A centralized cognitive radio (CR) network is proposed and its system capacity is studied. The CR network is designed with power control and multi-user scheduling schemes to support best-effort traffics under peak interference power constraints. We provide an analytical framework to quantify its system capacity, taking into account various key factors such as interference constraints, density of primary users, cell radius, the number of CR users, and propagations effects. Furthermore, closed-form formulas are derived for its capacities when only path loss is considered in the channel model. Semi-analytical expressions for the capacities are also given when more realistic channel models that include path loss, shadowing, and small-scale fading are used. The accuracy of the proposed analytical framework is validated by Monte Carlo simulations. Illustrated with a practical example, the provided analytical framework is shown to be useful for the strategic planning of centralized CR networks.