On Minimizing the MSE in the Presence of Channel State Information Errors

We consider the uplink of a multiuser multiple input multiple output (MU MIMO) system, in which the base station acquires channel state information (CSI) for which the estimation error depends on the resources assigned to the uplink pilot symbols. For this system, we first derive the receiver that minimizes the mean square error (MSE) of the uplink detected data symbols, as opposed to the naïve receiver that does not minimize the MSE in the presence of CSI errors. We then derive a closed form expression for the MSE as a function of the employed pilot-to-data power ratio, number of antennas and the MU MIMO interference power. This expression allows us to gain the insight that the gain of using the actual MMSE receiver as opposed to the naïve receiver becomes particularly important when the number of BS antennas is large.