# Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water
## 4 Experimental Results
### Correlation and Array Gain in the Shadow Zone
Based on the different arrival time, we regard the S1B1 wave with negative angle and S0B1 wave as the first group, and S2B1 wave, S1B1 wave with positive angle as the second group. It is observed from Figure 21 and Table 2 that the first group has a larger amplitude than the second group and the arrival time is earlier. It is because the sound rays of second group incident to the bottom at a large grazing angle and reflection attenuation is severe. Thus, the arrival amplitude decreases accordingly. The second group experiences a longer path, and it arrives later. It is apparent that there is a time difference of nearly 0.15 s between these two groups. Moreover, the amplitudes of two rays within each group are also different. For example, the amplitude of S1B1 is slightly higher than that of S0B1 because the paths do not entirely coincide. The received signals are a mixture of signal with different arrival angles and powers. In this case, when the signal received is compensated with a single time delay by conventional beamforming technology, signal correlation decreases, accordingly. Further, we calculate the correlation coefficients of the received noise and show them in Figure 22. The figure shows that noise correlation coefficients are nearly equal to 0 except diagonal elements, which means the received noise is almost uncorrelated for every two different sensors. Compared with the noise received in the direct-arrival zone, the noise correlation in the shadow zone is slightly lower. The reason is that when the array is in the shadow zone, the distance from the sound-source ship to the receivers is significantly further, and there is less ship noise received. Figure 17:0 (**a**) Arrival structure of the eigen-rays (10.3 km). (**b**) Ray trace in the shadow zone (10.3 km). Then, the signal gain, noise gain, and array gain are calculated by the signal and noise correlation coefficients. As shown in Figure 23a, the curve of SG fluctuates around 8 dB because of the weak signal correlation, and the value of NG is about 0 dB. The value of AG is nearly equal to that of SG and is about 4 dB lower than the ideal value of 12 dB. The reason for the lower AG is the time delays of each element cannot be compensated accurately by using only one single angle when the plane wave model is not satisfied. In order to verify the previous discussion, the beamforming output of the VLA and power spectrum of the single element are calculated and shown in Figure 23b. Using the same normalization method as before, the SNR of beamforming output for the VLA is about 7 dB higher than that of the single element, which is very close to the average AG value of 8 dB. We also intercept three 30-s signals to calculate the array gains. As shown in Figure 24, the average AG in the middle and late segment is 6.5 dB and 5.5 dB, respectively. The marine environment changed with the time slightly, and the tilt angle of the array changed about \(1^{\circ}\), which causes a little difference in the AG. We can consider that the AG remains constant basically during the measurement time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Amplitude (\(\mu\)Pa)** & **Arrival Time (s)** & **Arrival Angle (\({}^{\circ}\))** & **Number of** \\  & & & **Surface-Reflection** & **Bottom-Reflection** \\ \hline S1B1 & \(9.87\times 10^{-5}\) & 7.218 & \(-10.56\) & 1 & 1 \\ S0B1 & \(9.17\times 10^{-5}\) & 7.211 & \(-10.56\) & 0 & 1 \\ S2B1 & \(7.85\times 10^{-5}\) & 7.36 & 16.59 & 2 & 1 \\ S1B1 & \(6.51\times 10^{-5}\) & 7.348 & 16.59 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structure of S1B1, S0B1, and S2B1 wave. Figure 23: Calculation results in the shadow zone (**a**) signal gain, noise gain, and array gain; (**b**) power spectrum of single element and array beamforming output power spectrum. Figure 22: Noise correlation coefficients. Through the above analysis, it is found that the influence of the measurement time on the array gain can be ignored. Next we discuss the effect of ship auxiliary engine noise on the array gain.