This paper analyzes and simulates some ergodic capacities of several typical systems such as SISO, SIMO, MISO and MIMO, especially studies on the channel capacity for MIMO system. Then, the research on the effects of correlation on the capacity of MIMO systems is emphasized. The results of the analysis and Matlab simulation show that as the wireless space increases and the spread angle becomes smaller, the angle of arrival of the receiving signal will be vertical with the array, the capacity of the channel will roll-off. Also, the effect on capacity is negligible with a correlation coefficient between two antennas blow 0.3, but when the correlation coefficient is as large as 0.7, the capacity will fall significantly.