Robust Minimax MSE Equalizer Designs for MIMO Wireless Communications With Time-Varying Channel Uncertainties

In this paper, we propose robust equalizers based on a minimax mean-squares-error (MSE) scheme for wireless multi-input-multi-output (MIMO) communications subject to time-varying channel uncertainties. We consider channel uncertainties within a neighborhood of the estimated channel matrix formed by placing a bound on the spectral matrix norm of channel estimation errors. First, we derive a linear-matrix-inequality (LMI) based solution to the targeted problem. Next, we modify the MSE cost function of the targeted problem and derive a guaranteed cost-based solution, which may save computational cost. Subsequently, channel uncertainty is partitioned into finite Markov-transitioned channel uncertainty states based on the least upper bound of the set of the tightest upper bounds on the matrix spectral norm of channel uncertainty. This leads to a multiple model-based minimax MSE approach. On this basis, a feasible equalizer can be obtained from a weighted combination of multiple over-guaranteed cost-based equalizers, each of which is designed with respect to a channel uncertain state. Simulation results show that a weighted combination of a moderate number of multiple over-guaranteed cost-based equalizers can achieve robust equalization effectively with superior MSE and bit-error-rate (BER) performance.