Extracting modulation line spectrum from ship radiated noise using normal mode separation

The underwater radiated noise from ships undergoes distortion due to multipath propagation in shallow water environments, leading to attenuation of the relative intensity and distance-dependent fluctuations in the modulation line spectrum of received signals, thereby impeding the accurate extraction of modulation line spectrum. To mitigate the adverse effects of multipath distortion on modulation spectrum extraction, this paper proposes a novel method integrating normal mode separation with incoherent superposition of modulation spectrum for enhanced extraction of modulation line spectrum. The proposed method constructs a complex pressure matrix by acquiring signals from vertical array receivers at varying depths and frequencies. Through normal mode filtering, individual modes are separated from the received signal. Subsequent incoherent superposition of the modulation spectrum from each separated mode enhances the relative amplitude of the modulation line spectrum. Numerical simulation results demonstrate that the proposed method achieves an average improvement of 2 dB to 8 dB in the narrowband amplitude ratio of extracted line spectrum compared with conventional demodulation techniques, accompanied by a significant reduction in distance-dependent variance. Experimental validation conducted with measured ship radiated noise data demonstrates that the proposed method achieves a significant enhancement in the relative intensity of modulation line spectrum.