This paper presents a study on multicast communications in cognitive radio networks (CRNs)using directional antennas. The objective is to maximize the throughput of the CRN. The spectrum is divided into multiple channels and licensed to the primary network. While the CRN is accessing the spectrum, the interference power is carefully controlled to avoid impacting the operation of the primary network. The mathematical model is presented and subsequently formulated as a mixed integer non-linear programming (MINLP) problem, which is non-deterministic polynomial-time hard. Therefore, a greedy algorithm is designed to approximate the optimal performance. The MINLP problem is then relaxed and an upper bound is developed. Simulation results are presented to compare the performance of the greedy algorithm and the upper bound, which demonstrates the efficacy of the greedy algorithm as well as the tightness of the upper bound. He previously worked at the Wireless Advanced Technology Laboratory, Bell Labs of Lucent Technologies. His research interests are in circuits and systems design for embedded computing, including computer architectures, reconfigurable computing, embedded systems, and wireless networks.Wirel. Commun. Mob. Comput. 2015; 15:260-275