We consider a point-to-multipoint cognitive radio network that shares a set of channels with a primary network. Within the cognitive radio network, a base station controls and supports a set of fixed-location wireless subscribers. The objective is to maximize the throughput of the cognitive network while not affecting the performance of primary users. Both downlink and uplink transmission scenarios in the cognitive network are considered. For both scenarios, we propose two-phase mixed distributed/centralized control algorithms that require minimal cooperation between cognitive and primary devices. In the first phase, a distributed power updating process is employed at the cognitive and primary nodes to maximize the coverage of the cognitive network while always maintaining the constrained signal to interference plus noise ratio of primary transmissions. In the second phase, centralized channel assignment is carried out within the cognitive network to maximize its throughput. Numerical results are obtained for the behaviors and performance of our proposed algorithms.