MMSE transmit optimization for multi-user multi-antenna systems

We address the problem of linear mean square error (MSE) transmitter design for point-to-multipoint multiuser systems, where the transmitter is equipped with multiple antennas and each of the independent receivers has a single antenna. This downlink scenario is more difficult to handle than its uplink counterpart, since all users are coupled by transmit filters and powers. Our main result is to show that downlink and uplink share the same normalized MSE achievable region under a sum power constraint. Thus, the problem of downlink transmitter design can be solved by focusing on an equivalent uplink problem, which has a more suitable structure and allows for efficient algorithmic solutions. As application examples, we solve the problem of minimizing the maximal normalized MSE of all users (fairness), and the problem of minimizing the sum of all normalized MSE (overall efficiency).