This paper investigates the application of independent component analysis (ICA) on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless communication systems. We present first the ICA based blind equalization for MIMO OFDM systems, where the non-redundant linear precoding is employed to resolve the ambiguity in the ICA equalized signal and reduce peak-to-average power ratio (PAPR) of OFDM signal. Then we discuss the application of ICA to the blind compensation for both frequency-dependent and frequency-independent inphase/quadrature (I/Q) imbalance in MIMO OFDM systems. Simulation results show that the ICA based equalization approach provides a much better performance than that of the subspace method with significant PAPR reduction. In addition, the ICA based I/Q compensation approach outperforms not only previous methods, but also the case with perfect channel state information and no I/Q imbalance due to additional frequency diversity gains.