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We assess the impact of the channel and carrier frequency offset (CFO) estimation errors on the performance of single-carrier systems with MMSE linear equalizers. Performance degradation is caused by the fact that a mismatched MMSE linear equalizer is applied to channel output samples with imperfectly canceled CFO. We develop asymptotic expressions for the excess mean square error (EMSE) induced by the channel and CFO estimation errors. Under some realistic assumptions, we derive a simple EMSE approximation which reveals that performance degradation is mainly caused by the imperfectly canceled CFO. Furthermore, the EMSE is approximately proportional to the CFO estimation error variance, with the proportionality factor being independent of the training sequence. Thus, optimal training sequence (TS) design for CFO estimation is also highly relevant for joint channel and CFO estimation.