# Intelligent Transmit Antenna Selection Schemes for High-Rate Fully Generalized Spatial Modulation
## 5 Discussion on the Simulation Results  
This section presents an ABER analysis of the classic FD-TAS method, four distinct ML-based TAS methods, and the FGSM-NTAS scheme. Table 5 lists the parameters used in this investigation. In MATLAB 2022b, all ML models are trained using the Statistics and ML toolbox. All the simulation results are generated for distinct values of \(N_{T}\), \(N_{tx}\), \(N_{rx}\), and \(M\). FD-TAS and ML-based TAS are labeled as \((N_{T},N_{tx},N_{rx},M)\) in the figures, while FGSM-NTAS is labeled as \((N_{tx},N_{rx},M)\). From Figure 4, it is observed that with an increased dataset size, ML models show an improvement in classification accuracy. Since the accuracy of classification does not improve any further after 10,000 samples, all models are trained for the same number of samples. Table 6 compares the classification accuracies of several ML algorithms with different sample counts. SVM has the highest accuracy in classification (71.1%), NB has the second greatest accuracy (70.2%), followed by KNN (67.2%), and DT has the lowest classification accuracy (43.8%). \begin{table}
\begin{tabular}{c c c} \hline \hline
**ML-Based TAS Scheme** & **Order of Complexity** & **Configuration 1 (\(N_{tx}=N_{rx}=4\), & **Configuration 2 (\(N_{tx}=N_{rx}=6\), \\  & \(N_{T}=5\), \(M=4\)) & \(N_{T}=7\), \(M=16\)) \\ \hline FD-TAS & \(\mathcal{O}(N_{s}N_{T}^{2}N_{rx}^{2\pi_{FGSM}}(2^{\pi_{FGSM}}-1))\)[20] & \(1.98\times 10^{6}\) & \(3.23\times 10^{9}\) \\ SVM-based TAS & \(\mathcal{O}\Big{(}N_{Q}^{2}+N_{Q}\Big{)}\)[22] & 420 & 1806 \\ NB-based TAS & \(\mathcal{O}(N_{Q})\)[21, 27] & 20 & 42 \\ DT-based TAS & \(\mathcal{O}(N_{Q}\log_{2}N_{Q})\)[21, 28] & 86.44 & 226.48 \\ KNN-based TAS & \(\mathcal{O}(BN_{Q})\)[22] & \(4\times 10^{6}\) & \(8.4\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of distinct TAS techniques based on their complexity order. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \(N_{T}\) & \(4,5,6\) \\ \(N_{tx}\) & \(3,4\) \\ \(N_{rx}\) & \(4\) \\ \(M\) & \(4,16\) \\ Constellation mapping & Quadrature amplitude modulation (QAM) \\ \(\pi_{FGSM}\) & \(4,5,6\) \\ \(B\) & \(2\times 10^{5}\) \\ Fading environment & Uncorrelated Rayleigh flat fading \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation parameters. After performing normalization, these models are trained for four distinct features, as discussed earlier in subsection 3.3. The complexities of all features based on their attribute vector lengths are listed in Table 8. The worst-performing attribute is \(\measuredangle\left(h_{i,j}^{n}\right)\). Attribute 4 performs well only for DT, but its complexity increases with a higher-order configuration, so it is discarded. Combining features lengthens the feature vector and increases model complexity; hence, feature combination is avoided in this study. The absolute feature outperforms the other features in SVM, NB, and KNN, and its complexity is low; thus, only the absolute feature is utilized for this work. After conventional FD-TAS, the SVM-based TAS scheme outshines other ML-based systems, as shown in Figure 6. In comparison to the FGSM-NTAS method, the SVM-based TAS scheme cut downs the SNR need by \(\sim\)2 dB. This analysis is conducted for \(N_{T}\) = 4, \(N_{tx}\) = 3, \(N_{rx}\) = 4, and \(M\) = 4. The ABER performance of the system is re-examined in Figure 7 by increasing the constellation order to 16. For larger values of \(M\), the SNR requirement for all ML-based methods increases. For FGSM-NTAS and conventional FD-TAS SNR gain requirements increase by \(\sim\)1.3 dB and \(\sim\)1.61 dB, respectively. SVM outperforms the FGSM-NTAS system in this circumstance as well, with a gain improvement of \(\sim\)2 dB. Figure 5: Comparing the classification accuracies of several ML algorithms for distinct values of \(k\).