## 5 Simulation Analysis
### Evaluation of Comprehensive Approaches
Although T-GANE has unstable performance improvement compared to the others, it is expected that T-GANE can have stable performance improvement if appropriate datasets are provided for T-GANE as mentioned earlier. Figure 7: Estimation accuracy of AIC, MDL, SORTE, and our two proposed approaches (AREG, T-GANE) versus SNR. The number of signal sources \(D\) is randomly selected from a set \(\{1,2,3,4\}\) at each trial. Figure 10 shows the estimation accuracy of AIC, MDL, T-GANE (\(-20\) to \(10\)), and T-GANE (\(-14\) to \(-11\)), where T-GANE (\(-20\) to \(10\)) and T-GANE (\(-14\) to \(-11\)) denote that the learning datasets for T-GANE are generated with the SNR range from \(-20\) dB to \(10\) dB and from \(-14\) dB to \(-11\) dB, respectively. The reason why the learning datasets SNR is set to range from \(-14\) dB to \(-11\) dB is to improve the performance of T-GANE in the range of \(-14\) dB to \(-11\) dB, where the performances of AIC and MDL in Figure 7 begin to sharply decrease, respectively. Note that \(\hat{\gamma}\) of T-GANE (\(-20\) to \(10\)) is \(0.0113\) and \(\hat{\gamma}\) of T-GANE (\(-14\) to \(-11\)) is \(0.0125\). In this evaluation, the number of signal sources \(D\) is randomly selected from a set \(\{1,2,\ldots,6\}\) at each trial; hence, SORTE and AREG are excluded from this evaluation. As shown in Figure 10, the estimation accuracy of T-GANE (\(-14\) to \(-11\)) is higher than T-GANE (\(-20\) to \(10\)) for SNR over \(-14\) dB (maximum \(5.06\%\) higher at SNR \(-12\) dB). In addition, T-GANE (\(-14\) to \(-11\)) shows the best performance that surpasses AIC and MDL. From the results, it can be concluded that T-GANE has the feasibility of  
Figure 8: Required number of snapshots (\(L\)) to provide \(70\%\) accuracy versus SNR. The number of signal sources \(D\) is randomly selected from a set \(\{1,2,3,4\}\) at each trial. Figure 9: Required number of ULA elements (\(M\)) to provide \(70\%\) accuracy versus SNR. The number of signal sources \(D\) is randomly selected from a set \(\{1,2,3,4\}\) at each trial. improvement performance at low SNR (roughly from \(-15\) dB to \(-10\) dB at this result) if appropriate learning datasets are used for T-GANE. Although the learning SNR range of T-GANE (\(-14\) to \(-11\)) is less than that of T-GANE (\(-20\) to \(10\)), T-GANE (\(-14\) to \(-11\)) has better performance for both low and high SNR than T-GANE (\(-20\) to \(10\)). Typically, the NS gap is greater than NN gaps when the SNR is not too low. The difference between NS gap and NN gap is larger when the SNR is higher. If the slight difference between NS gap and NN gaps can be detected in a low SNR range, it is easy to detect the difference between them in a high SNR range; this is why T-GANE (\(-14\) to \(-11\)) also has good performance at high SNR. Meanwhile, if T-GANE learns too much high SNR information, it may be not easy to detect the slight difference between the NS gap and NN gaps because the difference between them is larger when the SNR is higher; this is why T-GANE (\(-20\) to \(10\)) has worse performance than T-GANE (\(-14\) to \(-11\)). Intuitively, if the learning SNR range is too high level like from \(0\) dB to \(10\) dB, it probably has worse performance than T-GANE (\(-20\) to \(10\)) at low SNR. Therefore, how to select the learning SNR range for T-GANE provides a good starting point for discussion and further research work.