## 3 Method  
As in Table 2, the azimuth and elevation angles considered are \((25^{\circ},25^{\circ})\), \((185^{\circ},35^{\circ})\), \((245^{\circ},45^{\circ})\), and \((305^{\circ},55^{\circ})\). The number of array elements is 8 along both the X-axis and Y-axis, with an element spacing of \(\lambda/2\). The number of snapshots, \(O\), is set to 50, and the angular resolution is considered at both \(1^{\circ}\) and \(0.1^{\circ}\). The signal-to-noise ratio (SNR) is 20 dB [30]. A total of 1000 Monte Carlo simulations were conducted using the 2D-MUSIC algorithm, and the results of a typical search are shown in Figure 3a. By analyzing the elevation and azimuth search results of the MUSIC algorithm in Tables 3 and 4 under different angular search steps, the following conclusions can be drawn. Decreasing the angular search step from 1\({}^{\circ}\) to 0.1\({}^{\circ}\) substantially reduces the average error, particularly for larger elevation and azimuth angles. As the elevation angle increases, the search error also increases, whereas the azimuth search error tends to reach its maximum at intermediate angles. At a search step of 0.1\({}^{\circ}\), the algorithm demonstrates stable performance, with the average error generally remaining below 0.05\({}^{\circ}\). Overall, the azimuth search exhibits slightly smaller mean error compared to the elevation search. These results indicate that the MUSIC algorithm provides excellent angle estimation performance under the same angular search step. Figure 3: Spectrum plot of the MUSIC algorithm with different angle search steps. high-precision conditions. However, achieving real-time performance with high-precision searches poses a significant challenge due to the increased computational demands. The traditional MUSIC algorithm necessitates a two-dimensional search across a predefined grid space to identify the local maxima of the objective function. At each grid point, the values of the function are computed and stored, followed by the identification of peaks. High-resolution methods, such as MUSIC, typically generate extremely sharp \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Azimuth** & **Angle Search Step** & **Average Error (*)** & **Standard Deviation (*)** \\ \hline \(5^{\circ}\) & \(1^{\circ}\) & 0.02 & \textless{}0.001 \\  & \(0.1^{\circ}\) & 0.01 & \textless{}0.001 \\ \hline \(65^{\circ}\) & \(1^{\circ}\) & 0.20 & \textless{}0.001 \\  & \(0.1^{\circ}\) & 0.04 & \textless{}0.001 \\ \hline \(125^{\circ}\) & \(1^{\circ}\) & 0.38 & 0.013 \\  & \(0.1^{\circ}\) & 0.05 & \textless{}0.001 \\ \hline \(185^{\circ}\) & \(1^{\circ}\) & 0.49 & 0.055 \\  & \(0.1^{\circ}\) & 0.05 & \textless{}0.001 \\ \hline \(245^{\circ}\) & \(1^{\circ}\) & 0.26 & \textless{}0.001 \\  & \(0.1^{\circ}\) & 0.03 & \textless{}0.001 \\ \hline \(305^{\circ}\) & \(1^{\circ}\) & 0.08 & \textless{}0.001 \\  & \(0.1^{\circ}\) & 0.01 & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Search results when the angle search step is \(0.1^{\circ}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(M\) & 8 \\ \(N\) & 8 \\ Signal Frequency & \(35\,\text{GHz}\) \\ Element Spacing & \(\lambda/2\) \\ Noise Type & Gaussian Noise \\ SNR & \(20\,\text{dB}\) \\ Signal Elevation & \(5^{\circ},15^{\circ},25^{\circ},35^{\circ},45^{\circ},55^{\circ}\) \\ Signal Azimuth & \(5^{\circ},65^{\circ},125^{\circ},185^{\circ},245^{\circ},305^{\circ}\) \\ Number of Snapshots & \(50\) \\ Angular Search Step & \(1^{\circ}/0.1^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for simulated MUSIC angle search.