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We consider cyclic prefixed single carrier and adaptive multicarrier transmission over a frequency selective channel. We compare the achievable bit rate for a target bit error rate. We analytically prove that the bit rate achieved with multicarrier transmission with adaptive modulation is always higher than that obtained with single carrier transmission when a one-tap frequency domain equalizer is used. We also show that the same adaptively loaded multicarrier scheme reaches the performance of single carrier transmission with a block decision-feedback equalizer.