Downlink sum-MSB transceiver optimization for linear multi-user MIMO systems

We address the problem of Mean Square Error (MSE) transceiver design for point-to-multipoint transmission in multi-user Multiple-Input-Multiple-Output (MIMO) systems. We solve the problem of minimizing the downlink sum MSE under a sum power constraint by jointly optimizing the linear transmitters and receivers. Our result is based on a "duality" between downlink and uplink MSE regions. It states that downlink and uplink share the same achievable MSE region under a sum power constraint. Thus, the problem of downlink design can be solved efficiently by focusing on an equivalent uplink problem.