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In this letter, we investigate multiple-input multiple-output (MIMO) communications under energy harvesting (EH) constraints. In our considered EH system, there is one information transmitting (ITx) node, one traditional information receiving (IRx) node and multiple EH nodes. EH nodes can transform the received electromagnetic waves into energy to enlarge the network operation life. When the ITx node sends signals to the destination, it should also optimize the beamforming/precoder matrix to charge the EH nodes efficiently simultaneously. Additionally, the charged energy should be larger than a predefined threshold. Under the EH constraints, in our work both minimum mean-square-error (MMSE) and mutual information are taken as the performance metrics for the beamforming designs at the ITx node. In order to make the proposed algorithms suitable for practical implementation and have affordable overhead, our work focuses on the beamforming designs with partial CSI and this is the distinct contribution of our work. Finally, numerical results are given to show the performance advantages of the proposed algorithms.