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Unlike point-to-point cognitive radio, where the constraint imposed by the primary rigidly curbs the secondary throughput, multiple secondary users have the potential to efficiently harvest the spectrum and share it among themselves. This paper analyzes the sum throughput of a multiuser cognitive radio system with multiantenna base stations, either in the uplink or downlink mode. The primary and secondary have N and n users, respectively, and their base stations have M and m antennas, respectively. We show that an uplink secondary throughput grows with m/N+1 log n if the primary is a downlink system, and grows with m/M+1 log n if the primary is an uplink system. These growth rates are shown to be optimal and can be obtained with a simple threshold-based user selection rule. In addition, we show that the secondary throughput can grow proportional to , while simultaneously the interference on the primary is forced down to zero, asymptotically. For a downlink secondary, it is shown that the throughput grows with in the presence of either an uplink or downlink primary system. In addition, the interference on the primary can be made to go to zero asymptotically, while the secondary throughput increases proportionally to . The effect of unequal path loss and shadowing is also studied. It is shown that under a broad class of path loss and shadowing models, the secondary throughput growth rates remain unaffected.