primary user. How to fuse the sensing information from different secondary users is its key component. This paper focused on the cooperative detection with hard combination in centralized secondary networks, and discussed the popular k-out-of-m fusion rule. Different from those special cases of OR rule (k=1), Half-voting rule (k=m/2) as well as AND rule (k=m), this paper considered the scenario that k was arbitrary, and deduced a closed-form expression for the optimal value of k from minimizing the Bayesian cost point of view. Simulation results verified the closed-form expression, and demonstrated that the optimal k decreased as decision threshold, priori probability ratio of spectrum unavailability to spectrum idleness as well as impact factor ratio of missed detection to false alarm increased, and was more valuable in the scenarios with lower signal to noise ratios.