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In this paper, a weighted space-time block-coding (STBC)-like matrix-wise block adaptive frequency-domain equalization (WSB-FDE), which has a flexibility over the STBC-like matrix-wise block length as compared to a normalized least-mean-square (NLMS)-FDE and a recursive-least-square (RLS)-FDE, is proposed for the cyclic-prefixed STBC single-carrier systems equipped with a diversity combining. In the WSB-FDE, the STBC-like matrix-wise block is first formulated from received blocks. The correction terms of the equalizer coefficients in each block are then updated so as to minimize a weighted squared-norm of the a posteriori error vector for the formulated block. Moreover, a square-root adaptive algorithm based on an unitary Givens rotation is proposed to achieve the numerical stability and computational efficiency in update procedure of the WSB-FDE. The theoretic convergence and the steady-state excess mean-square error (EMSE) of the WSB-FDE are analyzed, where it is observed that the EMSE decreases as the STBC-like matrix-wise block length and the number of antenna increase. Finally, the performance evaluation shows in a typical urban (TU) channel that the bit-error-rate (BER) performance of the WSB-FDE is superior to that of the RLS-FDE as the STBC-like matrix-wise block length increases.