It is widely believed that cognitive radio (CR) networks have an opportunistic nature and therefore can only support best-effort traffics without quality-of-service (QoS) guarantees. In this paper, we propose a centralized CR network that adopts interference averaging techniques to support QoS guaranteed traffics under interference outage constraints. In such a CR network, a CR user adaptively adjusts its transmit power to compensate for the channel loss, thereby keeping the receive signal power at the CR base station (BS) at a constant level. The closed-form system capacity of such a CR network is analyzed and derived for a single cell with one CR BS and multiple CR users, taking into account various key factors such as interference outage constraints, channel fading, cell radius, and locations of primary users. The accuracy of the theoretical results is validated by Monte Carlo simulations. Numerical and simulation results show promising capacity potential for deploying QoS-guaranteed CR networks in frequency bands with fixed primary receivers. Our work can provide theoretical guidelines for the strategic planning of centralized CR networks.