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We consider the behavior of the transmit Wiener filter for broadcast channels with non-cooperating users under channel uncertainties. We derive a second-order approximation to the excess mean-square error (EMSE) induced by using a channel estimate as if it were the true channel. In the high SNR cases, we develop a simple approximation to the EMSE. It turns out that the EMSE is proportional to the minimum mean square error with the proportionality factor determined by the total transmit power and the length of the training block.