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A novel decoder covariance optimization approach is proposed for jointly designing the minimum mean square error (MMSE) transceivers of downlink multicell multiuser multiple-input-multiple-output (MIMO) systems subject to general linear power constraints. Per-antenna power constraint (single cell or multicell), total power constraint (single cell) and per-cell power constraint (multicell) are presented as examples. With the source covariance matrices set as identity matrices and with the rank constraints on the decoders relaxed, the MMSE problem is reformulated as a convex optimization problem. The global optimum solution can then be found numerically by means of a primal-dual algorithm. Furthermore, the proposed approach is shown to be equivalent to another approach of ours, the newly developed generalized iterative approach when the decoder covariance optimization approach is applicable and when all decoders obtained from the MMSE design have full column rank. The global optimality and comparison of the two approaches are supported by numerical results.