High‐resolution beamforming with oversampled arrays

Abstract

Plane‐wave beamforming is interpretable as estimation of the Fourier wave vector spectrum from samples of the spatially dependent acoustic field. Because spatially localized sources contribute discrete peaks to the wave vector spectrum, the use of high‐resolution nonlinear techniques (such as Burg's maximum entropy method—MEM) to resolve closely spaced sources has received much attention [Johnson, Proc. IEEE 70(9), 1018–1028 (1982)]. Such techniques are expected to be most useful for short arrays, whose dimensions do not exceed a few wavelengths, for which case conventional beamforming offers poor resolution. Such short arrays typically contain a number of hydrophones and thus oversample the spatial field; the spacing between adjacent hydrophones is less than one half a wavelength. When MEM is applied to oversampled arrays, spurious features are often produced due to the concentration of the spectrum within the visible region of wave vectors. These spurious features can be eliminated through the use of a more general high resolution procedure, the weighted reciprocal spectrum approximation method [Byrne and Fitzgerald, IEEE Trans. Acoust. Speech Signal Process. ASSP‐31, 276–279 (1983)].