Robust MSE precoder design for imperfectly known MIMO flat-fading channels

The paper considers a robust precoder design problem for multiple-input multiple-output (MIMO) flat-fading channels with imperfect channel knowledge at the transmitter. The robust design problem requires finding the optimal precoder minimizing the equalization mean-square error (MSE) for the least favorable channel located in a ball centered about the estimated channel. Lagrangian optimization is used to convert this min-max problem into a min-min convex minimization problem over a convex domain which is solved by interchanging the minimization order. The robust precoder and associated least favorable channel have an intuitive interpretation since the least-favorable channel zeroes out the weakest subchannels, and the robust precoder implements a pseudo-inverse only for the remaining subchannels.