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Based on the assumption that the transmitted symbols are independent and identically distributed (i.i.d), we develop a simple blind channel estimation technique for OFDM systems. Instead of using partial information from the signal covariance matrix, as done in previous works where a fixed precoder is used and channel is only estimated from one column of the signal covariance, our work jointly consider all entries in the signal covariance matrix, and is applicable for much general precoders. A design criteria of the precoders by which the performance can be greatly improved is provided, and the stochastic CramÃ©r-Rao Bound (CRB) is derived in a close form. The numerical results clearly show the effectiveness and the improvement of our proposed algorithm in reducing the estimation errors.