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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.
Date of Publication: May 2006