Abstract: In MIMO-OFDM systems, data streams of multiple users can be simultaneously recovered up to a phase ambiguity when a VCMA criterion combined with a user decorrelation criterion is considered. Since a low complexity LMS algorithm is used in the iteration, the convergence speed and the steady state MSE performance become a contradiction. In this paper, a variable step size iteration method is proposed which has good performance in both convergence speed and steady state MSE. Moreover, the impact of channel noise on the tap refreshing process of the transverse filters is analyzed, and a simple method to remove the effect of noise is induced. As a result the convergence performance of the blind equalizer is further improved.