In the paper, performance of multiuser multiple-input multiple-output eigenbeam-space division multiplexing (ESDM) systems in the downlink transmission is evaluated in both uncorrelated and correlated time-varying fading environments based on computer-generated data. In the ideal case, using the block diagonalization (BD) scheme, inter-user interference can be completely eliminated at each user; and using the E-SDM technique for each user, optimal resource can be allocated, and spatially orthogonal substreams can be obtained. In realistic environments, however, due to the dynamic nature of the channel and the processing delay at both the transmitter and the receiver, the channel change during the delay may cause existence of inter-user interference even if the BD scheme is used. In addition, the change may also result in large inter-substream interference and no longer lead the allocated data resource for each user to the optimal condition. As a result, system performance may be degraded seriously. To overcome the problem, we propose a method of channel extrapolation to compensate for the channel change. Applying our proposed method, simulation results show that much better system performance can be obtained than the conventional case.