In this paper, we investigate the multiple-input multiple-output (MIMO) transceiver design under an interesting power model named mixed power constraints. In the considered power model, several antenna subsets are constrained by sum power constraints while the other antennas are subject to per-antenna power constraints. This kind of transceiver designs includes both the transceiver designs under sum power constraint and per-antenna power constraint as its special cases. This kind of designs is of critical importance for distributed antenna systems (DASs) with heterogeneous remote radio heads (RRHs) such as cloud radio access networks (C-RANs). In our work, we try to solve the optimization problem in an analytical way instead of using some famous software packages e.g., CVX or SeDuMi. In our work, to strike tradeoffs between performance and complexity, both iterative and non-iterative solutions are proposed. Interestingly the non-iterative solution can be interpreted as a matrix version water-filling solution extended from the well-known and extensively studied vector version. Finally, simulation results demonstrate the accuracy of our theoretical results.