  In this paper, we study two important metrics in multiple-input
multiple-output (MIMO) time-varying Rayleigh flat fading channels. One is the
eigen-mode, and the other is the instantaneous mutual information (IMI). Their
second-order statistics, such as the correlation coefficient, level crossing
rate (LCR), and average fade/outage duration, are investigated, assuming a
general nonisotropic scattering environment. Exact closed-form expressions are
derived and Monte Carlo simulations are provided to verify the accuracy of the
analytical results. For the eigen-modes, we found they tend to be
spatio-temporally uncorrelated in large MIMO systems. For the IMI, the results
show that its correlation coefficient can be well approximated by the squared
amplitude of the correlation coefficient of the channel, under certain
conditions. Moreover, we also found the LCR of IMI is much more sensitive to
the scattering environment than that of each eigen-mode.
