Having multiple secondary users (SUs) can be exploited to achieve multiuser diversity and improve the throughput of the underlay secondary network. In the cognitive setting, satisfying the interference constraint is essential, and thus, a scheduling scheme is considered where some SUs are preselected based on the low interference power. From this subset, the SU that yields the highest throughput is selected for transmission. This scheduling scheme helps to lower the interference power while giving good throughput. For an independent but not identically distributed Nakagami-m fading channel, we obtain exact closed-form expressions of the capacity of this scheduling scheme. Furthermore, the scheduling time of SUs is characterized and closed-form expressions for the mean time after which a SU is selected for transmission are obtained. Numerical simulations are performed to corroborate the derived analytical results. Our results show that at low interference threshold, increasing transmit power of the SUs is not beneficial and results in reduced capacity. Furthermore, the channel idle time (i.e. time that no user is utilizing the channel) reduces with increasing the number of SUs.