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Cognitive radio has been recently proposed as a promising technology to improve the spectrum utilization. In this paper, we consider the spectrum sharing between a large number of cognitive radio users and a licensed user in order to enhance the spectrum efficiency. With the deployment of M antennas at the cognitive base station, an opportunistic spectrum sharing approach is proposed to maximize the downlink throughput of the cognitive radio system and limit the interference to the primary user. In the proposed approach, cognitive users whose channels are nearly orthogonal to the primary user channel are pre-selected so as to minimize the interference to the primary user. Then, M best cognitive users, whose channels are mutually near orthogonal to each other, are scheduled from the preselected cognitive users. A lower bound of the proposed cognitive system capacity is derived. It is then shown that opportunistic spectrum sharing approach can be extended to the multiple input/ multiple-output (MIMO) case, where a receive antenna selection is utilized in order to further reduce the computational and feedback complexity. Simulation results show that our proposed approach is able to achieve a high sum-rate throughput, with affordable complexity, when considering either single or multiple antennas at the cognitive mobile terminals.