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The performance of multiuser MIMO-OFDM downlink systems with block diagonalization (BD) depends on the accuracy of the channel state information (CSI) available at the transmitter (CSIT) to a great extent. In time-varying channels, the CSIT is always outdated due to an inherent time delay between the uplink channel estimation and the downlink data transmission in TDD systems. This will lead to drastic degradation in system capacity. In this paper, based on the analysis of the effect of the outdated CSIT on multiuser MIMO- OFDM downlink systems with BD method, two linear processing methods, BD with user selection at the transmitter and total MMSE decoder at the receiver (TBDUS-RTMMSE) and BD at the transmitter and partial MMSE decoder at the receiver (TBD-RPMMSE), are proposed to mitigate the effect. To fulfill them, a new pilot-sending architecture is introduced. Analysis and simulation results show that the two proposed methods can effectively reduce the impairment of the outdated CSIT and improve the system sum capacity in suitable time delay regions of the CSIT.