Robust MSE equalizer design for MIMO communication systems in the presence of model uncertainties

This paper considers a robust mean-square-error (MSE) equalizer design problem for multiple-input multiple-output (MIMO) communication systems 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. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and estimated channel models. 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. The robust MSE equalizer and associated least favorable channel model can then be obtained by solving numerically a scalar convex minimization problem. Simulation results are presented to demonstrate the MSE and bit error rate (BER) performance of robust equalizers when applied to the least favorable channel model.