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In multiple antenna systems, channel estimation is a critical issue due to the large number of parameters to be estimated. For system analysis and design, it is of theoretical and practical relevance to derive a lower bound on the correlation matrix of the channel estimation error. We derive a lower bound that can be asymptotically attained for a large number of blocks in a block-fading channel. For two different frequency-selective channel models, the analytic bound is investigated for practical system settings through numerical results in order to show the impact of Doppler spectrum, spatial correlation, number of multipaths, and number of transmit/receive antennas on channel estimation performance.