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In this paper, we provide an information-theoretic analysis of a Gaussian multiple-input multiple-output multiple access channel (MIMO MAC) with imperfect channel knowledge at the receiver. In particular, we derive inner and outer bounds for the MIMO MAC rate region when the inputs are Gaussian. We then apply these bounds to a Gaussian interference network with receiver cooperation, in which a central processor with incomplete channel state information must jointly decode all the received signals. Then, in the case where the channel knowledge at the receiver is obtained through training signals, we derive the structure of the optimum training signals for all users under a definite and semidefinite rank constraint. Numerical results show that the bounds we derive can be quite tight, confirming the asymptotic analysis conducted for the finite case. Finally, we also investigate the low-SNR and high-SNR regimes, specifically analyzing the minimum required energy per information bit and the wideband slope region in the first case, and the high-SNR slope in the second.