In recent years, orthogonal frequency division multiplexing (OFDM) has emerged as a promising air-interface technique for various wireless communication systems. OFDM allows the use of different modulation schemes for different sub carriers or even for different users according to the specific signal to noise ratio (SNR) scenarios. The concepts of multiple input multiple output (MIMO) have been under development for many years for both wired and wireless systems. The earliest MIMO applications in wireless communications date back to the mid-1980?s, when Winters published a number of breakthrough contributions, where he introduced a technique of transmitting data from multiple users over the same frequency time channel using multiple antennas at both the transmitter and receiver ends.
Although MIMO-OFDM has high potential for deployment in current and futuristic high data rate wireless communication applications, the prevailing detection strategies have many limitations. Popular multiuser detection (MUD) schemes proposed for MIMO-OFDM systems are the classical linear least squares (LS) and minimum mean square error (MMSE) techniques that exhibit a low complexity at the cost of a reduced performance. By contrast, the high-complexity optimum maximum likelihood (ML) MUD is capable of achieving the best performance, which imposes a computational complexity typically increasing exponentially with the number of simultaneous users supported by the MIMO-OFDM system and, thus cannot be implemented in practical high user load scenarios. A range of sub optimal nonlinear MUD's have also been proposed based on successive interference cancellation (SIC) or parallel interference cancellation (PIC) techniques but they are prone to error propagation that occur during the consecutive detection stages, due to the erroneously detected signals of the previous stages.
Most of the above mentioned techniques are proposed for systems, where the number of users L is less than or equal to the number of receivers P, referred to as the under loaded or fully loaded scenarios respectively. In practical applications it is possible that L exceeds P, which is often referred to as a rank deficient scenario, where we have no control over the number of users roaming in the base station's coverage area. In rank deficient systems, the (P x L) dimensional MIMO channel matrix representing the (P x L) number of channel links becomes singular and hence, non invertible, thus making the degree of freedom of the detector insufficiently high for detecting the signals of all the transmitters in its vicinity. This will very much degrade the performance of numerous known detection approaches, such as for example, the Vertical Bell Labs Layered space-time architecture (V-BLAST) detector of the LS/MMSE algorithms and the QR Decomposition combined with the M-algorithm (QRD-M). However, with the aid of the Genetic Simulated Annealing Algorithm (GSAA) aided MUDs, this problem can be efficiently solved.