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The robustness of the linear minimum mean square error (LMMSE) channel estimator is studied with respect to the reliability of the estimated channel correlation matrix used for its implementation. The analysis is of interest in practical applications of multiple-input multiple-output (MIMO) systems, where a perfect estimate of the channel correlation matrix is not available. The channel estimation mean square error (MSE) is analytically analyzed assuming a general structure for the estimated channel correlation matrix used to implement the LMMSE channel estimator. The obtained results are successively detailed to the case of channel correlation matrices derived by sample correlation estimation methods. It is observed that the use of a coarse estimate of the channel correlation matrix can lead to a severe degradation on the LMMSE channel estimator performance, whereas the simpler least-square (LS) channel estimator may provide comparatively better results. Nevertheless, it is shown that a robust approach, although suboptimal, relies on implementing the LMMSE channel estimator by assuming transmissions over uncorrelated channels, since, with such an assumption, the resulting estimation MSE is certainly smaller than for the LS channel estimator.