On the optimal transmission strategy for the MIMO MAC with MMSE receiver

We study the multiuser multiple-input multiple-output (MIMO) multiple access channel (MAC) under the assumption that the base station performs linear multiuser minimum mean-square error (MMSE) detection. We derive the average sum MSE and minimize it under a sum power constraint with respect to the transmit covariance matrices of the users. Furthermore, we characterize the optimum power allocation among the users in regard to the single-user region. For low SNR values, the optimum strategy is to have only the best user transmitting at a time. The single-user region decreases with the number of receive antennas at the base station and with the number of users in the system. In addition, we derive the individual MSE using single user MMSE detectors and study the fulfillment of MSE requirements. We illustrate all theoretical results by numerical simulations.