Single-Carrier Systems With MMSE Linear Equalizers: Performance Degradation due to Channel and CFO Estimation Errors

We assess the impact of the channel and the 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. Assuming a single-block training, we develop an asymptotic expression for the excess mean square error (EMSE) induced by the channel and CFO estimation errors and derive a simple EMSE approximation which reveals the following: 1) performance degradation is mainly caused by the imperfectly canceled CFO and 2) the EMSE is approximately proportional to the CFO estimation error variance, with the factor of proportionality being independent of the training sequence. We also highlight the fact that the placement of the single-block training at the middle of the packet is a good practice.