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In the space-time block-coded (STBC) single-carrier systems with a cyclic-prefix, decoupling and equalization procedures at the receiver require an exact channel impulse response (CIR). In this paper, we propose a weighted STBC-like matrix-wise block adaptive/iterative frequency-domain channel estimation (WSB-CE) that is operated iteratively by using soft information obtained from the SISO decoder. In the WSB-CE, the correction terms of the channel estimator coefficients in each block are calculated so as to minimize a weighted conditional squared norm of the a posteriori error vector in a weighted least-square (LS) sense. Our simulation results verify the superiority of the WSB-CE by comparing with an approximated modified recursive-least-square (RLS)-CE in the time-varying typical urban (TU) channel.