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Practical multiple-input/multiple-output (MIMO) systems often do not have channel information at the transmitter and use receivers that are restricted linear front-end processing. Such constraints make it impossible to achieve the full "Log-Det" capacity. The channel capacity for such systems with exact channel knowledge at the receiver has been found previously. In this paper, we determine a new capacity bound for linear receivers that explicitly estimate the channel based on training data. Using optimum MMSE channel estimation, the resulting channel estimation error is effectively an additional noise source that leads to a reduced system capacity.