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In this paper, we consider the problem of blind channel estimation for multi-input, multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems via second order statistics (SOS) only. By an appropriate re-modulation on the received signal blocks, we find an effective way to apply the subspace based channel estimation for the cyclic prefix (CP) based MIMO-OFDM system when the number of the receive antennas is no less than the number of transmit antennas. Suitable relationships are built between the proposed algorithm and one existing technique (called ZPSOS in the future) for zero-padding (ZP) based MIMO-OFDM systems, thanks to the re-modulation considered. Consequently, many advantages could be directly inherited from ZPSOS, for example, robustness to channel order over-estimation, guaranteeing the estimation identiflability. By comparing these two algorithms, we found that they could provide similar channel estimation accuracy but the proposed method could beat the other in terms of bit error rate (BER). Moreover, adopting CP-based OFDM is compatible with many existing standards and applications, which shows great potential of our proposed algorithm.