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In this paper, a weighted element-wise block adaptive frequency-domain equalization (WEB-FDE) is proposed for a single-carrier system with the cyclic-prefix. In the WEB-FDE, the one-tap equalizer corresponding to a frequency-bin first preserves input DFT elements (element-wise block). Its coefficient in each block is then calculated by minimizing a weighted squared norm of the a posteriori error. Simulation results in a time-varying typical urban (TU) channel show that the bit-error-rate (BER) performances of the WEB-FDE outperform those of the normalized least-mean-square (NLMS)-FDE and recursive-least-square (RLS)-FDE.