# Optimized Sonar Broadband Focused Beamforming Algorithm
## 4 Water Pool Experiments  
The algorithm in this paper was verified by pool experiments in an anechoic pool. The block diagram of the water pool experiment is shown in Figure 8. The water pool was 20 m long, 8 m wide, and 7 m deep. The water depth was approximately 6.7 m. The pool was a straight-wall reinforced concrete structure, and the tapered rubber wedge was used in the silencing unit. Units were arranged on six surfaces of the pool at equal intervals to eliminate reflected sound and simulate the marine environment. For frequencies above 2 kHz, the sound absorption coefficient is more than 98%. The anechoic pool is mainly used for the research and development of sonar, underwater acoustic physical field, underwater acoustic communication, and other key models of national research and development, underwater acoustic engineering disciplines and underwater acoustic physical field, and other basic scientific research. The center of the 24-element array was placed at a depth of 2 m. The radius of the circular array was 0.5 m. The received signal was transformed into a data file by a preamplifier, A/D transform, and data acquisition/storage system and transferred to a PC for offline processing. The filter amplifier model was KEMO, corresponding to the website [[http://www.kemo.com/index.php/filters/lab-filters/cardmaster-21-255g-2](http://www.kemo.com/index.php/filters/lab-filters/cardmaster-21-255g-2)]([http://www.kemo.com/index.php/filters/lab-filters/cardmaster-21-255g-2](http://www.kemo.com/index.php/filters/lab-filters/cardmaster-21-255g-2)). The AD acquisition equipment was BK's 3053 LAN-XI module, which has 12 channels. This experiment used two blocks, a total of 24 channels. Specific parameters can be found on the following websites: [[https://www.bksv.com/zh-HK/products/data-acquisition-systems-and-hardware/LAN-XI-data-acquisition-hardware/modules/type-3053](https://www.bksv.com/zh-HK/products/data-acquisition-systems-and-hardware/LAN-XI-data-acquisition-hardware/modules/type-3053)]([https://www.bksv.com/zh-HK/products/data-acquisition-systems-and-hardware/LAN-XI-data-acquisition-hardware/modules/type-3053](https://www.bksv.com/zh-HK/products/data-acquisition-systems-and-hardware/LAN-XI-data-acquisition-hardware/modules/type-3053)). The transmitted signal was generated by an HP33120A function/arbitrary waveform generator, amplified by a power amplifier with a gain of 80 dB, and sent to a mosaic ring transducer as the sound source. The distance between the sound source and the receiving array center was 5 m. In each frequency, the position of the source relative to the circular array was determined first, and the circular array was rotated to 360\({}^{\circ}\) with a 2\({}^{\circ}\) interval. The acoustic was recorded at 5-s time intervals. Six sets of measurements with different array configurations were obtained. First, the six measured groups of array manifold were corrected by the RCB algorithm. Second, the corrected focusing matrix was determined by the corrected array manifold. The optional focusing frequency determined by the above method was 2760 Hz in the frequency range of 2250-3000 Hz. Finally, the weight designed by an ideal circle array manifold with 24 arrays was the SOCP broadband focusing beamforming algorithm based on the optimal focusing frequency. Figure 9 shows the pool experiment results. Figure 10 shows the results of the comparison with the conventional broadband focusing beamforming algorithm as well as the SOCP broadband focusing beamforming algorithm, which are based on the optional focusing frequency. Figure 8: Block diagram of the water pool experiment. Figure 10: Beam pattern of measured array manifold at six frequency points. (**a**) Comparison of beam pattern at 2250 Hz; (**b**) comparison of beam pattern at 2400 Hz; (**c**) comparison of beam pattern at 2550 Hz; (**d**) comparison of beam pattern at 2700 Hz; (**e**) comparison of beam pattern at 2850 Hz; (**f**) comparison of beam pattern at 3000 Hz. Figure 9: Superposition of measured array manifold at six frequency points.