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In this letter, we address multiuser multi-hop multiple-input multiple-output (MIMO) relay communication systems with correlated MIMO fading channels. In particular, we consider the practical scenario where the channel fading is fast and thus the instantaneous channel state information (CSI) is only available at the destination node, but unknown at all users and all relay nodes. We derive the structure of the optimal user precoding matrices and relay amplifying matrices that maximizes the users-destination ergodic sum mutual information. Compared with existing works, our results are more general, since we address multiuser scenarios, consider MIMO relays with a finite dimension, and take into account the noise vector at each relay node.