Robust minimax equalizer design for wireless MIMO communications under time-varying channel uncertainties

In this paper, we consider the problem of a robust mean-square-error (MSE) equalizer design for wireless multi-input multi-output (MIMO) communication systems subject to channel matrix uncertainties. Our goal is to find the equalizer minimizing the MSE of the error symbol vectors under the worst channel uncertainty. As we show, the optimal minimax MSE equalizer can be formulated as a solution to a semidefinite programming problem (SDP). In addition, we derive a suboptimal solution for the problem, which may save computational cost as well as have comparable MSE performance, since the amount of computations in the SDP may grow rapidly as the MIMO dimension increases. We further partition the MIMO channel uncertainty range into finite Markov-transitioned channel uncertain states. On this basis, a feasible equalizer can be obtained from a weighted combination of either multiple quasi-optimal minimax MSE equalizers or multiple quasi-suboptimal minimax MSE 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 quasi-suboptimal minimax MSE equalizers can achieve robust equalization with satisfactory MSE performance as well as with superior bit-error-rate performance.