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In this paper, we consider blind channel estimation for cyclic-prefixed single-carrier (CP-SC) systems via second-order statistics only. By exploiting the existence of real symbols in the transmitted data block, we develop a simple technique for blind channel estimation that does not need redundant precoding or virtual carriers. Hence, the proposed algorithm provides bandwidth efficiency. A side benefit of the proposed algorithm is that the phase ambiguity, which is an inherent problem in traditional blind channel estimation, is reduced to sign ambiguity only. This side benefit facilitates signal detection in digital communications where symbols are usually taken from a finite alphabet. Although the proposed method is mainly developed for channel estimation in single-input-single-output CP-SC systems, it can also be applied straightforwardly to single-input-multiple-output systems (either with CP-SC or other kinds) and multiple-input-multiple-output systems whenever real symbols exist or are deliberately inserted in the transmission.