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The performance of multiple-input multiple-output (MIMO) systems using spatial multiplexing is analyzed under channel prediction errors. We derive exact closed-form expressions for the conditional and average bit error rate (BER) for both fixed and adaptive modulation. We apply our analysis to design a rate adaptation policy that optimally adapts antenna use between beamforming and spatial multiplexing. Our results indicate that the prediction error degrades BER in MIMO systems with spatial multiplexing much more than in MIMO systems with beamforming due to the self-interference that arises from channel coupling. In particular, if interference between eigenchannels is high, spatial multiplexing should not utilize the weakest eigenchannels. In our policy, beamforming is used when prediction error is high to avoid interference, whereas multiplexing is used when it is low to achieve the maximum multiplexing gain. We show that this policy improves performance over prior adaptive policies that have been proposed in the literature.