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Using multiple antennas at both the transmitter and receiver of a wireless communication system enables the system to increase its data rate and enhance its performance without the need to increase the transmitted power or the used bandwidth. The channel in such systems has multiple inputs which are the transmitted signals from different antennas, and multiple outputs which are the signals received using the receiver antennas. Systems that use this technique are called MIMO systems, and they have received so much attention recently (Shubhi, & Sanada, 2017), (Xu, Sugiura, Ng, Zhang, Wang, & Hanzo, 2017).
In general, there are two coding techniques used in MIMO systems. The first one is space-time diversity coding, and the second technique is Bell laboratories layered space-time (BLAST) coding. Space-time diversity coding is not suitable to transmit with high data rates, because it has a spatial rate 
, whereas the maximum achievable value of 
is 
which is the number of transmit antennas. Spatial rate 
is defined as the average number of symbols per unit time that are transmitted using 
antennas, it takes values from the interval 
depending on the coding scheme. The advantage of space-time diversity coding technique is that it provides the maximum available diversity order in MIMO systems which is equal to 
, where 
is the number of antennas at the receiver side.
BLAST coding technique has the ability to provide a communication with a very high data rate in wireless systems. It allows to increase the spectral efficiency of the system. BLAST systems can be implemented practically by converting the multi-dimensional decoding problem at the receiver side into multiple 1-D decoding processes (Foschini, 1996).
Turbo-BLAST (T-BLAST) is a MIMO system that uses BLAST coding technique. Its main idea is the application of the turbo principle in the detection of wireless MIMO systems. It is based on three main concepts. The first one is the BLAST architecture, which aims to increase the spectral efficiency of the system. The second concept is the random space-time interleaving whose purpose is to produce random-like codes and to get benefit of the available diversity in MIMO systems. This interleaver enables T-BLAST system to achieve a transmit diversity of order 
. The third concept is the turbo principle, which is an iterative decoding/detection technique used to enhance the performance of communication systems with low complexity. In the iterative turbo principle, the decoding problem is split into two main stages. Information that is learned from each stage is passed to the other stage after permuting it using interleavers (or deinterleavers). This “message passing” procedure is repeated for many times until the decoder converges or a maximum number of iterations is reached.