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Subcarrier based space processing was conventionally employed in Orthogonal Frequency Division Multiplexing (OFDM) systems under Multiple-Input and Multiple-Output (MIMO) channels to achieve optimal performance. At the receiver of such systems, multiple Discrete Fourier Transform (DFT) blocks, each corresponding to one receive antenna, are required to be used. This induces considerable complexity. In this paper, we propose a pre-DFT processing scheme for the receiver of MIMO-OFDM systems with space-time-frequency coding. With the proposed scheme, the number of DFT blocks at the receiver can be any number from one to the number of receive antennas, thus enabling effective complexity and performance tradeoff. Using the pre-DFT processing scheme, the number of input signals to the space-time-frequency decoder can be reduced compared with the subcarrier based space processing. Therefore, a high dimensional MIMO system can be shrunk into an equivalently low dimension one. Due to the dimension reduction, both the complexity of the decoder and the complexity of channel estimation can be reduced. In general, the weighting coefficients calculation for the pre-DFT processing scheme should be relevant to the specific space-time-frequency code employed. In this paper, we propose a simple universal weighting coefficients calculation algorithm that can be used to achieve excellent performance for most practical space-time-frequency coding schemes. This makes the design of the pre-DFT processing scheme independent of the optimization of the space-time-frequency coding, which is desirable for multiplatform systems.