The authors present a blind channel estimation of cyclic prefix (CP) OFDM systems with non-redundant 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 signalto-noise ratios (SNRs) the estimation error in diagonal entries of the covariance matrix exhibits a lower error than that of the offdiagonal 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. Also, they illustrate the better performance of the new methods compared to previous proposals and to the Cramér−Rao bound. Index Terms-Blind channel estimation, OFDM, nonredundant precoding, cyclic prefix (CP), variance of the estimation of a covariance matrix, Cramér−Rao bound (CRB).