High-resolution frequency-difference beamforming for a short linear array

Conventional beamforming (CBF) is a commonly employed approach for detecting and estimating the direction-of-arrival (DOA) of acoustic signals in underwater environments. However, CBF becomes ambiguous due to spatial aliasing when the received signal's half wavelength is smaller than the array spacing. Frequency-difference beamforming (FDB) allows for processing data in the lower frequency Δf without encountering spatial aliasing by utilizing the product of array data at frequency f with its complex conjugate at frequency f+Δf. However, lower frequency results in a wider mainlobe, which can lead to poorer DOA performance for short arrays. In this paper, a fourth-order cumulants FDB method and a conjugate augmented FDB method are proposed to extend an M-element uniform linear array to 2M-1 and 4M-3 elements. The proposed methods generate narrower beams and lower sidelobe levels than the original FDB for short arrays with large spacing. And by setting the signal subspace dimension reasonably, the proposed methods can improve the weak target detection ability under strong interference compared with FDB. Last, we verify the excellent performance of the proposed methods through simulations and experimental data.