In this work, we introduce the notion of the diversity gain region for a multi-user channel. This region specifies the set of diversity-gain vectors that are simultaneously achievable by all users in a multi-user channel. This is done by associating different probabilities of error for different users, contrary to the traditional approach where a single probability of system error is considered. We derive an inner bound (achievable region) and an outer bound for the diversity gain region of a MIMO fading multiple access channel. We also show that the DGR inner bound and DGR outer bound are indeed tight for some operating points inside the MGR.
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