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This paper proposes new limited-feedback Channel State Information (CSI) calculation schemes for Zero Forcing (ZF)-precoded downlink Multi-User Multiple-Input Multiple-Output (MU-MIMO) systems. It is a common understanding that the feedback quantized by the codebook limits the performance of MU-MIMO. In this paper, through a quasi-ZF or a quasi-Minimum Mean-Squared Error (MMSE) weight, the channel matrix is transferred to one of the codebook vectors, based on which, the CSI is calculated. Thus, the quantization error is minimized. Meanwhile, the selection for the codebook vector guarantees the maximizing of the estimated Signal to Interference plus Noise Ratio (SINR). We verify that the proposed scheme obtains accurate feedback information, and the predicted weight can be the same as the optimal linear decoder as if the receiver knew all the precoder information that is fed-forward from the BS, as long as the number of antennas for each receiver equals that for the transmitter, and equals that for the total transmit data streams. Compared to the commonly used Precoding Matrix Index (PMI) based method, which uses rank-one single user (SU)-MIMO feedback, simulation results show that the proposed schemes achieve higher sum capacities in different scenarios. Moreover, since the weight can be directly used as the decoder, the feed-forward overhead is reduced.