Owing to the forever growing demand for faster data transmission speed in the recent or future telecommunication systems, the multiple antenna systems have been actively investigated and successfully deployed for the emerging broadband wireless access networks (e.g., Mobile WiMAX). Even when a wireless channel with high channel capacity is known, we still require to find superior techniques to achieve high speed data transmission or high reliability. Multiple antenna techniques can be broadly classified into two categories: diversity techniques and spatial-multiplexing techniques. The diversity techniques intend to receive the same information-bearing signals in the multiple antennas or to transmit them from multiple antennas, in so doing improving the transmission consistency. Diversity techniques are used to mitigate degradation in the error performance due to unstable wireless fading channels, for example, subject to the multipath fading etc. A basic idea of the diversity techniques is to convert Rayleigh fading wireless channel into more stable AWGN-like channel without any catastrophic signal fading. When the spatial-multiplexing Techniques are used, the maximum achievable transmission speed can be the same as the capacity of the MIMO channel; however, when the diversity techniques are used, the achievable transmission speed can be much lower than the capacity of the MIMO channel. Spatially multiplexed MIMO (SM-MIMO) systems can transmit data at a higher speed than MIMO systems using antenna diversity. However, spatial demultiplexing or signal detection at the receiver side is a challenging task for SM MIMO systems. This paper addresses the signal detection technique using maximum likelihood detection for SM MIMO systems.