  This paper addresses the joint transceiver design for downlink multiuser
multiple-input multiple-output (MIMO) systems, with imperfect channel state
information (CSI) at the base station (BS) and mobile stations (MSs). By
incorporating antenna correlation at both ends of the channel and taking
channel estimation errors into account, we solve two robust design problems:
minimization of the weighted sum mean-square-error (MSE) and minimization of
the maximum weighted MSE. These problems are solved as follows: first, we
establish three kinds of MSE uplink-downlink duality by transforming only the
power allocation matrices from uplink channel to downlink channel and vice
versa. Second, in the uplink channel, we formulate the power allocation part of
each problem ensuring global optimality. Finally, based on the solution of the
uplink power allocation and the MSE duality results, for each problem, we
propose an iterative algorithm that performs optimization alternatively between
the uplink and downlink channels. Computer simulations verify the robustness of
the proposed design compared to the non-robust/naive design.
