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The authors present a blind channel estimation of cyclic prefix (CP) orthogonal frequency-division multiplexing (OFDM) systems with nonredundant precoding based on second-order statistics. The study analyzes first the mean square error for the estimation of the covariance matrix of the received symbols. We prove that, for high and medium signal-to-noise ratios (SNRs), the estimation error in the diagonal entries of the covariance matrix exhibits a lower error than that in the off-diagonal elements. This behavior holds for SNR values in digital communication. Contrary to general belief, we prove that the diagonal of this matrix can be used for channel estimation. Hence, we develop a novel algorithm that utilizes this result. We also develop a low-complexity version that provides acceptable results with reduced computational requirements. Finally, we analyze the covariance matrix and propose another new algorithm with noise suppression capabilities. Some experimental results for Rayleigh channels are included to support these conclusions. In addition, they illustrate better performance of the new methods, compared with previous proposals and with the Cramér-Rao bound (CRB).