The novel fast iterative approach (FIA), transmit covariance optimization approach (TCOA) and decoder covariance optimization approach (DCOA) are proposed for jointly designing the minimum mean square error (MMSE) precoder and decoder of single-user multiple-input and multiple-output (MIMO) systems subject to general power constraints. Specifically, the total power constraint and the more practical per-antenna power constraint are discussed. With the rank constraint on the precoder or decoder relaxed, both the TCOA and DCOA are shown to yield the global optimum solution. The FIA is also shown to provide the global optimum solution when the transmit covariance matrix is full rank (equivalent to the TCOA) and/or the decoder covariance matrix is full rank (equivalent to the DCOA). These three approaches form a unified framwork for MMSE transceiver designs for both single-user and multiuser MIMO systems. The global optimality and comparison of the proposed three approaches are supported by numerical results.