# Deep-Learning-Based Stream-Sensing Method for Detecting Asynchronous Multiple Signals
## 6 Evaluation
### Case with the Same SNR for All Mobile Devices
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Precision**} & \multicolumn{10}{c}{**The Number of Transmitted Signals**} \\ \hline SNR & d & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
6 dB & 0 & 1.00 & 0.91 & 0.33 & 0.00 & 0.00 & 0.00 & 0.05 & 0.30 & 0.22 & 0.14 \\
1 & - & - & - & 0.10 & 0.00 & 0.01 & 0.27 & 0.67 & 0.51 & 0.35 \\ \hline
8 dB & 0 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.11 & 0.30 & 0.20 & 0.14 \\
1 & - & - & - & 0.20 & 0.00 & 0.01 & 0.30 & 0.68 & 0.52 & 0.36 \\ \hline
10 dB & 0 & 1.00 & 1.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.10 & 0.31 & 0.21 & 0.15 \\
1 & - & - & - & 0.30 & 0.00 & 0.00 & 0.32 & 0.73 & 0.51 & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Precision and recall of MDL. In Table 3, when \(d=0\), for all SNR values, precision and recall values decrease as the number of transmitted signals increases. This naturally means that it is difficult to detect a large number of transmitted signals. From \(k=6\), precision values become smaller than 0.9, while recall values become smaller than 0.9 from \(k=7\). Moreover, our proposed scheme has high reliability with respect to the least relaxed criterion of \(d=1\). The precision values for \(d=1\) are higher than 0.9 in all cases. In other words, if a value detected by our ASensNet is \(k\), the actual number of signals is within \([k-1,k+1]\), with probability greater than 0.9. As in precision, the recall values for \(d=1\) are larger than 0.9 in all cases. As a result, while our scheme shows high detection performance in most cases of the number of transmitted signals at \(d=0\), it also has high detection performance in terms of the minimum relaxation criterion of \(d=1\). In Tables 4 and 5, both AIC and MDL have small precision and recall in almost all cases. Although existing solutions have large recall values for \(k=8\) and \(k=9\), the precision is very low. Only for \(k=0\), both schemes show high precision and recall. Even with respect to the relaxed criterion \(d=1\), the values detected by these techniques are not reliable. As a result, they can only be used to determine whether there is a transmitted signal or not. To understand in detail why precision and recall become larger as \(d\) increases from 0 to 1, we investigate the confusion maps of our ASensNet, AIC, and MDL. Figure 7 shows the confusion maps of three schemes for the SNR of 6 dB. For each scheme, the tendency of confusion maps for other SNR values is the same as that of Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Recall**} & \multicolumn{8}{c}{**The Number of Transmitted Signals**} \\ \hline SNR & d & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
6 dB & 0 & 1.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.13 & 0.41 & 1.00 \\  & 1 & - & - & - & 0.00 & 0.00 & 0.00 & 0.00 & 0.08 & 0.43 & 1.00 & 1.00 \\ \hline
8 dB & 0 & 1.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.03 & 0.13 & 0.36 & 1.00 \\  & 1 & - & - & - & 0.00 & 0.00 & 0.00 & 0.10 & 0.45 & 1.00 & 1.00 \\ \hline
10 dB & 0 & 1.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 0.12 & 0.41 & 1.00 \\  & 1 & - & - & - & 0.00 & 0.00 & 0.00 & 0.09 & 0.49 & 1.00 & 1.00 \\ \hline
12 dB & 0 & 1.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 0.13 & 0.40 & 1.00 \\  & 1 & - & - & - & 0.00 & 0.00 & 0.01 & 0.10 & 0.47 & 1.00 & 1.00 \\ \hline
14 dB & 0 & 1.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 0.14 & 0.40 & 1.00 \\  & 1 & - & - & - & 0.00 & 0.00 & 0.00 & 0.08 & 0.47 & 1.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._Figure 7(a) shows that our ASensNet usually misjudges \(k\) transmitted signals as \((k+1)\) or \((k-1)\) transmitted signals. Therefore, for our proposed scheme, the precision and recall with \(d=1\) are greater than 0.9 in all cases. Figure 7(b,c), however, show that regardless of the number of signals actually transmitted, both AIC and MDL determine that there are 9 transmitted signals. Therefore, although the recall for \(k=9\) is 1, the precision is very small.