  This paper presents new results on linear transceiver designs in a
multiple-input-multiple-output (MIMO) link. By considering the minimal total
mean-square error (MSE) criterion, we prove that the robust optimal linear
transceiver design has a channel-diagonalizing structure, which verifies the
conjecture in the previous work \cite{JW_2011}. Based on this property, the
original design problem can be transformed into a scalar problem, whose global
optimal solution is first obtained in this work. Simulation results show the
performance advantages of our solution over the existing schemes.
