# Efficient Transmit Antenna Subset Selection for Multiuser Space-Time Line Code Systems
## 5 Simulation Results  
In this section, several TAS selection algorithms for the MU-STLC system with \(N_{T}\) transmit antennas and \(K\) users are evaluated through Monte Carlo simulations over static Raleigh flat-fading channels. Each user has two receive antennas. The SNR is defined as \(\sigma_{x}^{2}/\sigma_{z}^{2}\). In the case of \(N_{S}=N_{T}\), there is no TAS selection. We assume that the CSI is perfectly known at the transmitter of the MU-STLC system. The quadrature phase shift keying (QPSK) modulation is assumed. In the simulations, the BER performance of the linear precoded MU-STLC system is compared using the following TAS selection algorithms:  
1. SINR-greedy-based TAS selection [14] (greedy);
2. Proposed SNR-based efficient incremental TAS selection (proposed incremental);
3. Proposed ZF-based efficient decremental TAS selection (proposed ZF decremental);
4. Proposed MMSE-based efficient decremental TAS selection (proposed MMSE decremental);
5. Optimal ZF-based TAS selection (optimal ZF);
6. Optimal MMSE-based TAS selection (optimal MMSE). It should be pointed out that the linear precoded MU-STLC TAS systems with (a), (b), (d), and (f) employ MMSE precoders at the transmitter, whereas the systems based on TAS selection of (c) and (e) use ZF precoders. The BER performance of the proposed TAS selection algorithms is given in Figure 3 in the scenario of \((N_{T},N_{S},K)=(8,4,4)\). We observe that the proposed incremental TAS  
Figure 2: The complexity of the proposed TAS selection algorithms as a function of \(N_{S}\) for \(\mathbf{(a)}(8,N_{S},4)\), \(\mathbf{(b)}(16,N_{S},4)\), \(\mathbf{(c)}(32,N_{S},8)\), and \(\mathbf{(d)}(200,N_{S},32)\) MU–STLC systems. selection algorithm achieves a slightly worse performance than the greedy algorithm in the high SNR regime with lower complexity (which is confirmed from Figure 1). It is also shown that the proposed decremental TAS selection algorithm outperforms the greedy and proposed incremental algorithms. The performance of the latter may be poorly affected by an initially selected antenna. Furthermore, the proposed MMSE decremental TAS selection algorithm can achieve better BER performance compared to that of the proposed ZF decremental TAS selection one. In addition, the BER results of the proposed ZF and MMSE decremental selection algorithms are close to those of the optimal exhaustive search-based ZF and MMSE TAS selection algorithms, respectively. Figure 4 depicts the BER results of the proposed TAS selection algorithms for the \((8,N_{S},K)\) MU-STLC system when \(N_{S}\) is equal to \(K\). It is assumed that the values of \(K\) are given as \(K=2,4,\text{ and }8\). Note that \((8,8,8)\) indicates no TAS selection case. It is observed that the BER performance of all the TAS selection algorithms improves as \(K\) decreases. The good performance for small \(K\) results from the decreased multiuser interference. Especially, the proposed MMSE decremental TAS selection algorithm is shown to provide the best BER performance. In this scenario, the computational complexity of the greedy, the proposed incremental, and the proposed MMSE decremental algorithms is shown in Figure 1. For \(N_{S}=2\), the complexity of the greedy algorithm is the smallest, while the BER performance of the greedy algorithm is slightly less than that of the proposed MMSE decremental algorithm and similar to that of the proposed incremental algorithm. We can observe that the BER performance difference between the proposed ZF and MMSE decremental algorithms becomes smaller as the diversity gain gets larger. It should be noted that the diversity gain of the \((8,2,2)\) MU-STLC system is larger than that of the \((8,4,4)\) case. Figure 3: Bit error rate (BER) of the proposed TAS selection algorithm and optimal selection algorithm for \((8,4,4)\) MU–STLC system. In Figures 5 and 6, as the number of active transmit antennas decreases in the proposed MMSE decremental TAS selection algorithm, the received SNR penalty increases. Here, the number of users is fixed as \(K=4\).