# Automatic Wireless Signal Classification: A Neural-Induced Support Vector Machine-Based Approach
## 4 Simulation Results and Discussion
### Basic Classification Performance  
The performance of NSVM under ideal channel conditions for individual modulation schemes are shown by Figure 6. The confusion matrix at SNR = \(-\)4 dB and SNR = 0 dB is given by Table 2. One-dimensional modulation schemes 4 ASK and BPSK are easily recognizable even at low SNR. However, the performance NSVM for higher dimensional modulation types in the dataset requires a high signal-to-noise ratio (SNR) to achieve satisfactory performance. The performance of QAM 16, QPSK and 8-PSK is lower than QAM64 in the low SNR region. Similar results were reported in Reference [6], in which QAM64 achieves better performance than QAM16 with different learning-based modulation classifier methods based on machine learning techniques. This is due to the fact that the distinctive features learned by CNN hidden layers are increased in the case of high modulation, such as QAM64. The performance of QPSK and 8 PSK degrades with a decrease in the SNR of received signals. However, at SNR > 3 dB, the algorithm manages to achieve classification accuracy of <98%. In this experiment, the performance of NSVM in classifying individual modulation schemes has been analyzed. The receiver is assumed to have the information of all the parametric information about the signal (e.g., if there is any phase offset, symbol timing offset, frequency offset, etc.), except the modulation format needs to be inferred. In our experiments, by default, the value of \(N\) is 2048, in case a change will be mentioned. The result of classifying six different modulation schemes is given Figure 7. The modulation schemes 4 Ask and BPSK can be easily classified by our model in the dataset. However, the distinctive features learned by CNN are increased in the case of QAM 64. Therefore, it achieved performance much better than QPSK, 8 PSK, and QAM 16. The performance of QAM 16 is misclassified at low SNR due to its similar constellation map with QAM64. However, similar behavior has been seen in QPSK, as they required higher SNR to be classified correctly. Therefore, in this section, confusion matrices at SNR = \(-\)4 dB and SNR = 0 dB are given in Tables 2 and 3, respectively. As it is clear from the tables, more misclassification occurs in higher order modulation due to low SNR. In the low SNR regime, QPSK is often misclassified as the 8 PSK, this can be explained by the assumption in which QPSK is taken as subset 8 PSK. In order to improve the performance of the proposed scheme, more MPSK/M-ary QAM modulation schemes can be considered, which will enable the CNN model to gather more information about the same constellation but different symbol order sequences. The following experiment was conducted with a fixed number of symbols in the frame. In the next section, the different symbol length effect is discussed.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**SNR = 4 dB**} & \multicolumn{6}{c}{**True Class**} \\ \cline{2-7}  & & BPSK & 4-ASK & QPSK & 16-QAM & 64-QAM & 8-PSK \\ \hline \multirow{4}{*}{**Predicted Class**} & BPSK & 100 & & & & & \\  & 4-ASK & & 100 & & & & \\ \cline{1-1}  & QPSK & & 91.18 & & & 8.82 \\  & 16-QAM & & & 79.90 & 7.67 & 12.43 \\  & 64-QAM & & & 1.83 & 98.17 & \\  & 8-PSK & & 18.87 & 12.26 & & 68.87 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Confusion Matrix of NSVM at SNR = \(-\)4 dB.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**SNR = 0 dB**} & \multicolumn{6}{c}{**True Class**} \\ \cline{2-7}  & BPSK & 100 & & & & & \\  & 4-ASK & & 100 & & & & \\ \cline{1-1}  & QPSK & & 95.57 & & & 2.43 \\  & 16-QAM & & & 94.49 & 1.28 & 4.23 \\  & 64-QAM & & & 0.54 & 99.46 & \\  & 8-PSK & & & 5.87 & 0.85 & & 93.28 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion Matrix of NSVM at SNR = 0 dB.