Exploring the De-correlation Effect of Low-frequency Active Sonar Echoes in Shallow Water Waveguide

Low-frequency high-power active sonar supplies an effective way for submarine detection, and at the same time the adaptive beamformer (ABF) are often adopted to obtain an improved detection performance. Nevertheless, the performance of ABF tends to degrade seriously when resolving coherent targets. Spatial smoothing technique is an effective way to solve the coherent targets discrimination problem, yet the reduction on the aperture is inevitable. Focusing on the submarine detection problem with ABF in shallow water, the effect of de-correlating echoes from multiple coherent targets by multi-path propagation (in the vertical direction) is discovered. To explore the de-correlation effect, a specific simplified signal propagation model using shallow water waveguide is introduced. And accordingly, the particular form of receiving signals modulated by multipath channel is analyzed. Meanwhile, the specific derivation and calculation for correlation coefficients of echoes reflected back from multiple targets are also given. From the formulation, we can directly conclude that larger time delays between paths (especially the strong paths) and a wider bandwidth of the transmitting pulse could produce lower correlation coefficients between different targets' echoes, which mean a better de-correlation effect. In numerical simulations, a couple of targets (one submarine and one surface ship) with different horizontal angles are assumed for correlation coefficients calculation. With active sonar, surface ship set at a certain depth, we give out a map on correlation coefficients whose vertical axis denotes submarine depth and horizontal axis denotes ranges between sonar and targets. Numerical results effectively show the validity of proposed assumption. Finally, the beam output by ABF and a comparison of spatial spectrums using MVDR under direct path and multipath are given to validate the de-correlation effect.