# Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water
## 4 Experimental Results
### Correlation and Array Gain in the Direct-Arrival Zone  
We collect the acoustic signal data received by the vertical hydrophone line array when the sound source is placed at a depth of 30 m and the horizontal range of 2.4 km. A segment of signal for 30 s is intercepted from the early of the received signal and filtered by a band-pass filter with a frequency range of 300-400 Hz. Therefore, the SNR near the signal frequency is increased. The top element is regarded as the reference element in the following discussion. Figure 5 shows waveforms of the signal received by the reference element in the time domain, frequency domain, and time-frequency domain. In Figure 5a, because of the high SNR it is obvious to view the pulse shape of the received signal and the reception gap between the two 5-second signals. Figure 5b,c display the signal frequency steadily. In order to estimate the elevation angle of the sound source, conventional beamforming technology is applied to process the receiving data above. After the time compensatio  
Figure 4: (**a**) Measured sound speed profile; (**b**) Calculated transmission loss (the source depth is 30 m and the frequency is 350 Hz). Figure 5: Received signal of the reference element in the direct-arrival zone (**a**) time domain; (**b**) frequency domain; (**c**) time–frequency domain. output of each beam is shown in Figure 6. The 0\({}^{\circ}\) of the elevation angle corresponds to the direction along the vertical array axis and toward the sea surface. As seen in Figure 6, there are two distinct bright columns at 78\({}^{\circ}\) and 133\({}^{\circ}\), respectively. According to the experiment setup, the direction of the received direct-arrival wave is downward. Hence, the real elevation angle of the acoustic source is 78\({}^{\circ}\), and the other power peak of 133\({}^{\circ}\) is corresponding to the grating lobe due to \(d/\lambda>0.5\). The explanation for the grating lobe is validated through the simulation in Figure 7, in which the element number of the line array is 16, and the element interval is 5 m. The simulation frequency is 350 Hz, and the elevation angle of the sound source is set to 78\({}^{\circ}\). It is indicated that the grating lobe appears at the elevation angle of 133\({}^{\circ}\), which is consistent with the experimental result. As shown in Section 2, the correlation coefficient of the received signal describes its similarity. Generally speaking, in an unbounded homogeneous medium, the signal from the sound source propagates freely without distortion, and hence, the signal between arbitrary receiving points are completely correlated. However, in the real marine environment, multipath propagation and sound scattering cause the waveform distortion, which results in a decrease of signal correlation. The correlation coefficients of the signal received by the array are calculated and presented in Figure 8. Each square stands for the signal correlation between the element and the reference element. We can see that the value of correlation coefficients slightly descend with the increase of element spacing, but the majority are still higher than 0.7. Also, the correlation coefficients between adjacent elements are nearly equal to 1. Figure 6: Power output after conventional beamforming processing (main lobe of 78\({}^{\circ}\) and grazing lobe of 133\({}^{\circ}\)). Figure 7: Simulation result of beamforming output (\(d/\lambda=1.37\), main lobe of 78\({}^{\circ}\) and grazing lobe of 133\({}^{\circ}\)). The ray acoustics can better reflect the propagation characteristics of sound waves in the deep sea. In the direct-arrival zone, the high vertical correlation of the acoustic field could be explained by BELLHOP model, which can calculate the time arrival structure, ray trace, and sound intensity in the marine environment. Since the sound source is near the sea, and the array length is a small amount relative to the horizontal range, the receiving structure of the topmost element is not much different from the bottommost element.