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Relay networks have received considerable attention recently, especially when limited size and power resources impose constraints on the number of antennas within a wireless sensor network. In this context, signal processing techniques play a fundamental role, and optimality within a given relay architecture can be achieved under several design criteria. In this paper, we extend recent optimal minimum-mean-square-error (MMSE) and SNR designs of relay networks to the corresponding multiple- input-multiple-output (MIMO) scenarios, whereby the source, relays and destination comprise multiple antennas. We shall investigate maximum SNR solutions subject to power constraints and zero-forcing (ZF) criteria, as well as approximate MMSE equalizers with specified target SNR and global power constraint.