Robust MSE equalizer design for MIMO flat-fading channels in the presence of model uncertainties

This paper considers a robust mean-square error (MSE) equalizer design problem for flat-fading multiple-input multiple-output (MIMO) channels with imperfect channel and noise information at the receiver. When the channel state information (CSI) and the noise covariance are known exactly at the receiver, a minimum mean square error (MMSE) equalizer can be employed to estimate the transmitted signal. However, in actual systems, it is necessary to take into account channel and noise estimation errors. We consider here a worst-case equalizer design problem where the goal is to find the equalizer minimizing the equalization MSE for the least favorable channel model within a neighborhood of the estimated model. Lagrangian optimization is used to convert this min-max problem into a convex min-min problem over a convex domain which is solved by interchanging the minimization order.