Optimal power allocation for MSE and bit-loading in MIMO systems and the impact of correlation

The optimal power allocation to minimize the mean square error (MSE) in MIMO systems with and without channel knowledge at the transmitter (Tx) is investigated. Furthermore, the impact of correlation is discussed. We show that, for MIMO systems with no channel knowledge at the Tx, correlation increases the MSE at the receiver. This does not hold in general when channel knowledge is available at the Tx. The optimum transmit solution can then be obtained by solving an MSE minimization problem. Based on this solution, we present a bit loading algorithm which matches the optimum power allocation with a set of finite modulation alphabets with the constraint to certain bit error rate requirements.