Effect of three-dimensional propagation characteristics on the horizontal array gain in wedge-shaped transitional water

Array gain is the fundamental determinant of the detection performance of large-aperture arrays in applications for long-range underwater target detection. However, field experiments conducted on the continental slope of the South China Sea reveal significant discrepancies between measured and theoretical array gains. To quantitatively explain this phenomenon, this study derives an array gain expression based on the exponential-cosine coherence model, which provides a coherent physical interpretation of the effects of three-dimensional (3D) propagation characteristics on array gain. Using a rigorous controlled-variable approach, we quantitatively isolate the independent contributions of the three core spatial coherence parameters (coherent amplitude coefficient A, spatial coherence attenuation coefficient \gamma , and spatial oscillation angular frequency \kappa ) and element signal energy E_i to array gain. The analysis demonstrates that, in wedge-shaped sloping environments, bathymetric variability induces horizontal divergence of acoustic energy, which leads to degradation of horizontal spatial coherence and ultimately results in array performance degradation. Incomplete accounting for the horizontal energy divergence effect inherent in 3D propagation systematically overestimates the coherence amplitude coefficient A — the dominant factor determining array gain — and thus leads to significant array gain underestimation. The theoretical analysis is experimentally validated using field measurement data from eight sites across the study area. The derived array gain expression accurately reproduces the experimentally observed array gain behavior, with excellent quantitative agreement between theoretical model calculations and experimental results. As a result, the normalized mean squared error is less than 0.08 at all measurement sites. The agreement between the calculated and experimental array gains supports the proposed mechanism analysis. The consistent results across the eight sites also indicate that the identified relationships among 3D propagation, spatial coherence, and array gain apply throughout the investigated continental slope region.