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We consider a single user OFDM system that experiences time-varying and frequency selective channels. We study a training based scenario, where the channel is estimated based on pilots that proceed the transmission of the information bearing blocks, and then used to equalize the subsequent data blocks. In such a scheme, due to the time-varying channel, the BER increases as the index of the data block increases. Considering commonly used models for time-varying channels, we derive an analytical expression for the bit error rate as a function of the block index. The proposed analysis is important in optimizing the system performance, as it can be exploited at the transmitter to determine how often pilots need to be transmitted, or what kind of modulation should be used on each carrier in order to maintain a certain error level.