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A unified framework is proposed for the minimum mean square error (MMSE) transceiver design of general multiple-transmitter-multiple-receiver (MTMR) multiple-input and multiple-output (MIMO) systems subject to general linear power constraints. Two novel approaches, the generalized iterative approach (GIA) and fast iterative approach (FIA), are proposed. The two proposed approaches, along with two convex optimization approaches, the transmit covariance optimization approach (TCOA) and decoder covariance optimization approach (DCOA), are included in the unified framework. The optimality of the approaches and the relationships between the approaches are shown.