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We consider a network of cognitive users (also referred to as secondary users (SUs)) coexisting and sharing the spectrum with primary users (PUs) in an underlay cognitive radio network (CRN). Specifically, we consider a CRN wherein the number of SUs requesting channel access exceeds the number of available frequency bands and spatial modes. In such a setting, we propose a joint fast optimal resource allocation and beamforming algorithm to accommodate maximum possible number of SUs while satisfying quality of service (QoS) requirement for each admitted SU, transmit power limitation at the secondary network basestation (SNBS) and interference constraints imposed by the PUs. Recognizing that the original user maximization problem is a nondeterministic polynomial-time hard (NP), we use a mixed-integer programming framework to formulate the joint user maximization and beamforming problem …