# Efficient Transmit Antenna Subset Selection for Multiuser Space-Time Line Code Systems
## 1 Introduction  
Multiple-input multiple-output (MIMO) transmission techniques have been employed as an integral part of present-day communication systems to improve the overall radio link capacity and reliability [1, 2, 3, 4]. Space-time block code (STBC) has been used as one of the general MIMO transmission strategies when no channel state information (CSI) is available at the transmitter [5, 6, 7, 8]. It spreads over time and over space (transmit antennas). STBC is an effective way to exploit the potential of MIMO systems because it is a very simple code requiring a low encoding and decoding complexity. Although it does not require multiple antennas at the receiver, the use of multiple receive antennas offers extra diversity gain and array gain. Recently, a space-time line code (STLC) in [9] was presented as a new transmission method having full rate and diversity. In the STLC scheme, two information symbols are encoded by channel gains coming from multiple receive antennas and are sent consecutively in time. The STLC transmission is a dual version of Alamouti STBC [6], based on the symmetric CSI and antenna configurations. The STLC assumes the knowledge of the full CSI at the transmitter (CSIT), whereas the STBC requires the CSI at the receiver (CSIR). The STLC scheme is also advantageous because of its low complexity encoding and decoding procedure. Owing to its implementation simplicity, the STLC transmission technique has been used for various communication systems. For example, they include massive MIMO and multiuser systems [10, 11], two-way relay systems [12], and machine learning-based blind decoding [13]. In the basic STLC scheme, multiple transmit antennas are not required at the transmitter. In case multiple transmit antennas are present, STLC benefits from additional diversity gain and array gain. In [14], a new multiuser (MU)-STLC scheme is designed to support simultaneous transmission of multiple STLC signals for multiple users through preprocessing at the transmitter. Moreover, a transmit antenna subset (TAS) selection problem for the proposed MU-STLC system has been initially investigated for performance enhancement. Firstly, an exhaustive search-based optimal TAS selection algorithm that maximizes the detection signal-to-interference-plus-noise ratio (SINR) is presented with tremendously huge complexity. To alleviate the complexity problem, an SINR-based greedy TAS selection algorithm is also proposed at the cost of performance degradation. However, it requires an \(N_{R}\times N_{R}\) matrix inverse operation in each greedy step, where \(N_{R}\) denotes the total number of receive antennas and is given as the product of the number of multiple users and the number of receive antennas per user. When the total number of receive antennas is large, its computational complexity is huge. Additionally, TAS selection in [14] does not guarantee optimal performance. Furthermore, the effects of TAS selection on the SINR performance have not been sufficiently studied. Recently, the performance of the STLC systems with TAS selection has been analyzed and evaluated in [15]. However, it considers only the single-user model. To the best of our knowledge, no other study, except for [14], has been previously made for effective TAS selection in the MU-STLC systems. Antenna subset selection at the transmitter and/or receiver has been researched extensively in many kinds of MIMO systems [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. It has been employed to improve the performance and reliability over those achievable with wireless communication systems without antenna subset selection. It can be also performed to reduce the number of expensive radio frequency (RF) chains while preserving spatial diversity gains.