# Optimized Sonar Broadband Focused Beamforming Algorithm
## 3 Simulation and Performance Analysis
### Validity Verification of the Optimal Focusing Frequency  
Five group simulation experiments were conducted to verify the effectiveness of the best focusing frequency in broadband focusing beamforming. First, the broadband signal was divided into 21 sub-band signals through filtering or DFT processing. Second, the 21 sub-band signals were focused on 2250, 2450, 2900, 3000, and the optimal focusing frequency 2760 Hz, respectively, using the RSS algorithm. Next, the conventional delay-and-sum beamforming was used to achieve the constant beam width beamforming. The beam patterns on the different focusing frequencies are shown in Figures 1-5. Figure 1a shows the narrowband signal beam with the frequency 2760 Hz using the conventional delay-and-sum beamforming method. Figure 1b shows the beam superposition graph of the broadband signal, whose frequency range is within 2250-3000 Hz using RSS. Figures 2-5 show the simulation results on the focusing frequency of 2250, 2450, 2900, and 3000 Hz, respectively. Tables 1 and 2 shows the comparison of beamforming parameters for narrowband signals and broadband signals. The comparison of beamforming parameter change between narrowband and broadband signals is shown in Table 3.  
As shown in Tables 1-3, The effects of broadband beamforming at five focused frequencies were compared and analyzed from the main lobe width and the sidelobe level of the beam. The comparison results in Table 3 show that the main lobe width of the broadband focusing beam differs with its corresponding narrowband beam of 2.4\({}^{\circ}\), and the sidelobe level of the broadband focusing beam differs with its corresponding narrowband beam of 0.17 dB. The simulation results with the selected focusing frequency less than 2760 Hz are shown in Figures 2 and 3. The wideband and narrowband beams have poor consistency before and after focusing. The main lobe width of the wideband focusing beam can be kept consistent with each other. The main lobe width varies slightly, but the sidelobe level varies greatly, reaching 2 dB. The simulation results with the selected focusing frequency greater than 2760 Hz are shown in Figures 4 and 5. The wideband beams are not consistent with the narrowband beams before and after focusing. The main lobe width of the wideband focusing beams can also  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency of Narrowband Signals** & **Main Lobe Width** & **Sidelobe Level** \\
**(Hz)** & **(\({}^{\circ}\))** & **(dB)** \\ \hline
2250 & 27.4 & \(-\)7.9 \\
2450 & 25.1 & \(-\)7.9 \\
2760 & 22.2 & \(-\)7.92 \\
2900 & 21.1 & \(-\)7.93 \\
3000 & 20.5 & \(-\)7.91 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of beamforming parameters for narrowband signals.  
Figure 4: Experimental comparison of focusing frequency at 2900 Hz. (**a**) Narrowband beam pattern at 2900 Hz; (**b**) broadband beam pattern focused on the focusing frequency of 2900 Hz.  
Figure 5: Experimental comparison of focusing frequency at 3000 Hz. (**a**) Narrowband beam pattern at 3000 Hz; (**b**) broadband beam pattern focused on the focusing frequency of 3000 Hz.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency of Broadband Signals** & **Main Lobe Width** & **Sidelobe Level** \\
**(Hz)** & **(\({}^{\circ}\))** & **(dB)** \\ \hline
2250 & 27.2 & \(-\)7.2 \\
2450 & 25.8 & \(-\)5.9 \\
2760 & 24.6 & \(-\)7.35 \\
2900 & 24.2 & \(-\)7.21 \\
3000 & 23.6 & \(-\)6.15 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of beamforming parameters for broadband signals.