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A single carrier pilot-assisted transmission scheme is considered in this letter. Specifically, we focus on the case of synchronous transmission where one pilot symbol is periodically inserted in the transmitted sequence on a time-division multiplexing basis. A new equalization scheme, where the knowledge of pilot symbols is exploited by the equalizer to generate an estimate of the noise affecting the symbol to be detected, is introduced and analyzed. The criterion used to compute the equalizer coefficients is the minimization of the mean-square error (MSE). The main result of our analysis is that the optimal pilot aided equalizer (PAE) can be decomposed as the cascade of a minimum MSE (MMSE) linear equalizer (LE) and a data-aided noise estimation filter. This result completes and extends the noise-predictive view of decision feedback equalization to general data-aided equalization. The performance of the proposed PAE is compared to that of theMMSE-LE and that of theMMSE decision feedback equalizer both for static and for fading channels.