Multi-user MIMO (Multiple Input Multiple Output) systems, in which multiple Mobile Stations (MSs) equipped with multiple antennas simultaneously communicate with a Base Station (BS) equipped with multiple antennas, at the same frequency, are attracting attention because of their potential for improved transmission performance in wireless communications. In the uplink of Space Division Multiplexing based multi-user MIMO (multi-user MIMO/SDM) systems that do not require full Channel State Information (CSI) at the transmitters, selecting active MS antennas, which corresponds to scheduling transmit antennas, is an effective technique. The Full search Selection Algorithm based on exhaustive search (FSA) has been studied as an optimal active MS antenna selection algorithm for multi-user MIMO systems. Unfortunately, FSA suffers from extreme computational complexity given large numbers of MSs. To solve this problem, this paper introduces the Gram-Schmidt orthogonalization based Selection Algorithm (GSSA) to uplink multi-user MIMO/SDM systems. GSSA is a suboptimal active MS antenna selection algorithm that offers lower computational complexity than the optimal algorithm. This paper evaluates the transmission performance improvement of GSSA in uplink multi-user MIMO/SDM systems under realistic propagation conditions such as spatially correlated BS antennas and clarifies the effectiveness of GSSA.