## 4 Experimental Results
### Performance of DOA Estimation Model  
In this segment, we evaluate the proposed model against algorithms such as MUSIC, ASMUSIC, DeepMUSIC, ILSSE, CNN, LSTM, and CNN-LSTM to demonstrate its superiority and efficacy. Assume that the signal is of the same power \(p\). The SNR is used to indicate the influence degree of environmental noise, and the expression is given as follow:  
Figure 7: Signals and filtered signals. \[\text{SNR}=\frac{1}{M}\sum_{m=1}^{M}\frac{p}{q_{m}} \tag{9}\]  
where \(M\) is the number of sensors, and \(q_{m}\) is the \(m\)th diagonal element of the covariance matrix. To verify the performance of each algorithm, the root mean square error (RMSE) is expressed as:  
\[\text{RMSE}=\sqrt{\frac{1}{IQ}\sum_{i=1}^{I}\sum_{q=1}^{Q}\left(\hat{\theta_{q }^{i}}-\theta_{q}\right)^{2}} \tag{10}\]  
where \(I\) represents the total number of Monte Carlo simulations conducted, while \(Q\) denotes the quantity of signal sources requiring estimation. For each source \(q\) in the \(i\)th Monte Carlo experiment, \(\hat{\theta_{q}^{i}}\) stands for the estimated DOA, and \(\theta_{q}\) corresponds to its true DOA. The accuracy metric is subsequently defined as:  
\[Acc=\frac{K_{c}}{K}\times 100\% \tag{11}\]  
where \(K\) and \(K_{c}\) are the total number of samples and the number of correctly estimated samples. **Experiment 1:** Assessment of RMSE performance as SNR increases. During this experimental setup, predictions were made for all test set samples. We set the number of snapshots to \(T=500\) and computed the average RMSEs for DOA estimates. As SNR increases, the RMSEs for MUSIC, ASMUSIC, DeepMUSIC, ILSSE, CNN, LSTM, CNN-LSTM, and our model are depicted in Figure 8a and summarized in Table 1. Observations from Figure 8a and Table 1 reveal that DL-based approaches (i.e., those utilizing deep learning) exhibit superior performance in low-SNR conditions. Conversely, MUSIC shows poor performance within the SNR range of \(-20\) dB to \(0\) dB. The high power of colored noise significantly impairs the predictive capabilities of the traditional algorithm. On the whole, the deep learning-based methods, i.e., CNN, LSTM, CNN-LSTM, CNN-LSTM+SAM are superior to MUSIC, ASMUSIC, DeepMUSIC, and ILSSE, mainly because the performance of the traditional algorithms will be degraded severely due to the colored noise field. Furthermore, in a low-SNR environment, specifically at \(-20\) dB SNR, the RMSE of CNN-LSTM+SAM is notably lower than that of CNN-LSTM by a significant margin of \(24.41^{\circ}\), as it reduces the noise weight of the received signal in the frequency domain. Specifically, this enhanced neural network incorporates more distinguishing information. In summary, our proposed model demonstrates comparable performance to other algorithms in high-SNR environments, with RMSEs for all algorithms converging to approximately \(0.01^{\circ}\). However, it exhibits a notable advantage in low-SNR conditions. Traditional algorithms are more prone to being affected by colored noise compared to deep learning-based algorithms. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Methods** & \(\mathbf{-20}\) **dB** & \(\mathbf{-15}\) **dB** & \(\mathbf{-10}\) **dB** & \(\mathbf{-5}\) **dB** & \(\mathbf{0}\) **dB** & \(\mathbf{5}\) **dB** & \(\mathbf{10}\) **dB** & \(\mathbf{15}\) **dB** & \(\mathbf{20}\) **dB** \\ \hline MUSIC & 64.03 & 63.89 & 33.29 & 30.63 & 16.31 & 1.07 & 0.05 & 0.01 & 0.01 \\ ASMUSIC & 62.11 & 60.08 & 32.35 & 20.55 & 9.33 & 0.22 & 0.01 & 0.01 & 0.01 \\ DeepMUSIC & 50.91 & 41.92 & 30.88 & 18.43 & 6.08 & 0.15 & 0.01 & 0.01 & 0.01 \\ ILSSE & 50.12 & 40.32 & 28.59 & 16.65 & 5.16 & 0.14 & 0.01 & 0.01 & 0.01 \\ CNN & 50.09 & 30.31 & 20.11 & 10.56 & 1.84 & 0.09 & 0.01 & 0.01 & 0.01 \\ LSTM & 50.80 & 32.71 & 23.68 & 9.55 & 1.54 & 0.08 & 0.01 & 0.01 & 0.01 \\ CNN-LSTM & 45.92 & 27.22 & 18.32 & 5.44 & 1.16 & 0.02 & 0.01 & 0.01 & 0.01 \\
**CNN-LSTM+SAM** & **21.51** & **11.93** & **5.45** & **2.03** & **0.41** & **0.01** & **0.01** & **0.01** \\ \hline \hline \end{tabular}
\end{table}