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Employing multiple antennas at both the transmitter and the receiver linearly boosts the channel capacity by min (nT , nR), where nT and nR are the number of transmit and receive antennas, respectively A. Telatar (1999). Multiple-Input Multiple-Output (MIMO) technologies are classified into three categories: (i) MIMO diversity, (ii) MIMO Spatial Multiplexing (MIMO-SM) and (iii) beamforming that will not be addressed here since it particularly deals with transmitter algorithms. MIMO diversity techniques are deployed to increase the reliability of communications by transmitting or receiving multiple copies of the same signal at different resource entities of the permissible dimensions, i.e., time, frequency, or space. In contrast, the target of MIMO-SM is to increase the capacity of the communication channel. To this end, independent symbols are transmitted simultaneously from the different transmit antennas. Due to its attracting implementation advantages, Vertical Bell Laboratories Layered Space-Time (V-BLAST) transmitter structure is often used in the practical communication systems P. Wolniansky, G. Foschini, G. Golden, and R. Valenzuela (1998). In 3GPP Long Term Evolution-Advanced (3GPP LTE-A) 3GPP (2009), the challenge of de-multiplexing the transmitted symbols via SM techniques, i.e. detection techniques, stands as one of the main limiting factors in linearly increasing system’s throughput without requiring additional spectral resources. The design of detection schemes with high performance, low latency, and applicable computational complexity is being a challenging research topic due to the power and latency limitations of the mobile communication systems M. Mohaisen, H.S. An, and K.H.Chang (2009).

From Linear Equalization to Lattice-Reduction-Aided Sphere-Detector as an Answer to the MIMO Detection Problematic in Spatial Multiplexing Systems