# 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
It is indicated that the noise correlation coefficient in the real ocean is higher than those of the two theoretical noise models, although there exists a similar trend. Also, from Figure 13 we reveal that the correlation coefficient of measured noise is 0.2 at the frequency of 350 Hz as shown in purple round, basically close to that of surface noise. Next, the actual noise correlation coefficient of the array is discussed as follows. Further, the correlation coefficients of noise are calculated by Equation (7) and shown in Figure 14, where the correlation coefficient of the noise received by two adjacent elements is slightly higher than zero. Moreover, as the receiver depth increases, the noise correlation coefficient decreases. In other words, the noise received at different depths is largely uncorrelated to each other. Figure 12: Comparison result of signal correlation coefficient. Figure 13: Correlation coefficient of noise with change of \(d/\lambda\) in real ocean noise environment, isotropic noise field and surface noise field. According to the correlation coefficient of signal and noise above, the signal gain, noise gain, and array gain are estimated. In Figure 15a, the blue line, red line, and yellow line represent SG, NG, and AG, respectively. It is manifested that the curve of SG fluctuates around 11 dB and the value of NG ranges from \(-1\) dB to 0 dB. The value of AG fluctuates around the ideal value of 12 dB, and the average value of AG is about 11.9 dB. It is noteworthy that the value of AG exceeds the ideal value of \(10\log M\) during the time of 5 s to 8 s. That is because SGs during these periods are very close to \(10\log M\), and the corresponding NGs are relatively stable and remain at a negative value. For validating the AG analysis above, the beamforming output spectrum of the VLA and the power spectrum of a single element are compared and given in Figure 15b. In order to intuitively display the difference between the two spectrums, we normalize the peak corresponding to the signal frequency and thus, the difference of two noise power spectrums among the whole frequency band is regarded as the AG after eliminating outliers. We can see that the average AG is about 10 dB, which is close to the calculation result of 11.9 dB in Figure 15a. In the frequency band from 100 Hz to 200 Hz, there exist some small fluctuated peaks, which are caused by low-frequency environmental noise. The experimental time for each measurement point is half an hour. To verify the effect of time changes on the array gain, we divide the half-hour measurement time into three segments and intercept 30-s signal from each division to calculate the array gain. Array gains of the early segment (1-10 min) have been discussed in Figure 15b. Array gains in the middle (11-20 min) and late (21-30 min) period are shown in Figure 16. The average AG in the early, middle, and late period is 10 dB, 9 dB, and 9 dB, respectively. The little difference may be because the marine environment changed slightly during the  
Figure 14: Noise correlation coefficients. Figure 15: Calculation results in the direct-arrival zone (**a**) signal gain, noise gain, and array gain; (**b**) power spectrum of single element and array beamforming output power spectrum. entire measurement time. Moreover, the tilt angle of the array changed about 1\({}^{\circ}\) due to the disturbance of the ocean current (as shown in Figure 3b). It can be concluded that the array gain remains constant basically throughout the measurement time. In this subsection, we have discussed the correlation and AG in the direct-arrival zone and explained the reason for high value of AG from the perspective of sound rays. Next, the correlation and AG in the shadow zone are analyzed.