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We propose a method of obtaining the autocorrelation matrix to improve the performance of the subspace-based channel estimation method. By exploiting the circulant property of the received signal, the proposed method reduces the number of received blocks required to satisfy the persistency of excitation (POE) criterion for the input and decreases the residual error which affects the accuracy of the noise subspace. To verify the proposed method, we derive the analytical method for evaluating the POE criterion for the input. In simulation results, we demonstrate the efficiency of the proposed method.