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A discrete-time matrix transmission model is introduced for wideband multiuser multiple-input multiple-output (MIMO) transmission systems. The model is more general than existing ones in the sense that it incorporates correlated interference and noise by means of prewhitening. It allows a flexible treatment of users that may or may not be included in a joint detection process. On the basis of the matrix transmission model, conventional multiuser detection techniques are easily adapted for the multiuser MIMO case. It is shown that for certain types of interference, a linear matrix transmission model exists only for a real-valued notation. Moreover, the real-valued notation provides the possibility to include space-time block codes in the linear transmission model. In order to endorse the introduction of this particular matrix model, we show that the discrete-time transmission matrix immediately determines the capacity of the MIMO transmission system. Some simulation results based on optimum and suboptimum detection techniques indicate that the loss of performance due to the exclusion of users from joint detection is quite small.