# Design of a SIMO Deep Learning-Based Chaos Shift Keying (Dlcsk) Communication System
## 4 Simulation Results
### Confusion Matrix, Sensitivity, and Specificity  
We provide the confusion matrix of the proposed method, which helps in analyzing the performance of our classification algorithm. Figure 6 depicts an example of two confusion matrices with 10,000 chaotic symbols for AWGN channels for \(\beta=50\), \(\sigma_{tr}^{(n)}\in[19,23]\) dB, and test SNRs = \(\{16,\ 23\}\) dB.  
Figure 5: BER curve of the SISO DLCSK under AWGN channel, trained at a random SNR \(\in[19,23]\) dB, and \(\beta=50\), for case 1, and case 2. There is also the results for \(\rho_{test}\in\{3.3,3.6\}\).  
In Figure 7, the sensitivity and specificity measures extracted from the confusion matrix are introduced. Both are statistical measures for the performance of a binary classification test that are widely used in the literature [84; 85]. The sensitivity or True Positive Rate (TPR) measures the proportion of Logistic maps that are correctly identified. The specificity or True Negative Rate (TNR) measures the proportion of Chebyshev maps that are correctly identified. The terms \"True Positive (TP)\", \"False Positive (FP)\", \"True Negative (TN)\", and \"False Negative\" address the correctness of a classification test. For example, if the condition is sending the signals generated by the Logistic map, \"TP\" means \"correctly predicted as Logistic map\", \"FP\" means \"incorrectly predicted as Logistic map\", \"TN\" means \"correctly predicted as Chebyshev map\", and \"FN\" means \"incorrectly predicted as Chebyshev map\".  
Figure 8 shows the sensitivity and specificity of different bifurcation parameters. The sensitivity curve in this test shows how capable LSTM can classify samples that are generated by the Logistic maps. Sensitivity can also be referred to as the recall or hit rate [86]. It is the percentage of true Logistic maps out of all samples generated by the Logistic maps (i.e., \(TP/(TP+FN)\)). The specificity is a measure of how well the test can identify true Chebyshev maps, which can be expressed as \(TN/(TN+FP)\). For high SNRs (i.e., \(SNR>16\) dB), even using a single LSTM-based classifier results in sensitivity and specificity rates \(>95\%\). However, there is a trade-off between sensitivity and specificity for low SNRs, where the curves show low sensitivity and high specificity. For example, when  
Figure 6: Confusion chart of the LSTM-based classifier under AWGN channel for \(\beta=50\), \(\sigma_{tr}^{(n)}\)\(\in[19,23]\) dB, and test SNRs\(=\{16,23\}\) dB.  
Figure 7: Calculation of sensitivity and specificity from the confusion matrix.  
\(SNR=12\) dB, \(\rho_{train}=3.6\), and \(\rho_{test}=3.3\), the sensitivity of a single LSTM-based classifier is 65.69% and its specificity is 99.96%, its false negatives and false positives rates are 34.31% and 0.04%, respectively.  
Sensitivity values contain useful information about the receiver's performance that can be utilized for different goals. Here, we evaluate the effect of the changes in bifurcation parameter on the classifier's performance. For example, \(\rho_{train}=3.6\) and \(\rho_{test}=3.3\) leads to a better classification accuracy than other parameter settings for \(SNR<14\) dB. However, with \(\rho_{test}=3.3\), the Logistic map shows a periodic behavior and this change can bring negative effect on security.  
Figure 9 presents the performance obtained for case 1 using different numbers of training epochs (\(E\)). The system achieves its peak when \(E=20\). This Figure also measures the sensitivity to the number of epochs. It can be observed that the SISO DLCSK system is relatively robust to the number of epochs. For example, for a target BER performance of \(10^{-2}\), there is a 1 dB gap between the worst-case and the best-case scenarios.