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Top1. Introduction
Wireless communication technology has profoundly changed the way we communicate. It is one of the most vibrant areas in the communication field today due to the confluence of several factors. First, there is a rapid evolution of cellular networks which embody a sophisticated communication systems concept. Additionally, there has been an exponential increase in demand for wireless connectivity driven mainly by cellular communication systems, and by wireless data applications. Therefore, technology such as MIMO communication have introduced new perspective on how to effectively communicate over the wireless channels.
To keep up with an exponential growth rate while providing a ubiquitous connectivity, academic researchers and industrial constantly need to propose solutions to sustain the current communication technology growth (Björnson et al., 2017).
In wireless communication system, the propagation channel is characterized by multipath propagation due to scattering phenomenon on different obstacle. In a rich urban area, signals bounce off obstacles (buildings, trees, etc.) and pursuing their way in different directions to their destination or to the receiver. The use of Multiple-Input Multiple-Output is often described by Spatial multiplexing.
In spatial multiplexing technique using MIMO system, multiple parallel data stream carries different data between transmitter and receiver, and therefore increases the data rate. The theoretical peak data rate is proportional to the minimum of the number of transmit and receive antennas.
The principles of operation of spatial multiplexing in an LTE system can be illustrated from Figure 1. Symbols travel from transmitter to the receiver antennas. In Figure 1, two channel transmitters have created four separate paths to the two channel receivers. From the receiver perspective, the signals can be represented, in real number, as:
(1)(2)
and 
are the signals sent from the two transmit antennas. 
and 
are the received signal from antenna 1 and 2. 
and 
represent the received noise and all type of interferences. 
illustrates the way in which the transmitted symbols get attenuated and phase shifted as they propagate to receive antenna 
from transmit antenna 
. Very often, all terms in the Equation (1) are complex. However, the use of complex number would make the example complicated and without adding too much extra information.