## 5 Simulation Analysis
### Evaluation of Comprehensive Approaches  
Evaluation Parameter Settings
* Number of elements of ULA \(M\) is 7. * Distance of the two adjacent elements \(\xi\) is \(\eta/2\). * Number of signal sources \(D\) ranges from 1 to 4 (uniform random). * Arrival angle of signals \(\theta_{i}\) (\(i=1,\ldots,D\)) ranges from \(\theta_{\min}=-60^{\circ}\) to \(\theta_{\max}=60^{\circ}\) (uniform random, non-discrete). * Minimum angle difference between the two adjacent signals \(\Delta\theta_{ab}\geq 15^{\circ}\). * Number of snapshots \(L\) is 1000. * Number of trials for each SNR is 10,000 times. * T-GANE is trained the same as is mentioned in Section 5.2. Because the numerical detectability extent of SORTE is \(M-3\), the maximum \(D\) is set to 4. Note that \(\hat{\gamma}\) of T-GANE is set to 0.0113, and the source enumeration procedure of T-GANE is performed with Algorithm 2. Figure 7 shows the estimation accuracy of AIC, MDL, SORTE, and our two proposed approaches (AREG, T-GANE) versus SNR. The performances are evaluated in the SNR range from \(-20\) dB to \(10\) dB, which is roughly chosen in many other papers [4; 10; 12; 14; 16; 23; 24; 25; 31]. This paper is interested in improving accuracy of AIC at high SNR--where MDL has 100% accuracy, but AIC does not reach 100% accuracy--and it of MDL at low SNR--where the MDL accuracy begins to decrease sharply, but AIC maintais good accuracy. The results show that MDL, SORTE, AREG, and T-GANE have 100% accuracy at high SNR (roughly above \(-5\) dB at this result), while AIC has about 90% accuracy despite a high SNR; however, AIC keeps its performance at about \(-13\) dB and shows the best performance in SNR \(-15\) dB to \(-13\) dB among the approaches. SORTE and T-GANE begin to decrease below \(-5\) dB, while AREG maintains 100% accuracy the same as MDL does. In the SNR range \(-14\) dB to\(-5\) dB, among AREG, SORTE, and T-GANE, AREG shows the best performance, the next is SORTE, and the third is T-GANE and its performance gradually decreases at that range of SNR. It is worth mentioning that the learning datasets certainly affect the performance of T-GANE; hence, T-GANE with another datasets is also evaluated, and the results are described afterwards. Figure 8 shows the required number of snapshots (\(L\)) to provide 70% accuracy versus SNR. Note that the learning data for T-GANE are newly generated when the number of snapshots is changed (among the parameters, only the number of snapshots is changed; other parameters are not changed) and then the optimal thresholds are updated. Regardless of the approaches, the required number of snapshots sharply increases when SNR decreases. At the same SNR, AIC requires the smallest number of snapshots, while MDL requires the largest number of snapshots. SORTE, AREG, and T-GANE have similar performances, but our two proposed approaches have better performances than SORTE has. At the small number of snapshots (1000 to 5000), T-GANE has slightly better performance than AREG, while, for the large number of snapshots (6000 to 8000), AREG has slightly better performance than T-GANE. Over 8000 snapshots, the performance improvement of T-GANE is not as good as the other approaches. The reason is considered that the designated SNR range for generating datasets is fixed to \(-20\) dB to \(10\) dB; if the designated SNR range for generating datasets is flexibly adjusted when the number of snapshots is changed, T-GANE may have better performance than that shown in Figure 8.  
Figure 9 shows the required number of ULA elements (\(M\)) to provide 70% accuracy versus SNR. Note that the learning data for T-GANE are newly generated when the number of ULA elements is changed (among the parameters, only the number of ULA elements is changed; other parameters are not changed) and then the optimal thresholds are updated. Similar to the results of Figure 8, the required number of ULA elements sharply increases when SNR decreases regardless of the approaches. Our two proposed approaches have better performance than MDL and SORTE.