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In underwater radiated noise measurement using a vertical linear array, a diagonalization-decorrelation-based diagonal denoising method is proposed to improve the denoising effect for spatially correlated noise. Firstly, the ambient noise cross-spectral matrix is measured without the radiated noise source. Subsequently, the eigenvector matrix of the ambient noise cross-spectral matrix is utilized to implement a unitary transformation for the received data, which eliminates the correlation of the received noise and transforms the received noise cross-spectral matrix into a diagonal matrix, then the noise components are removed by diagonal denoising. Finally, the denoised cross-spectral matrix is used to estimate the power of the radiated noise by beamforming. Consequently, the influence of spatially correlated noise on radiated noise measurement is reduced. The effectiveness of the proposed method is validated and compared with the diagonal denoising method and the whitening-decorrelation-based diagonal denoising method via numerical simulations and experimental data. Under the ideal condition, the noise reduction performances of the proposed method and the whitening-decorrelation-based diagonal denoising method are equal and better than that of the diagonal denoising method. In practice, the number of snapshots is limited, so there is an inevitable mismatch between the ambient noise cross-spectral matrix and the received noise cross-spectral matrix due to the randomness of noise. The mismatch results in imperfect whitening and diagonalization, which reduces the denoising effect. However, the simulation results indicate that the proposed method still reduces more correlated noise and has a better performance on underwater radiated noise measurement compared with the diagonal denoising method and the whitening-decorrelation-based diagonal denoising method even if the number of snapshots is finite.

Diagonal Denoising for Spatially Correlated Noise Based on Diagonalization Decorrelation in Underwater Radiated Noise Measurement