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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 signal-to-noise ratio (SNR) designs of relay networks to the corresponding multiple-input-multiple-output (MIMO) scenarios, whereby the source, relays and destination comprise multiple antennas. We investigate maximum SNR solutions subject to power constraints and zero-forcing (ZF) criteria, as well as approximate MMSE equalizers with specified target SNR and power constraint at the receiver. We also maximize the transmission rate between the source and destination subject to power constraint at the receiver.