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We investigate the design of optimal linear transceiver for multi-input-multi-output (MIMO) systems under channel mean feedback. We consider the case in which the receiver has perfect channel knowledge while the transmitter has only mean and variance information of the channel coefficients. We aim to minimize the mean square error of symbol detection by jointly designing the transmitter linear precoder and the receiver linear decoder. We present the optimal transceiver structure for any rank of channel mean matrix together with the sufficient and necessary conditions for optimal power loading. Furthermore, we provide a numerical optimal power loading strategy using water-filling principle, as well as one sub-optimal solution based on Jensen's inequality.