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According to the cognitive radio paradigm, a terminal or subsystem will opportunistically select a frequency band for data transmission. Because the spectrum is shared, a cognitive system may face interference that cannot be given a statistical description. An adversarial interference model may be appropriate for finding achievable rates under these conditions. In this work we investigate the benefit offered by using many antennas. In addition to adding spatial diversity and multiplexing gains, multiple antennas can allow a cognitive system to mitigate the effects of adversarial interference that is known to come from a system with fewer antennas.