On the Sensitivity of the Transmit MIMO Wiener Filter With Respect to Channel and Noise Second-Order Statistics Uncertainties

We consider the sensitivity of the transmit multiple-input multiple-output (MIMO) Wiener filter with respect to channel and noise second-order statistics (SOS) uncertainties. Using results from matrix perturbation theory, we derive second-order approximations to the excess mean-square error (EMSE) induced by using the channel or noise SOS estimates as if they were the true quantities. Assuming optimal training and sufficiently high signal-to-noise ratio (SNR), we develop simple and informative approximations to the EMSE, which indicate that the channel estimation errors are much more significant than the noise SOS estimation errors. Uncertainties due to channel time variations induce EMSE that increases with increasing SNR and asymptotically tends to a constant value.