# Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water
## 5 Conclusions  
Array gain is a critical factor in evaluating the detection performance for the vertical line array and can be expressed by signal correlation and noise correlation. In this work, based on a trial conducted in the South China Sea, the experimental signal correlation and noise correlation were analyzed when the vertical line array was deployed in the direct-arrival zone and the shadow zone, respectively. Ray interference theory was utilized to analyze the structure of the sound field and  
Figure 24: Average AGs in the shadow zone (**a**) data in the middle measurement period; (**b**) data in the late measurement period.  
Figure 25: Noise correlation in point A and B.  
interpret the vertical correlation characteristic. Based on the measured marine environmental noise instead of independent noise assumption, the effect of noise correlation on the array gain was analyzed. According to the correlation coefficients, the array gain of the corresponding zone was also discussed. Hence, several conclusions are summarized as follows:  
1. The correlation coefficient of signal and noise can directly represent signal gain and noise gain, respectively, and the difference between these two gains is the array gain. Positive signal gain and negative noise gain can increase the array gain, which improves the detection ability of underwater targets.
2. For the direct-arrival zone, D wave and S1B0 wave are the main components of the sound field, and some waves reflected from the seabed can be ignored. These two waves have almost identical arrival structures and ray traces and add up constructively. Hence, the correlation coefficients of the received signal are close to 1. Accordingly, the measured noise correlation coefficient fluctuates in a small range near 0, and thus the array gain is about 10 dB, nearly equal to the ideal value of 10 logM. In some cases, it even exceeds the ideal value.
3. For the shadow zone, the sound field is dominated by S1B1 wave, S0B1 wave, and S2B1 wave. There are apparent differences in their arrival time and arrival angle because of the multipath effect. The multipath interference structure of the signal becomes complex. Therefore, the signal correlation coefficient is lower than that in the direct-arrival zone. Its correlation decreases as the vertical depths increase and presents periodic oscillation. Furthermore, the received noise of each element is almost completely uncorrelated. At this time, the value of AG is 7 dB, which is less than the ideal value. The effect of time variation and ship auxiliary noise on the array gain can be neglected during the experiment.  
Conceptualization and methodology, Y.L. and Y.C.; validation, Y.L. and Z.Z.; formal analysis, Y.L., Z.Z., and M.C.; investigation, M.C.; project administration, Z.M.; writing--original draft preparation, Y.L.; writing--review and editing, Y.C. and Z.M.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Natural Science Foundation of China (61901488).  
The authors declare no conflict of interest.