Transmission strategies for the MIMO MAC with MMSE receiver: average MSE optimization and achievable individual MSE region

In this work, 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 normalized MSE and the individual MSEs of users. At first, we optimize the average normalized MSE with respect to the transmit covariance matrices of the users. Next, adaptive power allocation is applied to further minimize the average normalized MSE. This leads to the general average normalized MSE optimization under a sum power constraint. We analyze the optimization problems and their connections by their Karush-Kuhn-Tucker conditions. The covariance matrix optimization is solved by iteratively single-user average MSE optimization in which the interference is treated as noise. We develop an iterative algorithm that performs power allocation and covariance matrix optimization. In addition to this, we study the achievable MSE region. We show that the MSE region is convex for the two-user MIMO case. Furthermore, we characterize the optimum power allocation among the users with regard to the single-user range. We show that the user with the maximum singular value of its channel matrix is the first supported user. For low SNR values, the optimal strategy is to have the best user transmitting only. In addition, we derive the individual MSE using single-user MMSE detectors and study the fulfillment of MSE requirements.