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We provide an analysis of the performance of maximum likelihood detection (MLD) over flat fading channels in a wireless multiple input-multiple output (MIMO) antenna system. A tight union bound with an asymptotic form on the probability of symbol error rate (SER) for MIMO MLD systems with two-dimensional signal constellations (such as QAM and PSK) is introduced. Using this analytic bound, the performance of the MIMO antenna system is demonstrated quantitatively with respect to channel estimation, constellation size, and antenna configuration.