We investigate the effects of fading correlations on wireless communication systems employing multiple antennas at both the receiver and the transmitter side of the link, so called multiple-input multiple-output (MIMO) systems. The use of multiple antennas for wireless communication system has gained overwhelming interest during the last decade- both in academia and industry. Multiple antennas can be used in order to accomplish a multiplexing gain , diversity gain or antenna gain. thus , enhancing the bit rate , error performance or the signal-to-noise-plus-interference ratio of wireless system, respectively. With an enormous amount of yearly publications , the field of multiple antenna systems , often called MIMO systems, has evolved rapidly. Desired attributes can be obtained like significant increase in spectral efficiency and data rates ,high Quality–of–Service (QoS)-bit error rate , wide coverage , low deployment , maintenance and operation cost.The objective of this literature survey is to provide non specialist working in the general area of digital communication with a comprehensive overview of this exciting research field.