Conventional beamforming (CBF) is an important processing step in underwater array signal processing. Previous researches have shown that the sound field structure as manifested by amplitude nonhomogeneity and wave-front corrugation can reduce the array gain of CBF. The acoustic environment of the continental shelf slope area is very complex. For an underwater acoustic array in this area, the amplitude and phase of the received signals will be distortional seriously. Recently, the acoustic field correlation has been the focus of research on the array gain relations with the underwater acoustic filed. However, the attenuation of acoustic field correlation is not the only factor that induces the array gain to decline, and the analyses of the array gain in the shallow water based on normal-mode model are not applicable to the continental slope area. In this paper, the array gain relations with the structure of acoustic field in continental slop area are investigated based on the theory of underwater acoustic signal propagation. The effects of acoustic field on the signal and noise gains are considered respectively. The analytic expressions of the array gain of CBF in an isotropic noise field are derived from the primal definition of array gain, which indicates that acoustic field correlation and transmission loss in continental slope are the intrinsic factors that affect the array gain of CBF. A horizontal uniform linear array (ULA) with a wide aperture receiving signals from a source in the deep water region is considered in the upslope propagation condition. The RAM program is utilized in the numerical simulations to generate the sound field of this specific environment with given parameters. The array gains, the ATLs and the horizontal longitudinal correlation coefficients of the acoustic field corresponding to three different locations are compared. Conclusions can be drawn as follows. 1) The array gain of CBF is determined by acoustic field correlation and the acoustic average transmission loss (ATL), and its maximum is less than 10lg M as the signal waveform distortion. 2) when the ATLs corresponding to hydrophones at two different receiving locations are similar, the correlation of acoustic filed is higher, and the array gain of CBF is larger. 3) When the ATLs corresponding to hydrophones at two different receiving locations are greatly different, the relation between the array gain of CBF and the acoustic filed correlation is no longer positive. The simulation results verify the array gain of CBF relations with the acoustic filed correlation and the transmission loss in the continental slope area.

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The inhomogenous ocean waveguide, which leads the amplitude and phase of the signal arriving at a hydrophone array to fluctuate, is one of the causes that make the array gain deviate from its ideal value. The relationship between the array gain and the fluctuant acoustic channel is studied theoretically. The analytical expression of the array gain is derived via an acoustic channel transfer function on the assumption that the ambient noise field is isotropic. The expression is expanded via the Euler formula to give an insight into the effect of the fluctuant acoustic channel on the array gain. The result demonstrates that the amplitude fluctuation of the acoustic channel transfer functions has a slight effect on the array gain; however, the uniformity of the phase difference between the weighting coefficient and the channel transfer function on all the hydrophones in the array is a major factor that leads the array gain to further deviate from its ideal value. The numerical verification is conducted in the downslope waveguide, in which the gain of a horizontal uniform linear array (HLA) with a wide-aperture operating in the continental slope area is considered. Numerical result is consistent with the theoretical analysis.

Frequency-difference beamforming (FDB) provides a robust estimation of wave propagation direction by shifting signal processing to a lower frequency which, however, produces a decline in the spatial resolution. In this letter, the beam pattern of FDB for a distant point source is proved to be shift invariant and therefore can be regarded as the point spread function corresponding to FDB's beam output. Then, deconvolved frequency-difference beamforming (Dv-FDB) is proposed to improve array performance. Dv-FDB yields a narrower beam and lower sidelobe levels while maintaining robustness. The superior performance of Dv-FDB is verified by simulations and experimental data.